Gage R&R | MinitabBlog posts and articles about Gage Repeatability and Reprodicibility (Gage R&R) studies for quality improvement.
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Wed, 26 Jul 2017 10:48:58 +0000FeedCreator 1.7.3See the New Features and Enhancements in Minitab 18 Statistical Software
http://blog.minitab.com/blog/understanding-statistics/see-the-new-features-and-enhancements-in-minitab-18-statistical-software
<p>It's a very exciting time at Minitab's offices around the world because we've just announced the availability of Minitab® 18 Statistical Software.</p>
<p><a href="http://www.minitab.com/products/minitab/whats-new/"><img alt="What's new in Minitab 18?" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/64e5153baa676ef27cd0672296ff2a2d/minitab18_whatsnew_blue_twitter.png" style="width: 400px; height: 200px; margin: 10px 15px; float: right;" /></a>Data is everywhere today, but to use it to make sound, strategic business decisions, you need to have tools that turn that data into knowledge and insights. We've designed Minitab 18 to do exactly that. </p>
<p>We've incorporated a lot of <a href="http://www.minitab.com/products/minitab/whats-new/">new features</a>, made some great enhancements and put a lot of energy into developing a tool that will make getting insight from your data faster and easier than ever before, and we're excited to get feedback from you about the new release. </p>
<p>The advanced capabilities we've added to Minitab 18 include tools for measurement systems analysis, statistical modeling, and Design of Experiments (DOE). With Minitab 18, it’s much easier to test how a large number of factors influence process output, and to get more accurate results from models with both fixed and random factors.</p>
<p>We'll delve into more detail about these features in the coming weeks, but today I wanted to give you a quick overview of some of the most exciting additions and improvements. You can also check out one of our <a href="http://www.minitab.com/en-us/products/minitab/webinars/">upcoming webinars</a> to see the new features demonstrated. Then I hope you'll check them out for yourself—you can <a href="http://www.minitab.com/products/minitab/free-trial/">get Minitab 18 free for 30 days</a>.</p>
Updated Session Window
<img alt="updated session window in Minitab 18" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/9d32d30bb81f568e265afc3549b9569e/whats_new_1_1_.png" style="width: 300px; height: 208px; margin: 10px 15px; float: right;" />
<p>The first thing longtime Minitab users are likely to notice when they launch Minitab 18 is the enhancements we've made to the Session window, which contains the output of all your analyses. </p>
<div>The Session window looks better, and also now includes the ability to:</div>
<ul>
<li>Specify the number of significant digits (decimal places) in your output</li>
<li>Go directly to graphs by clicking links in the output</li>
<li>Expand and collapse analyses for easier navigation</li>
<li>Zoom in and out </li>
</ul>
<img alt="sort worksheets in Minitab 18's project manager" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/b5ba230cd2917d387da0b0eb9a59986e/whats_new_2_1_.png" style="width: 200px; height: 139px; margin: 10px 15px; float: right;" />
Sort Worksheets in the Project Manager
<p>We've also added the option to sort the worksheets in your project by title or in chronological order, so you can manage and work with your data in the Project Manager more easily.</p>
Definitive Screening Designs
<p>Many businesses need to determine which inputs make the biggest impact on the output of a process. When you have a lot of inputs, as most processes do, this can be a huge challenge. Standard experimental methods can be costly and time-consuming, and may not be able to distinguish main effects from the two-way interactions that occur between inputs.</p>
<p>That challenge is answered in Minitab 18 with Definitive Screening Designs, a type of designed experiment that minimizes the number of experimental runs required, but still lets you identify important inputs without confounding main effects and two-way interactions.</p>
Restricted Maximum Likelihood (REML) Estimation
<p>Another feature we've added to Minitab 18 is restricted maximum likelihood (REML) estimation. This is an advanced statistical method that improves inferences and predictions while minimizing bias for mixed models, which include both fixed and random factors.</p>
New Distributions for Tolerance Intervals
<p>With Minitab 18 we've made it easy to calculate statistical tolerance intervals for nonnormal data with distributions including the Weibull, lognormal, exponential, and more.</p>
Effects Plots for Designed Experiments (DOE)
<p>In another enhancement to our Design of Experiments (DOE) functionality, we've added effects plots for general factorial and response surface designs, so you can visually identify significant X’s.</p>
Historical Standard Deviation in Gage R&R
<p>If you're doing the measurement system analysis method known as Gage R&R, Minitab 18 enables you to enter a user-specified process (historical) standard deviation in relevant calculations.</p>
Response Optimizer for GLM
<p>When you use the <a href="http://blog.minitab.com/blog/statistics-support/wave-a-magic-wand-over-your-doe-analyses">response optimizer</a> for the general linear model (GLM), you can include both your factors and covariates to find optimal process settings.</p>
Output in Table Format to Word and Excel
<p>The Session window output can be imported into Word and Excel in table format, which lets you easily customize the appearance of your results.</p>
Command Line Pane
<p>Many people use Minitab's command line to expand the software's functionality. With Minitab 18, we've made it easy to keep commands separate from the Session output with a docked command line pane. </p>
Updated Version of Quality Trainer
<p>Finally, it's worth mentioning that the release of Minitab 18 is complemented by a new version of <a href="http://www.minitab.com/products/quality-trainer/">Quality Trainer by Minitab®</a>, our e-learning course. It teaches you how to solve real-world quality improvement challenges with statistics and Minitab, and lets you refresh that knowledge anytime. If you haven't tried it yet, you can check out a sample chapter now. </p>
<p>We hope you'll try the latest Minitab release! And when you do, please be sure to let us know what you think: we love to get your feedback and input about what we've done right, and what we can make better! Send your comments to feedback@minitab.com. </p>
Data AnalysisInsightsLean Six SigmaSix SigmaStatisticsStatistics HelpStatsWed, 07 Jun 2017 17:09:00 +0000http://blog.minitab.com/blog/understanding-statistics/see-the-new-features-and-enhancements-in-minitab-18-statistical-softwareEston MartzDoing Gage R&R at the Microscopic Level
http://blog.minitab.com/blog/statistics-in-the-field/doing-gage-randr-at-the-microscopic-level
<p><em>by Dan Wolfe, guest blogger</em></p>
<p>How would you measure a hole that was allowed to vary one tenth the size of a human hair? What if the warmth from holding the part in your hand could take the measurement from good to bad? These are the types of problems that must be dealt with when measuring at the micron level.</p>
<img alt="a 10-micron fiber" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/bcf2f768b2e355d2d8e3113a404ceb36/320px_cfaser_haarrp_1_.jpg" style="width: 320px; height: 182px; margin: 10px 15px; float: right;" />
<div>
<p>As a Six Sigma professional, that was the challenge I was given when Tenneco entered into high-precision manufacturing. In Six Sigma projects “gage studies” and “Measurement System Analysis (MSA)” are used to make sure measurements are reliable and repeatable. It’s tough to imagine doing that type of analysis without <a href="http://www.minitab.com/products/minitab">statistical software</a> like Minitab.</p>
<div>Tenneco, the company I work for, creates and supplies clean air and ride performance products and systems for cars and commercial vehicles. Tenneco has revenues of $7.4 billion annually, and we expect to grow as stricter vehicle emission regulations take effect in most markets worldwide over the next five years.</div>
<p>We have an active and established Six Sigma community as part of the “Tenneco Global Process Excellence” program, and Minitab is an integral part of training and project work at Tenneco.</p>
Verifying Measurement Systems
<p>Verifying the measurement systems we use in precision manufacturing and assembly is just one instance of how we use Minitab to make data-driven decisions and drive continuous improvement.</p>
<p>Even the smallest of features need to meet specifications. Tolerance ranges on the order of 10 to 20 microns require special processes not only for manufacturing, but also measurement. You can imagine how quickly the level of complexity grows when you consider the fact that we work with multiple suppliers from multiple countries for multiple components.</p>
<p>To gain agreement between suppliers and Tenneco plants on the measurement value of a part, we developed a process to work through the verification of high precision, high accuracy measurement systems such as CMM and vision.</p>
<p>The following <a href="http://blog.minitab.com/blog/understanding-statistics/sipoc-alypse-now">SIPOC (Supplier, Input, Process, Output, Customer)</a> process map shows the basic flow of the gage correlation process for new technology.</p>
<p><a href="//cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/File/4bc224d356f7f41309744ee0da2b7988/sipoc_large.jpg"><img alt="sipoc " src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/6e031650e769d3c9c6b233a23bbf6199/sipoc_sm.jpg" style="width: 438px; height: 377px;" /></a></p>
What If a Gage Study Fails?
<p>If any of the gage studies fail to be approved, we launch a problem-solving process. For example, in many cases, the Type 1 results do not agree at the two locations. But given these very small tolerance ranges, seemingly small differences can have significant practical impact on the measurement value. One difference was resolved when the ambient temperature in a CMM lab was found to be out of the expected range. Another occurred when the lens types of two vision systems were not the same.</p>
<p>Below is an example of a series of Type 1 gage studies performed to diagnose a repeatability issue on a vision system. It shows the effect of part replacement (taking the part out of the measurement device, then setting it up again) before each measurement and the bias created by handling the part.</p>
<p>For this study, we took the results of 25 measurements made when simply letting the part sit in the machine and compared them with 25 measurements made when taking the part out and setting it up again between each of 25 measurements. The analysis shows picking the part up, handling it and resetting it in the machine changes the measurement value. This was found to be <a href="http://blog.minitab.com/blog/the-stats-cat/sample-size-statistical-power-and-the-revenge-of-the-zombie-salmon-the-stats-cat">statistically significant, but not <em>practically </em>significant</a>. Knowing the results of this study helps our process and design engineers understand how to interpret the values given to them by the measurement labs, and give some perspective on the considerations of the part and measurement processes.</p>
<p>The two graphs below show Type 1 studies done with versus without replacement of the part. There is a bias between the two studies. A test for equal variance shows a difference in variance between the two methods.</p>
<p><img alt="Type 1 Gage Study with Replacement" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/de9796cecba9ea3102fc659f6f4bcfe4/type1gagestudy_withreplacement.jpg" style="width: 572px; height: 384px;" /></p>
<p><img alt="Type 1 Gage Study without Replacement" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/cf8cd8158947fc22bd88087123a1b87f/type1gagestudy_withoutreplacement.jpg" style="width: 568px; height: 383px;" /></p>
<p>As the scatterplot below illustrates, the study done WITH REPLACEMENT has higher standard deviation. It is statistically significant, but still practically acceptable.</p>
<p><img alt="With Replacement vs. Without Replacement" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/380d8e62f6fbc15aac9f8299bed42924/scatterplot.jpg" style="width: 570px; height: 372px;" /></p>
<p>Minitab’s gage study features are a critical part of the gage correlation process we have developed. Minitab has been integrated into Tenneco’s Six Sigma program since it began in 2000.</p>
<p>The powerful analysis and convenient graphing tools are being used daily by our Six Sigma resources for these types of gage studies, problem-solving efforts, quality projects, and many other uses at Tenneco.</p>
<p> </p>
<p><strong>About the Guest Blogger</strong>:</p>
<p>Dan Wolfe is a Certified Lean Six Sigma Master Belt at Tenneco. He has led projects in Engineering, Supply Chain, Manufacturing and Business Processes. In 2006 he was awarded the Tenneco CEO award for Six Sigma. As a Master Black Belt he has led training waves, projects and the development of business process design tools since 2007. Dan holds a BSME from The Ohio State University and an MSME from Oakland University and a degree from the Chrysler Institute of Engineering for Automotive Engineering.</p>
<p> </p>
<p><em style="border: 0px; margin: 0px; padding: 0px;"><strong style="border: 0px; margin: 0px; padding: 0px;">Would you like to publish a guest post on the Minitab Blog? Contact <a href="mailto:publicrelations@minitab.com?subject=I%20Would%20Like%20to%20Be%20a%20Guest%20Blogger" style="border-width: 0px 0px 0.1em; border-bottom-style: dotted; border-bottom-color: rgb(0, 47, 97); margin: 0px; padding: 0px; color: rgb(0, 47, 97); text-decoration: none;">publicrelations@minitab.com</a>. </strong></em></p>
</div>
AutomotiveManufacturingQuality ImprovementSix SigmaTue, 06 Jun 2017 12:00:00 +0000http://blog.minitab.com/blog/statistics-in-the-field/doing-gage-randr-at-the-microscopic-levelGuest BloggerFundamentals of Gage R&R
http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr
<p>Before cutting an expensive piece of granite for a countertop, a good carpenter will first confirm he has measured correctly. Acting on faulty measurements could be costly.</p>
<p><img alt="gauge" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/b82fc879fa26a76f2b00424550aafe9e/gage.jpg" style="width: 300px; height: 208px; float: right; margin: 10px 15px;" />While no measurement system is perfect, we rely on such systems to quantify data that help us control quality and monitor changes in critical processes. So, how do you know whether the changes you see are valid and not just the product of a faulty measurement system? After all, if you can’t trust your measurement system, then you can’t trust the data it produces.</p>
<p>Performing a Gage R&R study can help you to identify problems with your measurement system, enabling you to trust your data and to make data-driven decisions for process improvement. </p>
What Can Gage R&R Do for Me?
<p>Gage R&R studies can tell you if inconsistencies in your measurements are too large to ignore—this could be due to a faulty tool or inconsistent operation of a tool.</p>
<p><strong>Reveal an inconsistent tool</strong></p>
<p>Let’s look at an example to better understand how Gage R&R studies work.</p>
<p>Suppose a company wants to use a control chart to monitor the fill weights of cereal boxes. Before doing so, they conduct a Gage R&R study to determine if the system which measures the weight of each cereal box is producing precise measurements.</p>
<p>The best way to ensure that measurements are valid is to look at repeatability, or the variation of the measurements taken by the same operator for the same part. If we weigh the same cereal box under the same conditions a number of times, will we observe the same weight every time? Weighing the same box over and over again can show us how much variation exists in our measurement system.</p>
<p><img alt="plot" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/497eee17946361547404397e1c606de6/gage_fundamentals_1.jpg" style="width: 400px; height: 267px;" /></p>
<p>For this experiment, we can look at repeatability based on two different operators’ measurements. The Gage R&R results show that even when the same person weighs the same box on the same scale, the measurements can vary by several grams. Most likely, the scale is in serious need of recalibration. The faulty scale would have rendered a control chart for these measurements virtually useless. Although the average measurements for each operator are not far apart, the spread of the measurements is huge!</p>
<p><strong>Highlight operator differences</strong></p>
<p>But the variation that exists in the measurement system is just one aspect of a Gage R&R study. We must also look at reproducibility, or the variation due to different operators using the measurement system. A Gage R&R study can tell us whether a measurement differs from one operator to the next and by how much.</p>
<p>Suppose the same company who wishes to monitor fill weights of cereal boxes hires new employees to help record measurements. The company uses a Gage R&R to evaluate both the new operators and experienced operators.</p>
<p><img alt="gage R&R " src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/25b59ba04a57260bab6b3195f5dfaded/gage_fundamentals_2.jpg" style="width: 400px; height: 267px;" /></p>
<p>The study reveals that when employees weigh the same cereal box, the measurements of new hires are too high or too low more often than the measurements of experienced employees. This finding might indicate that the company should conduct more training for the new hires.</p>
How to Analyze a Gage R&R Study in Minitab
<p>Awareness of how well you can measure something can have substantial financial impacts. Minitab <a href="http://www.minitab.com/products/minitab">Statistical Software</a> makes it easy to analyze how precise your measurements are.</p>
<p>In the case of the company evaluating cereal box fill weights, problems of over- and under-filling have different implications. Overfilling cereal boxes is costing the company money they could be saving with a calibrated measurement system and properly trained staff. Similarly, not filling cereal boxes fully is making customers angry because they didn’t get the amount of product they paid for. </p>
Getting started
<p>Preparing to analyze your measurement system is easy because Minitab’s Create Gage R&R Study Worksheet can generate a data collection sheet for you. The dialog box lets you quickly specify who takes the measurements (the operators), which item they measure (the parts), and in what order the data are to be collected.</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/bd575431b6841c8c30a15eb7862ef85b/gage_fundamentals_3.jpg" style="width: 400px; height: 375px;" /></p>
<ol>
<li>Choose <strong>Stat > Quality Tools > Gage Study > Create Gage R&R Study Worksheet</strong>.</li>
<li>Specify the number of parts, number of operators, and the number of times the same operator will measure the same part.</li>
<li>Give descriptive names to the parts and operators so they’re easy to identify in the output.</li>
<li>Click <strong>OK</strong>.</li>
</ol>
The main event
<p>After you create your data collection sheet and record the measurements you observe, you can use Gage R&R Study (Crossed) to analyze the measurements.</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/3abd7c04618ffe20125ce7c70121c9d9/gage_fundamentals_4.jpg" style="width: 400px; height: 253px;" /></p>
<ol>
<li>Choose <strong>Stat > Quality Tools > Gage Study > Gage R&R Study (Crossed)</strong>.</li>
<li>In Part Numbers, enter <em>Parts</em>.</li>
<li>In Operators, enter <em>Operators</em>.</li>
<li>In Measurement Data, enter <em>'Fill Weights'</em>.</li>
<li>Click <strong>OK</strong>.</li>
</ol>
<p><img alt="Gage R&R Output" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/586798e925a3e524022899e185750b04/gage_fundamentals_5.jpg" style="width: 500px; height: 384px;" /></p>
<p>The study reveals that Jordan’s measurements are lower than Pat’s or Taylor’s. In fact, the %Study Variation for our total Gage R&R is high—90.39%—indicating that our measurement system is unacceptable. Identifying and eliminating the source of the difference will improve the measurement system.</p>
<p>Some of my colleagues offer <a href="http://blog.minitab.com/blog/quality-data-analysis-and-statistics/how-to-interpret-gage-output-part-2">more information on Gage R&R tools and how to interpret the output</a>.</p>
Putting Gage R&R Studies to Use
<p>Taking measurements is like any other process—it’s prone to variability. Assessing and identifying where to focus efforts for reducing this variation with Minitab’s Gage R&R tools can help you ensure your measurement system is precise. </p>
Data AnalysisQuality ImprovementStatisticsWed, 31 May 2017 12:00:00 +0000http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rrMeredith GriffithWhat Do Ventilated Shelf Installation and Measurement Systems Analysis Have in Common?
http://blog.minitab.com/blog/quality-business/what-do-ventilated-shelf-installation-and-measurement-systems-analysis-have-in-common
<p><img alt="Ventilated Shelf" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/3c89dfbf7dc1971b6031bf669ac45625/ventilated_shelf.jpg" style="margin: 10px 15px; float: left; width: 148px; height: 113px;" />Have you ever tried to install ventilated shelving in a closet? You know: the heavy-duty, white- or gray-colored vinyl-coated wire shelving? The one that allows you to get organized, more efficient with space, and is strong and maintenance-free? Yep, that’s the one. Did I mention this stuff is strong? As in, <em>really </em>hard to cut? </p>
<p>It seems like a simple 4-step project. Measure the closet, go the store, buy the shelving, and install when you get home. Simple, right? Yeah, it sounded good in my head!</p>
<p>The lessons I learned in this project underscore the value of doing measurement system analysis in your quality improvement projects, with <a href="http://www.minitab.com/products/minitab/">statistical software such as Minitab</a>. Whatever you're trying to accomplish, if you don't get reliable measurements or data, the task is going to become more challenging.</p>
<p align="center"><img alt="Before Process Map" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/56432bf83b2d106b61f39f1ab76a8495/before_process_map.png" style="width: 600px; height: 145px; margin: 10px 15px;" /></p>
<p>Well it turned out to be more complicated and involved a lot of rework. Did I mention that this shelving is made of heavy gauge steel that is nearly impossible to cut with ordinary tools? So, my simple 4-step process turned into a 7-step process with lots of rework (multiple trips to the store to have the shelves re-cut).</p>
<p>My actual process looked more like this!</p>
<p><img alt="After Process Map" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/060c401c2db87e8176130b7e464441fb/after_process_map.png" style="width: 750px; height: 230px; margin: 10px 15px;" /></p>
<p>All the sources of variation from Measurement Systems Analysis (MSA) apply here: Repeatability, Reproducibility, Bias, Linearity, and Stability. Let’s review these terms and see how I could have done better at measuring the closet, the first time.</p>
<p align="center"><img alt="Components of Measurement Error" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/23550db0dc88ec22e9b5409ba6d6a592/components_of_measurement_error.png" style="width: 750px; height: 456px; margin: 10px 15px;" /></p>
<p>When it was time to measure the closet, I had a few measuring-device choices hanging around my garage: a yardstick, a cloth tape measure, and a steel tape measure. </p>
<p><strong>Bias</strong> examines the difference between the observed average measurement and a reference or master value. It answers the question: "How accurate is my gage when compared to a reference value?" Unless there is visible damage, all three of these measuring devices should be acceptable for my shelf project.</p>
<p><strong>Stability</strong> is the change in bias over time. Measurement stability represents the total variation in measurements obtained on the same part measured over time, also known as drift. It is important to assess stability on an ongoing basis. While calibrations and <span><a href="http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr">gage studies</a></span> provide some information about changes in the measurement system, neither provides information on what is happening to the measurement process over time. But unless there is visible damage, all three of these measuring devices should be acceptable for use.</p>
<p><strong>Linearity</strong> examines how accurate your measurements are through the expected range of the measurements. It answers the question: "Does my gauge have the same accuracy across all reference values?" If you use the yardstick or steel tape measure, then the answer might be “yes” because of its solid construction. But the cloth tape measure could stretch when extended, making it less reliable at longer lengths. Examine the cloth measuring tape for evidence of stretching or wear. If damage is present, do not use the measuring device.</p>
<p><strong>Repeatability</strong> represents the variation that occurs when the same appraiser measures the same part with the same device. This is best represented with the advice “Measure twice, cut once!” In my case, if I had measured the closet width multiple times, I would have realized I was getting a different answer each time and therefore needed to take better care when measuring. Then I could have gotten more accurate measurements for each shelf. </p>
<p><strong>Reproducibility</strong> represents the variation that occurs when different appraisers measure the same part with the same device. In my case, if I'd asked my son to measure the same locations that I just measured, I would have discovered that we got different answers: I should have accounted for the mounting brackets in my measurements. (The fact that he <em>did </em>is why he’s in school to become a Mechanical Engineer.)</p>
<p>In summary, my afternoon shelf installation project ended up taking two days to complete, resulting in multiple trips to the store, a lot of frustration for me, and late dinners for my family because I was too busy to cook! </p>
<p>My lessons learned from this project are:</p>
<ol>
<li>Don’t assume your closet walls are exactly parallel at the top, middle and bottom of the closet. Instead, measure at each location where a shelf is to be installed. Remember the Rule of Thumb for Gage R&R: take measurements representing the entire range of process variation.</li>
<li>Apply the Gage R&R sources of measurement error when measuring:
<ol style="list-style-type:lower-alpha;">
<li>Visually inspect the measuring device before using to verify it is in good condition.</li>
<li>Measure twice, cut once. (Repeatability)</li>
<li>Ask my family for assistance in measuring. (Reproducibility)</li>
</ol>
</li>
<li>Did you know that you can purchase a laser measure for about $30 these days? If only I had known…</li>
<li>Consider hiring a professional because this project was harder than it originally seemed.</li>
</ol>
Quality ImprovementMon, 17 Apr 2017 15:03:00 +0000http://blog.minitab.com/blog/quality-business/what-do-ventilated-shelf-installation-and-measurement-systems-analysis-have-in-commonBonnie K. StoneGauging Gage Part 3: How to Sample Parts
http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-3-how-to-sample-parts
<p>In <a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enough">Parts 1</a> and <a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-2-are-3-operators-or-2-replicates-enough">2 of Gauging Gage</a> we looked at the numbers of parts, operators, and replicates used in a Gage R&R Study and how accurately we could estimate %Contribution based on the choice for each. In doing so, I hoped to provide you with valuable and interesting information, but mostly I hoped to make you like me. I mean like me so much that if I told you that you were doing something flat-out wrong and had been for years and probably screwed somethings up, you would hear me out and hopefully just revert back to being indifferent towards me.</p>
<p>For the third (and maybe final) installment, I want to talk about something that drives me crazy. It really gets under my skin. I see it all of the time, maybe more often than not. You might even do it. If you do, I'm going to try to convince you that you are very, very wrong. If you're an instructor, you may even have to contact past students with groveling apologies and admit you steered them wrong. And that's the best-case scenario. Maybe instead of admitting error, you will post scathing comments on this post insisting I am wrong and maybe even insulting me despite the evidence I provide here that I am, in fact, right.</p>
<p>Let me ask you a question:</p>
When you choose parts to use in a Gage R&R Study, how do you choose them?
<p>If your answer to that question required anymore than a few words - and it can be done in one word—then I'm afraid you may have been making a very popular but very bad decision. If you're in that group, I bet you're already reciting your rebuttal in your head now, without even hearing what I have to say. You've had this argument before, haven't you? Consider whether your response was some variation on the following popular schemes:</p>
<ol>
<li>Sample parts at regular intervals across the range of measurements typically seen</li>
<li>Sample parts at regular intervals across the process tolerance (lower spec to upper spec)</li>
<li>Sample randomly but pull a part from outside of either spec</li>
</ol>
<p>#1 is wrong. #2 is wrong. #3 is wrong.</p>
<p>You see, the statistics you use to qualify your measurement system are all reported relative to the part-to-part variation and all of the schemes I just listed do not accurately estimate your true part-to-part variation. The answer to the question that would have provided the most reasonable estimate?</p>
<p>"Randomly."</p>
<p>But enough with the small talk—this is a statistics blog, so let's see what the statistics say.</p>
<p>In Part 1 I described a simulated Gage R&R experiment, which I will repeat here using the standard design of 10 parts, 3 operators, and 2 replicates. The difference is that in only one set of 1,000 simulations will I randomly pull parts, and we'll consider that our baseline. The other schemes I will simulate are as follows:</p>
<ol>
<li>An "exact" sampling - while not practical in real life, this pulls parts corresponding to the 5th, 15th, 25, ..., and 95th percentiles of the underlying normal distribution and forms a (nearly) "exact" normal distribution as a means of seeing how much the randomness of sampling affects our estimates.</li>
<li>Parts are selected uniformly (at equal intervals) across a typical range of parts seen in production (from the 5th to the 95th percentile).</li>
<li>Parts are selected uniformly (at equal intervals) across the range of the specs, in this case assuming the process is centered with a Ppk of 1.</li>
<li>8 of the 10 parts are selected randomly, and then one part each is used that lies one-half of a standard deviation outside of the specs.</li>
</ol>
<p>Keep in mind that we know with absolute certainty that the underlying %Contribution is 5.88325%.</p>
Random Sampling for Gage
<p>Let's use "random" as the default to compare to, which, as you recall from Parts 1 and 2, already does not provide a particularly accurate estimate:</p>
<p style="margin-left:40px"><img alt="Pct Contribution with Random Sampling" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/af91c4815469651cc698c3aa7d980c61/histogram_of_10_pctcontribution.gif" style="height:384px; width:576px" /></p>
<p>On several occasions I've had people tell me that you can't just sample randomly because you might get parts that don't really match the underlying distribution. </p>
Sample 10 Parts that Match the Distribution
<p>So let's compare the results of random sampling from above with our results if we could magically pull 10 parts that follow the underlying part distribution almost perfectly, thereby eliminating the effect of randomness:</p>
<p style="margin-left:40px"><img alt="Random vs Exact" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/f2b7c1cc6c3cede482e7251b2b55f28e/random_vs_exact.gif" style="height:384px; width:576px" /></p>
<p>There's obviously something to the idea that the randomness that comes from random sampling has a big impact on our estimate of %Contribution...the "exact" distribution of parts shows much less skewness and variation and is considerably less likely to incorrectly reject the measurement system. To be sure, implementing an "exact" sample scheme is impossible in most cases...since you don't yet know how much measurement error you have, there's no way to know that you're pulling an exact distribution. What we have here is a statistical version of chicken-and-the-egg!</p>
Sampling Uniformly across a Typical Range of Values
<p>Let's move on...next up, we will compare the random scheme to scheme #2, sampling uniformly across a typical range of values:</p>
<p style="margin-left:40px"><img alt="Random vs Uniform Range" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/d8e9f2f7a24a62457a2d517914baef73/random_vs_uniformrange.gif" style="height:384px; width:576px" /></p>
<p>So here we have a different situation: there is a very clear reduction in variation, but also a very clear bias. So while pulling parts uniformly across the typical part range gives much more consistent estimates, those estimates are likely telling you that the measurement system is much better than it really is.</p>
Sampling Uniformly across the Spec Range
<p>How about collecting uniformly across the range of the specs?</p>
<p style="margin-left:40px"><img alt="Random vs Uniform Specs" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/5da456e491792be021485c0e9a514298/random_vs_uniformspecs.gif" style="height:384px; width:576px" /></p>
<p>This scheme results in an even more extreme bias, with qualifying this measurement system a certainty and in some cases even classifying it as excellent. Needless to say it does not result in an accurate assessment.</p>
Selectively Sampling Outside the Spec Limits
<p>Finally, how about that scheme where most of the points are taken randomly but just one part is pulled from just outside of each spec limit? Surely just taking 2 of the 10 points from outside of the spec limits wouldn't make a substantial difference, right?</p>
<p style="margin-left:40px"><img alt="Random vs OOS" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/c0821d19873a65162535d231799052ce/random_vs_oos.gif" style="height:384px; width:576px" /></p>
<p>Actually those two points make a huge difference and render the study's results meaningless! This process had a Ppk of 1 - a higher-quality process would make this result even more extreme. Clearly this is not a reasonable sampling scheme.</p>
<strong>Why These Sampling Schemes?</strong>
<p>If you were taught to sample randomly, you might be wondering why so many people would use one of these other schemes (or similar ones). They actually all have something in common that explains their use: all of them allow a practitioner to assess the measurement system across a range of possible values. After all, if you almost always produce values between 8.2 and 8.3 and the process goes out of control, how do you know that you can adequately measure a part at 8.4 if you never evaluated the measurement system at that point?</p>
<p>Those that choose these schemes for that reason are smart to think about that issue, but just aren't using the right tool for it. Gage R&R evaluates your measurement system's ability to measure relative to the current process. To assess your measurement system across a range of potential values, the correct tool to use is a "Bias and Linearity Study" which is found in the Gage Study menu in Minitab. This tool establishes for you whether you have bias across the entire range (consistently measuring high or low) or bias that depends on the value measured (for example, measuring smaller parts larger than they are and larger parts smaller than they are).</p>
<p>To really assess a measurement system, I advise performing both a Bias and Linearity Study as well as a Gage R&R.</p>
<strong>Which Sampling Scheme to Use?</strong>
<p>In the beginning I suggested that a random scheme be used but then clearly illustrated that the "exact" method provides even better results. Using an exact method requires you to know the underlying distribution from having enough previous data (somewhat reasonable although existing data include measurement error) as well as to be able to measure those parts accurately enough to ensure you're pulling the right parts (not too feasible...if you know you can measure accurately, why are you doing a Gage R&R?). In other words, it isn't very realistic.</p>
<p>So for the majority of cases, the best we can do is to sample randomly. But we can do a reality check after the fact by looking at the average measurement for each of the parts chosen and verifying that the distribution seems reasonable. If you have a process that typically shows normality and your sample shows unusually high skewness, there's a chance you pulled an unusual sample and may want to pull some additional parts and supplement the original experiment.</p>
<p>Thanks for humoring me and please post scathing comments below!</p>
<p><a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enough">see Part I of this series</a><br />
<a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-2-are-3-operators-or-2-replicates-enough">see Part II of this series</a></p>
AutomotiveGovernmentHealth Care Quality ImprovementHealthcareLean Six SigmaManufacturingMedical DevicesMiningQuality ImprovementServicesWed, 12 Apr 2017 13:39:00 +0000http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-3-how-to-sample-partsJoel SmithGauging Gage Part 2: Are 3 Operators or 2 Replicates Enough?
http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-2-are-3-operators-or-2-replicates-enough
<p>In Part 1 of Gauging Gage, I looked at how adequate a <a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enough">sampling of 10 parts is for a Gage R&R Study</a> and providing some advice based on the results.</p>
<p>Now I want to turn my attention to the other two factors in the standard Gage experiment: 3 operators and 2 replicates. Specifically, what if instead of increasing the number of parts in the experiment (my previous post demonstrated you would need an unfeasible increase in parts), you increased the number of operators or number of replicates?</p>
<p>In this study, we are only interested in the effect on our estimate of overall Gage variation. Obviously, increasing operators would give you a better estimate of of the operator term and reproducibility, and increasing replicates would get you a better estimate of repeatability. But I want to look at the overall impact on your assessment of the measurement system.</p>
Operators
<p>First we will look at operators. Using the same simulation engine I described in Part 1, this time I did two different simulations. In one, I increased the number of operators to 4 and continued using 10 parts and 2 replicates (for a total of 80 runs); in the other, I increased to 4 operators and still used 2 replicates, but decreased the number of parts to 8 to get back close to the original experiment size (64 runs compared to the original 60).</p>
<p>Here is a comparison of the standard experiment and each scenario laid out here:</p>
<p style="margin-left:40px"><img alt="Operator Comparisons" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/ab84f3d0ae2d826f47786930ee54c611/operator_comparisons.gif" style="height:384px; width:576px" /></p>
<p style="margin-left:40px"><img alt="Operator Descriptive Stats" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/bc864992dcfd882e2c6066496b79ce19/operators_desc.GIF" style="height:68px; width:524px" /></p>
<p>It may not be obvious in the graph, but increasing to 4 operators while decreasing to 8 parts actually <em>increased</em> the variation in %Contribution seen...so despite requiring 4 more runs this is the poorer choice. And the experiment that involved 4 operators but maintained 10 parts (a total of 80 runs) showed no significant improvement over the standard study.</p>
Replicates
<p>Now let's look at replicates in the same manner we looked at parts. In one run of simulations we will increase replicates to 3 while continuing to use 10 parts and 3 operators (90 runs), and in another we will increase replicates to 3 and operators to 3, but reduce parts to 7 to compensate (63 runs).</p>
<p>Again we compare the standard experiment to each of these scenarios:</p>
<p style="margin-left:40px"><img alt="Replicate Comparisons" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/f5d14793691f9ad2d39a598ca41e9945/replicate_comparisons.gif" style="height:384px; width:576px" /></p>
<p style="margin-left:40px"><img alt="Replicates Descriptive Statistics" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/1c08fe3733c316f67e904e532c6b3e6e/replicates_desc.GIF" style="height:71px; width:528px" /></p>
<p>Here we see the same pattern as with operators. Increasing to 3 replicates while compensating by reducing to 7 parts (for a total of 63 runs) significantly increases the variation in %Contribution seen. And increasing to 3 replicates while maintaining 10 parts shows no improvement.</p>
<strong>Conclusions about Operators and Replicates in Gage Studies</strong>
<p>As stated above, we're only looking at the effect of these changes to the overall estimate of measurement system error. So while increasing to 4 operators or 3 replicates either showed no improvement in our ability to estimate %Contribution or actually made it worse, you may have a situation where you are willing to sacrifice that in order to get more accurate estimates of the individual components of measurement error. In that case, one of these designs might actually be a better choice.</p>
<p>For most situations, however, if you're able to collect more data, then increasing the number of parts used remains your best choice.</p>
<p>But how do we select those parts? I'll talk about that in my next post!</p>
<p><a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enough">see Part I of this series</a><br />
<a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-3-how-to-sample-parts">see Part III of this series</a></p>
AutomotiveData AnalysisGovernmentHealth Care Quality ImprovementHealthcareLean Six SigmaManufacturingMedical DevicesMiningServicesSix SigmaStatisticsStatsTue, 04 Apr 2017 12:00:00 +0000http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-2-are-3-operators-or-2-replicates-enoughJoel SmithGauging Gage Part 1: Is 10 Parts Enough?
http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enough
<p>"You take 10 parts and have 3 operators measure each 2 times."</p>
<p>This standard approach to a Gage R&R experiment is so common, so accepted, so ubiquitous that few people ever question whether it is effective. Obviously one could look at whether 3 is an adequate number of operators or 2 an adequate number of replicates, but in this first of a series of posts about "Gauging Gage," I want to look at 10. Just 10 parts. How accurately can you assess your measurement system with 10 parts?</p>
Assessing a Measurement System with 10 Parts
<p>I'm going to use a simple scenario as an example. I'm going to simulate the results of 1,000 Gage R&R Studies with the following underlying characteristics:</p>
<ol>
<li>There are no operator-to-operator differences, and no operator*part interaction.</li>
<li>The measurement system variance and part-to-part variance used would result in a %Contribution of 5.88%, between the popular guidelines of <1% is excellent and >9% is poor.</li>
</ol>
<p>So—no looking ahead here—based on my 1,000 simulated Gage studies, what do you think the distribution of %Contribution looks like across all studies? Specifically, do you think it is centered near the true value (5.88%), or do you think the distribution is skewed, and if so, how much do you think the estimates vary?</p>
<p>Go ahead and think about it...I'll just wait here for a minute.</p>
<p>Okay, ready?</p>
<p>Here is the distribution, with the guidelines and true value indicated:</p>
<p style="margin-left:40px"><img alt="PctContribution for 10 Parts" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/af91c4815469651cc698c3aa7d980c61/histogram_of_10_pctcontribution.gif" style="height:384px; width:576px" /></p>
<p>The good news is that it is roughly averaging around the true value.</p>
<p>However, the distribution is highly skewed—a decent number of observations estimated %Contribution to be at least double the true value with one estimating it at about SIX times the true value! And the variation is huge. In fact, about 1 in 4 gage studies would have resulted in failing this gage.</p>
<p>Now a standard gage study is no small undertaking—a total of 60 data points must be collected, and once randomization and "masking" of the parts is done it can be quite tedious (and possibly annoying to the operators). So just how many parts would be needed for a more accurate assessment of %Contribution?</p>
Assessing a Measurement System with 30 Parts
<p>I repeated 1,000 simulations, this time using 30 parts (if you're keeping score, that's 180 data points). And then for kicks, I went ahead and did 100 parts (that's 600 data points). So now consider the same questions from before for these counts—mean, skewness, and variation.</p>
<p>Mean is probably easy: if it was centered before, it's probably centered still.</p>
<p>So let's really look at skewness and how much we were able to reduce variation:</p>
<p style="margin-left:40px"><img alt="10 30 100 Parts" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/2a6885f40fda396703a0176a030ae332/histogram_of_10_30_100_parts.gif" style="height:384px; width:576px" /></p>
<p>Skewness and variation have clearly decreased, but I suspect you thought variation would have decreased more than it did. Keep in mind that %Contribution is affected by your estimates of repeatability and reproducibility as well, so you can only tighten this distribution so much by increasing number of parts. But still, even using 30 parts—an enormous experiment to undertake—still results in this gage failing 7% of the time!</p>
<p>So what is a quality practitioner to do?</p>
<p>I have two recommendations for you. First, let's talk about %Process. Often times the measurement system we are evaluating has been in place for some time and we are simply verifying its effectiveness. In this case, rather than relying on your small sampling of parts to estimate the overall variation, you can use the historical standard deviation as your estimate and eliminate much of the variation caused by the same sample size of parts. Just enter your historical standard deviation in the Options subdialog in Minitab:</p>
<p style="margin-left:40px"><img alt="Options Subdialog" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/cc286906ae0d7171affa92523707f722/options_dialog.png" style="height:422px; width:456px" /></p>
<p>Then your output will include an additional column of information called %Process. This column is the equivalent of the %StudyVar column, but using the historical standard deviation (which comes from a much larger sample) instead of the overall standard deviation estimated from the data collected in your experiment:</p>
<p style="margin-left:40px"><img alt="Percent Process" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/a7c6669b4b10272aac25b420e67d561c/pctprocess_output.GIF" style="height:130px; width:462px" /></p>
<p>My second recommendation is to include confidence intervals in your output. This can be done in the <em>Conf Int </em>subdialog:</p>
<p style="margin-left:40px"><img alt="Conf Int sibdialog" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/f3433eb79f2aacded976c9a2d7733e00/conf_int_dialog.gif" style="height:191px; width:381px" /></p>
<p>Including confidence intervals in your output doesn't inherently improve the wide variation of estimates the standard gage study provides, but it does force you to recognize just how much uncertainty there is in your estimate. For example, consider this output from the gageaiag.mtw sample dataset in Minitab with confidence intervals turned on:</p>
<p style="margin-left:40px"><img alt="Output with CIs" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/46889f0e-f0a5-4b4a-8a19-2d2b8dce6087/Image/68bc06ad673742b3f76922b1c31d813a/output_with_cis.GIF" style="height:162px; width:520px" /></p>
<p>For some processes you might accept this gage based on the %Contribution being less than 9%. But for most processes you really need to trust your data, and the 95% CI of (2.14, 66.18) is a red flag that you really shouldn't be very confident that you have an acceptable measurement system.</p>
<p>So the next time you run a Gage R&R Study, put some thought into how many parts you use and how confident you are in your results!</p>
<p><a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-2-are-3-operators-or-2-replicates-enough">see Part II of this series</a><br />
<a href="http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-3-how-to-sample-parts">see Part III of this series</a></p>
AutomotiveData AnalysisGovernmentHealthcareLean Six SigmaManufacturingMedical DevicesMiningQuality ImprovementServicesSix SigmaStatisticsStatsWed, 29 Mar 2017 15:31:00 +0000http://blog.minitab.com/blog/fun-with-statistics/gauging-gage-part-1-is-10-parts-enoughJoel SmithDMAIC Tools and Techniques: The Measure Phase
http://blog.minitab.com/blog/michelle-paret/dmaic-tools-and-techniques%3A-the-measure-phase
<p>In my last post on <a href="http://blog.minitab.com/blog/michelle-paret/dmaic-tools-and-techniques:-the-define-phase">DMAIC tools for the Define phase</a>, we reviewed various graphs and stats typically used to <em>define</em> project goals and customer deliverables. Let’s now move along to the tools you can use in <a href="http://www.minitab.com/products/minitab/">Minitab Statistical Software</a> to conduct the Measure phase.</p>
Measure Phase Methodology
<p>The goal of this phase is to <em>measure</em> the process to determine its current performance and quantify the problem. This includes validating the measurement system and establishing a baseline process capability (i.e., sigma level).</p>
I. Tools for Continuous Data
<strong><img alt="Gage RandR" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/6ff6ed7f4c0940a9eb1a548487b72b2b/gagerr.jpg" style="width: 350px; height: 263px; float: right; margin: 10px 15px;" /></strong>
Gage R&R
<p>Before you analyze your data, you should first make sure you can trust it, which is why successful Lean Six Sigma projects begin the Measure phase with Gage R&R. This measurement systems analysis tool assesses if measurements are both <a href="http://blog.minitab.com/blog/michelle-paret/do-you-know-the-truth-about-gage-repeatability-and-reproducibility">repeatable and reproducible</a>. And there are Gage R&R studies available in Minitab for both <a href="http://blog.minitab.com/blog/michelle-paret/a-simple-guide-to-gage-randr-for-destructive-testing">destructive and non-destructive tests</a>.</p>
<p>Minitab location:<strong> </strong><strong><em>Stat > Quality Tools > Gage Study > Gage R&R Study</em></strong> OR <strong><em>Assistant > Measurement Systems Analysis</em>.</strong></p>
Gage Linearity and Bias
<p>When assessing the validity of our data, we need to consider both <a href="http://blog.minitab.com/blog/real-world-quality-improvement/accuracy-vs-precision-whats-the-difference">precision and accuracy</a>. While Gage R&R assesses precision, it’s Gage Linearity and Bias that tells us if our measurements are accurate or are biased.</p>
<p>Minitab location: <em><strong>Stat > Quality Tools > Gage Study > Gage Linearity and Bias Study</strong>.</em></p>
<p style="margin-left: 40px;"><img alt="Gage Linearity and Bias" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/85a16583e2d97dd638b6ff21071a61dd/gage_linearity_and_bias.jpg" style="width: 350px; height: 263px;" /></p>
Distribution Identification
<p>Many statistical tools and p-values assume that your data follow a specific distribution, commonly the normal distribution, so it’s good practice to assess the distribution of your data before analyzing it. And if your data don’t follow a normal distribution, do not fear as there are various <a href="http://www.minitab.com/en-us/lp/Non-Normal-Data-Tips-And-Tricks">techniques for analyzing non-normal data</a>.</p>
<p>Minitab location: <strong><em>Stat > Basic Statistics > Normality Test</em></strong> OR <strong><em>Stat > Quality Tools > Individual Distribution Identification.</em></strong></p>
<p style="margin-left: 40px;"><img alt="Distribution Identification" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/1e6b3763f36f991cf5cf1eb142b0f8d0/distribution_id_plot.jpg" style="width: 350px; height: 233px;" /></p>
Capability Analysis
<p>Capability analysis is arguably the crux of “Six Sigma” because it’s the tool for calculating your sigma level. Is your process at a 1 Sigma, 2 Sigma, etc.? It reveals just how good or bad a process is relative to specification limit(s). And in the Measure phase, it’s important to use this tool to establish a baseline before making any improvements.</p>
<p>Minitab location: <strong><em>Stat > Quality Tools > Capability Analysis/Sixpack</em><em> </em></strong>OR <strong><em>Assistant > Capability Analysis.</em></strong></p>
<p style="margin-left: 40px;"><img alt="Process Capability Analysis" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/7f8e9183ad3a5b3ee66e0fadca51aea4/process_capability_sixpack_report.jpg" style="width: 350px; height: 263px;" /></p>
II. Tools for Categorical (Attribute) Data
Attribute Agreement Analysis
<strong><img alt="Attribute Agreement Analysis" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/5d1759e9ef4da886e677bb7c2a7b2c79/attribute_agreement_analysis.jpg" style="width: 300px; height: 233px; float: right; margin: 10px 15px;" /></strong>
<p>Like Gage R&R and Gage Linearity and Bias studies mentioned above for continuous measurements, this tool helps you <a href="http://blog.minitab.com/blog/statistics-and-quality-data-analysis/the-lady-tasting-beer-evaluating-a-gono-go-gage-part-ii">assess if you can trust categorical measurements</a>, such as pass/fail ratings. This tool is available for <a href="http://blog.minitab.com/blog/adventures-in-statistics-2/understanding-and-using-discrete-distributions">binary, ordinal, and nominal data types</a>.</p>
<p>Minitab location: <strong><em>Stat > Quality Tools > Attribute Agreement Analysis</em> </strong>OR <strong><em>Assistant > Measurement Systems Analysis.</em></strong></p>
Capability Analysis (Binomial and Poisson)
<p>If you’re counting the number of defective items, where each item is classified as either pass/fail, go/no-go, etc., and you want to compute parts per million (PPM) defective, then you can use binomial capability analysis to assess the current state of the process.</p>
<p>Or if you’re counting the number of defects, where each item can have multiple flaws, then you can use Poisson capability analysis to establish your baseline performance.</p>
<p>Minitab location:<em> <strong>Stat > Quality Tools > Capability Analysis</strong></em> OR <strong><em>Assistant > Capability Analysis.</em></strong></p>
<p style="margin-left: 40px;"><img alt="Binomial Process Capability" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/4aad5a79836d8105d3adba60388b16b1/binomial_process_capability.jpg" style="width: 350px; height: 263px;" /></p>
Variation is Everywhere
<p>As I mentioned in my last post on the Define phase, Six Sigma projects can vary. Every project does not necessarily use the same identical tool set every time, so the tools above merely serve as a guide to the types of analyses you may need to use. And there are other tools to consider, such as flowcharts to map the process, which you can complete using <a href="http://www.minitab.com/products/companion/">Companion by Minitab</a>.</p>
Capability AnalysisData AnalysisLean Six SigmaProject ToolsQuality ImprovementSix SigmaStatisticsStatsWed, 18 Jan 2017 13:00:00 +0000http://blog.minitab.com/blog/michelle-paret/dmaic-tools-and-techniques%3A-the-measure-phaseMichelle ParetCommon Assumptions about Data Part 3: Stability and Measurement Systems
http://blog.minitab.com/blog/quality-business/common-assumptions-about-data-part-3-stability-and-measurement-systems
<p><img alt="Cart before the horse" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/8230e7c2bc193a831158677a70eb0146/chile_road_sign_po_4.svg" style="width: 101px; height: 101px; float: right; margin: 10px 15px;" />In Parts <span><a href="http://blog.minitab.com/blog/quality-business/common-assumptions-about-data-part-1-random-samples-and-statistical-independence">1</a></span> and <span><a href="http://blog.minitab.com/blog/quality-business/common-assumptions-about-data-part-2-normality-and-equal-variance">2</a></span> of this blog series, I wrote about how statistical inference uses data from a sample of individuals to reach conclusions about the whole population. That’s a very powerful tool, but you must check your assumptions when you make statistical inferences. Violating any of these assumptions can result in false positives or false negatives, thus invalidating your results. </p>
<p>The common data assumptions are: random samples, independence, normality, equal variance, stability, and that your measurement system is accurate and precise. I addressed random samples and statistical independence last time. Now let’s consider the assumptions of stability and measurement systems.</p>
What Is the Assumption of Stability?
<p>A stable process is one in which the inputs and conditions are consistent over time. When a process is stable, it is said to be “in control.” This means the sources of variation are consistent over time, and the process does not exhibit unpredictable variation. In contrast, if a process is unstable and changing over time, the sources of variation are inconsistent and unpredictable. As a result of the instability, you cannot be confident in your statistical test results.</p>
<p>Use one of the various types of <span><a href="http://blog.minitab.com/blog/understanding-statistics/what-control-chart-should-i-use">control charts</a></span> available in Minitab <a href="http://www.minitab.com/products/minitab/">Statistical Software</a> to assess the stability of your data set. The Assistant menu can walk you through the choices to select the appropriate control chart based on your data and subgroup size. You can get advice about collecting and using data by clicking the “more” link.</p>
<p><img alt="Choose a Control Chart" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/6ec77f5dbc070eb0c2070ce6bcf8144c/1_control_chart.png" style="border-width: 0px; border-style: solid; width: 474px; height: 338px; margin: 10px 15px;" /></p>
<p><img alt="I-MR Control Chart" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/3d69fc444cd5dd09a962a11e645a3a2e/2_control_chart.png" style="border-width: 0px; border-style: solid; width: 474px; height: 338px; margin: 10px 15px;" /></p>
<p>In addition to preparing the control chart, Minitab tests for out-of-control or non-random patterns based on the <a href="http://blog.minitab.com/blog/statistics-in-the-field/using-the-nelson-rules-for-control-charts-in-minitab">Nelson Rules</a> and provides an assessment in easy-to-read Summary and Stability reports. The Report Card, depending on the control chart selected, will automatically check your assumptions of stability, normality, amount of data, correlation, and will suggest alternative charts to further analyze your data.</p>
<p><img alt="Report Card" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/195741e519156b95ee5feee8b521041f/3_control_chart.jpg" style="border-width: 0px; border-style: solid; width: 464px; height: 348px; margin: 10px 15px;" /></p>
What Is the Assumption for Measurement Systems?
<p>All the other assumptions I’ve described “assume” the data reflects reality. But does it?</p>
<p>The <span><a href="http://blog.minitab.com/blog/understanding-statistics/explaining-quality-statistics-so-my-boss-will-understand-measurement-systems-analysis-msa">measurement system</a> </span>is one potential source of variability when measuring a product or process. When a measurement system is poor, you lose the ability to truthfully “see” process performance. A poor measurement system leads to incorrect conclusions and flawed implementation. </p>
<p>Minitab can perform a Gage R&R test for both measurement and appraisal data, depending on your measurement system. You can use the Assistant in Minitab to help you select the most appropriate test based on the type of measurement system you have.</p>
<p><img alt="Choose a MSA" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/1a474c8c-3979-4eba-b70c-1e5a3f1d6601/Image/3ff089fcee9ab280c8e8d1da1c56d610/4_msa.png" style="border-width: 0px; border-style: solid; width: 474px; height: 345px; margin: 10px 15px;" /></p>
<p>There are two assumptions that should be satisfied when performing a Gage R&R for measurement data: </p>
<ol>
<li>The measurement device should be calibrated.</li>
<li>The parts to be measured should be selected from a stable process and cover approximately 80% of the possible operating range. </li>
</ol>
<p>When using a measurement device make sure it is properly calibrated and check for linearity, bias, and stability over time. The device should produce accurate measurements, compared to a standard value, through the entire range of measurements and throughout the life of the device. Many companies have a metrology or calibration department responsible for calibrating and maintaining gauges. </p>
<p>Both these assumptions must be satisfied. If they are not, you cannot be sure that your data accurately reflect reality. And that means you’ll risk not understanding the sources of variation that influence your process outcomes. </p>
The Real Reason You Need to Check the Assumptions
<p>Collecting and analyzing data requires a lot of time and effort on your part. After all the work you put into your analysis, you want to be able to reach correct conclusions. Some analyses are robust to departures from these assumptions, but take the safe route and check! You want to be confident you can tell whether observed differences between data samples are simply due to chance, or if the populations are indeed different! </p>
<p>It’s easy to put the cart before the horse and just plunge in to the data collection and analysis, but it’s much wiser to take the time to understand which data assumptions apply to the statistical tests you will be using, and plan accordingly.</p>
<p>Thank you for reading my blog. I hope this information helps you with your data analysis mission!</p>
Data AnalysisHypothesis TestingQuality ImprovementStatisticsMon, 05 Dec 2016 13:00:00 +0000http://blog.minitab.com/blog/quality-business/common-assumptions-about-data-part-3-stability-and-measurement-systemsBonnie K. StoneMinitab 17 and Minitab Express: A Comparison of Software Features
http://blog.minitab.com/blog/marilyn-wheatleys-blog/minitab-17-and-minitab-express-a-comparison-of-software-features
<p><span style="line-height: 1.6;">Since the release of Minitab Express in 2014, we’ve often received questions in technical support about the differences between Express and Minitab 17. In this post, I’ll attempt to provide a comparison between these two Minitab products.</span></p>
What Is Minitab 17?
<p>Minitab 17 is an all-in-one graphical and statistical analysis package that includes basic analysis tools such as hypothesis testing, regression, and ANOVA. Additionally, Minitab 17 includes more advanced features such as reliability analysis, multivariate tools, design of experiments (DOE), and quality tools such as gage R&R and capability analysis. A full list of features that are included Minitab 17 is available on this <a href="http://www.minitab.com/en-us/products/minitab/features-list/">page</a>. </p>
What Is Minitab Express?
<p>Minitab Express is a more basic all-in-one software package for graphical and statistical analysis, designed for students and professors teaching introductory statistics courses. Minitab Express includes statistical analysis options such as hypothesis testing, regression, and ANOVA, but does not include many of the other advanced features that are available in Minitab 17. A full list of the features that are included in Minitab Express is available <a href="http://www.minitab.com/en-us/products/express/features-list/">here</a>.</p>
Key Differences
<strong><em>Supported Operating Systems</em></strong>
<p>One main difference between the two packages is that Minitab 17 is a Windows-only application (however, Minitab 17 can be installed on Mac OS X using one of the options described <a href="http://support.minitab.com/en-us/installation/frequently-asked-questions/other/minitab-companion-on-mac/">here</a>). System requirements for Minitab 17 are available <a href="http://www.minitab.com/en-us/products/minitab/system-requirements/">here</a>. </p>
<p>Minitab Express is available for both Window and Mac OS X. The system requirements for Minitab Express are available <a href="http://www.minitab.com/en-us/products/express/system-requirements/">here</a>.</p>
<strong><em>The Interface</em></strong>
<p>While the menu options for both versions of the software are located at the top and the worksheet/data window are below, there are several differences in the interface. The first screen shot below is for Minitab 17, while the next two screen shots are for Minitab Express:</p>
<p style="margin-left: 40px;"><br />
<strong>Minitab 17:</strong><img alt="Minitab 17 Interface" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/f054ba83a85abb6245445502feb2ce86/minitab17interface.png" style="width: 800px; height: 481px;" /></p>
<p style="margin-left: 40px;"><strong>Minitab Express for Windows:</strong><img alt="Express for Windows" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/280aa535dde18d42aaf42eb517fbb9fe/expressforwindowsinterface.png" style="width: 800px; height: 571px;" /></p>
<strong>Minitab Express for OS X</strong><img alt="Minitab Express for OS X Interface" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/177920cdc081cd8d77458ccf3318d192/expressforosxinterface.png" style="width: 800px; height: 529px;" />
<em><strong>Comparison of Commonly Used Features</strong></em>
<p>In addition to cosmetic differences in appearance, the table below compares the features that are available in both versions:</p>
<p align="center"><strong>Feature</strong></p>
<p align="center"><strong>Minitab 17 </strong></p>
<p align="center"><strong>(Windows)</strong></p>
<p align="center"><strong>Minitab Express </strong></p>
<p align="center"><strong>(Windows & Mac OS X)</strong></p>
<p style="text-align: center;">Assistant menu</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Graphs</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Probability distributions</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Summary statistics</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Hypothesis tests</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">One-Way ANOVA</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Two-Way ANOVA</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">ANOVA with > 2 factors</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Linear regression</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Logistic regression</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Nonlinear regression</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Design of experiments</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Control charts</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Gage R&R</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Capability analysis</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Reliability</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Multivariate</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Time series</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Nonparametric tests</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;">Equivalence tests</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p style="text-align: center;"> </p>
<p style="text-align: center;">Power and sample size</p>
<ul>
<li style="text-align: center;"> </li>
</ul>
<p align="center"> </p>
<p>Although many of the same features are available in both packages, Minitab 17 has many graph editing options that are not available in Minitab Express. For many of the tests that are available in both packages, Minitab 17 allows more control over the results and has more options that Minitab Express. You can see a more detailed comparison <a href="http://www.minitab.com/academic/comparison/">here</a>. </p>
<p>I hope this post is useful in evaluating the two versions of Minitab. For any questions about either software package, we are more than happy to help here in <a href="http://www.minitab.com/en-us/support/">technical support</a>.</p>
StatisticsStatsMon, 17 Oct 2016 12:00:00 +0000http://blog.minitab.com/blog/marilyn-wheatleys-blog/minitab-17-and-minitab-express-a-comparison-of-software-featuresMarilyn WheatleyDo You Know the Truth about Gage Repeatability and Reproducibility?
http://blog.minitab.com/blog/michelle-paret/do-you-know-the-truth-about-gage-repeatability-and-reproducibility
<p>The ultimate goal of most quality improvement projects is clear: reducing the number of defects, improving a response, or making a change that benefits your customers.</p>
<p>We often want to jump right in and start gathering and analyzing data so we can solve the problems. Checking your measurement systems first, with methods like attribute agreement analysis or Gage R&R, may seem like a needless waste of time. </p>
<p>But the truth is that a Gage R&R Study is a critical step in <em>any </em>statistical analysis involving continuous data. That's because it allows you to determine if your measurement system for that data is adequate or not. If your measurement system isn’t capable of producing reliable measurements, then any analysis you conduct with those measurements is likely meaningless.</p>
<p>So let’s get to the “R&R” part of <span><a href="http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr">Gage R&R</a></span>—Repeatability and Reproducibility.</p>
<p>Suppose we’re measuring pencils with a ruler (which is an excellent hands-on activity you can use to teach Gage R&R). We want to determine if our measurement system can adequately measure the length of these pencils. To conduct a Gage R&R Study, we randomly select 10 pencils and 3 people—Abe, Brenda, and Charlie. Each person measures each pencil 2 times, using the same ruler. This gives us a total of 10 x 3 x 2 = 60 measurements.</p>
<p><img alt="parts and operators" src="https://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/6060c2db-f5d9-449b-abe2-68eade74814a/Image/c7685645ea8140d6ba67b1496ba57624/parts_and_ops.png" style="width: 548px; height: 293px;" /></p>
Repeatability
<p>Repeatability represents the variation observed when the same operator measures the same part multiple times with the same device. In other words, when Abe repeatedly measures the same pencil with the same ruler, will his measurements be consistent? If he measures 16.8 cm the first time, is he going to measure 16.8 cm the next time he measures that same pencil?</p>
Reproducibility
<p>Reproducibility represents the variation observed when DIFFERENT operators measure the same part multiple times with the same device. In other words, if Abe measures a pencil at 16.8 cm in length, will Brenda also measure 16.8 cm for that same pencil? And what about Charlie?</p>
<p><strong>Helpful Hint: </strong>To remember the difference between repeatability and reproducibility, note that reproducibility includes an ‘o’ – think ‘<strong>o</strong>’ for the variability across “<strong>o</strong>perators.”</p>
Answering Important Questions
<p>Gage R&R can help you answer questions such as:</p>
<ul>
<li>Is my measurement system capable of discriminating between parts?</li>
<li>Is the variability in my measurement system small compared with the manufacturing process variability?</li>
<li>How much variability is my measurement system is caused by differences between operators?</li>
</ul>
<p>And if your measurement system isn't great, you can also use Gage R&R to determine where the weaknesses are. For example, perhaps a study reveals that while repeatability is good, the reproducibility is poor. You can use Gage R&R to dig deeper and figure out why different operators reported different readings.</p>
<p>To easily setup your Gage R&R data collection plan and analyze the corresponding data to assess your measurement system, check out <a href="http://www.minitab.com/products/minitab">Minitab Statistical Software</a> and its <strong>Stat > Quality Tools > Gage Study</strong> and <strong>Assistant > Measurement Systems Analysis</strong> features.</p>
AutomotiveData AnalysisFun StatisticsGovernmentHealth Care Quality ImprovementHealthcareLean Six SigmaManufacturingMedical DevicesMiningQuality ImprovementServicesSix SigmaStatisticsStatistics HelpStatsFri, 07 Oct 2016 12:00:00 +0000http://blog.minitab.com/blog/michelle-paret/do-you-know-the-truth-about-gage-repeatability-and-reproducibilityMichelle ParetThose 10 Simple Rules for Using Statistics? They're Not Just for Research
http://blog.minitab.com/blog/understanding-statistics/those-10-simple-rules-for-using-statistics-theyre-not-just-for-research
<p><span style="line-height: 1.6;">Earlier this month, PLOS.org published an article titled "<a href="http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004961" target="_blank">Ten Simple Rules for Effective Statistical Practice</a>." </span><span style="line-height: 20.8px;">The 10 rules are good reading for </span><em style="line-height: 20.8px;">anyone </em><span style="line-height: 20.8px;">who draws conclusions and makes decisions based on data</span><span style="line-height: 20.8px;">, whether you're trying to extend the boundaries of scientific knowledge or make good decisions for your business. </span></p>
<p><span style="line-height: 20.8px;">Carnegie Mellon University's Robert E. Kass and several co-authors</span><span style="line-height: 20.8px;"> </span><span style="line-height: 1.6;">devised the rules in response to the increased pressure on scientists and researchers—many, if not most, of whom are <em>not</em> statisticians—to present accurate findings based on sound statistical methods. </span></p>
<p><span style="line-height: 20.8px;">Since </span><span style="line-height: 1.6;">the paper and the discussions it has prompted focus on scientists and researchers, it seems worthwhile to consider how the rules might apply to </span><span style="line-height: 20.8px;">quality practitioners or business decision-makers as well</span><span style="line-height: 1.6;">. </span><span style="line-height: 1.6;">In this post, I'll share the 10 rules, some with a few modifications to make them more applicable to the wider population of all people who use data to inform their decisions. </span></p>
<img alt="questions" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/d2c0571a-acbd-48c7-84f4-222276c293fe/Image/36fa08b0c862c669f4e41596fbb76ddd/question_mark_signs.jpg" style="width: 200px; height: 200px; float: right; margin: 10px 15px; border-width: 1px; border-style: solid;" />1. Statistical Methods Should Enable Data to Answer <span style="color:#FF0000;">Scientific Specific</span> Questions
<p>As the article points out, new or infrequent users of statistics tend to emphasize finding the "right" method to use—often focusing on the structure or format of their data, rather than thinking about how the data might answer an important question. But choosing a method based on the data is putting the cart before the horse. Instead, we should start by clearly identifying the question we're trying to answer. Then we can look for a method that uses the data to answer it. If you haven't already collected your data, so much the better—you have the opportunity to identify and obtain the data you'll need.</p>
2. Signals Always Come With Noise
<p>If you're familiar with <a href="http://blog.minitab.com/blog/understanding-statistics/control-chart-tutorials-and-examples">control charts</a> used in statistical process control (SPC) or the Control phase of a Six Sigma DMAIC project, you know that they let you distinguish process variation that matters (special-cause variation) from normal process variation that doesn't need investigation or correction.</p>
<p style="margin-left: 40px;"><img alt="control chart" src="http://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/d2c0571a-acbd-48c7-84f4-222276c293fe/Image/632a05ec67ddca317eb4bc1f4daabe9a/i_chart_of_ph.gif" style="line-height: 20.8px; width: 573px; height: 172px;" /><br />
<em style="line-height: 20.8px;">Control charts are one common tool used to distinguish "noise" from "signal." </em></p>
<p>The same concept applies here: whenever we gather and analyze data, some of what we see in the results will be due to inherent variability. Measures of probability for analyses, such as confidence intervals, are important because they help us understand and account for this "noise." </p>
3. Plan Ahead, Really Ahead
<p>Say you're starting a DMAIC project. Carefully considering and developing good questions right at the start of a project—the DEFINE stage—will help you make sure that you're getting the right data in the MEASURE stage. That, in turn, should result in a much smoother and stress-free ANALYZE phase—and probably more successful IMPROVE and CONTROL phases, too. The alternative? You'll have to complete the ANALYZE phase with the data you have, not the data you wish you had. </p>
4. Worry About Data Quality
<p><img alt="gauge" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/b82fc879fa26a76f2b00424550aafe9e/gage.jpg" style="width: 250px; height: 173px; float: right; margin: 10px 15px;" />"Can you trust your data?" My Six Sigma instructor asked us that question so many times, it still flashes through my mind every time I open Minitab. That's good, because he was absolutely right: if you can't trust your data, you shouldn't do anything with it. Many people take it for granted that the data they get is precise and accurate, especially when using automated measuring instruments and similar technology. But how do you <em>know </em>they're measuring precisely and accurately? How do you <em>know </em>your instruments are calibrated properly? If you didn't test it, <em>you don't know</em>. And if you don't know, you can't trust your data. Fortunately, with measurement system analysis methods like <span><a href="http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr">gage R&R</a></span> and <a href="http://blog.minitab.com/blog/understanding-statistics/got-good-judgment-prove-it-with-attribute-agreement-analysis">attribute agreement analysis</a>, we never have to trust <span style="line-height: 20.8px;">data</span><span style="line-height: 20.8px;"> </span><span style="line-height: 1.6;">quality to blind faith. </span></p>
5. Statistical Analysis Is More Than a Set of Computations
<p>Statistical techniques are often referred to as "tools," and that's a very apt metaphor. A saw, a plane, and a router all cut wood, but they aren't interchangeable—the end product defines which tool is appropriate for a job. Similarly, you might apply ANOVA, regression, or time series analysis to the same data set, but the right tool depends on what you want to understand. To extend the metaphor further, just as we have circular saws, jigsaws, and miter saws for very specific tasks, each family of statistical methods also includes specialized tools designed to handle particular situations. The point is that we select a tool to <em>assist </em>our analysis, not to <em>define </em>it. </p>
6. Keep it Simple
<p>Many processes are inherently messy. If you've got dozens of input variables and multiple outcomes, analyzing them could require many steps, transformations, and some thorny calculations. Sometimes that degree of complexity is required. But a more complicated analysis isn't always better—in fact, overcomplicating it may make your results less clear and less reliable. It also potenitally makes the analysis more difficult than necessary. <span style="line-height: 20.8px;">You may not </span><em style="line-height: 20.8px;">need </em><span style="line-height: 20.8px;">a complex process model that includes 15 factors if you can improve your output by optimizing the three or four most important inputs. </span><span style="line-height: 1.6;">If you need to improve a process that includes many inputs, </span><a href="http://blog.minitab.com/blog/statistics-and-quality-improvement/create-a-doe-screening-experiment-with-the-assistant-in-minitab-17" style="line-height: 1.6;">a short screening experiment</a><span style="line-height: 1.6;"> can help you identify which factors are most critical, and which are not so important. </span></p>
7. Provide Assessments of Variability
<p>No model is perfect. No analysis accounts for all of the observed variation. Every analysis includes a degree of uncertainty. Thus, no statistical finding is 100% certain, and that degree of uncertainty needs to be considered when using statistical results to make decisions. If you're the decision-maker, be sure that you understand the risks of reaching a wrong conclusion based on the analysis at hand. If you're sharing your results with stakeholders and executives, especially if they aren't statistically inclined, make sure you've communicated that degree of risk to them by offering and explaining confidence intervals, margins of error, or other appropriate measures of uncertainty. </p>
8. Check Your Assumptions
<p>Different statistical methods are based on different assumptions about the data being analyzed. For instance, many common analyses assume that your data follow a normal distribution. You can check most of these assumptions very quickly using functions like a normality test in your statistical software, but it's easy to forget (or ignore) these steps and dive right into your analysis. However, failing to verify those assumptions can yield results that aren't reliable and shouldn't be used to inform decisions, so don't skip that step. <a href="http://www.minitab.com/products/minitab/assistant/">If you're not sure about the assumptions for a statistical analysis, Minitab's Assistant menu explains them</a>, and can even flag violations of the assumptions before you draw the wrong conclusion from an errant analysis. </p>
9. <span style="color:#FF0000;">When Possible, Replicate Verify Success!</span>
<p><span style="line-height: 1.6;">In science, replication of a study—ideally by another, independent scientist—is crucial. It indicates that the first researcher's findings weren't a fluke, and provides more evidence in support of the given hypothesis. Similarly, when a quality project results in great improvements, we can't take it for granted those benefits are going to be sustained—they need to be verified and confirmed over time. Control charts are probably the most common tool for making sure a project's benefits endure, but depending on the process and the nature of the improvements, hypothesis tests, capability analysis, and other methods also can come into play. </span></p>
10. <span style="color:#FF0000;">Make Your Analysis Reproducible Share How You Did It</span>
<p>In the original 10 Simple Rules article, the authors suggest scientists share their data and explain how they analyzed it so that others can make sure they get the same results. This idea doesn't translate so neatly to the business world, where your data may be proprietary or private for other reasons. But just as science benefits from transparency, the quality profession benefits when we share as much information as we can about our successes. <span style="line-height: 20.8px;">Of course you can't share your company's secret-sauce formulas with competitors</span><span style="line-height: 20.8px;">—but i</span><span style="line-height: 1.6;">f you solved a quality challenge in your organization, chances are your experience could help someone facing a similar problem. If a peer in another organization already solved a problem like the one you're struggling with now, wouldn't you like to see if a similar approach might work for you? Organizations like <a href="http://asq.org/index.aspx" target="_blank">ASQ</a> and forums like <a href="https://www.isixsigma.com/" target="_blank">iSixSigma.com</a> help quality practitioners network and share their successes so we can all get better at what we do. And here at Minitab, we love sharing <a href="http://www.minitab.com/company/case-studies/">case studies and examples of how people have solved problems using data analysis</a>, too. </span></p>
<p>How do you think these rules apply to the world of quality and business decision-making? What are <em>your </em>guidelines when it comes to analyzing data? </p>
<p> </p>
Data AnalysisLean Six SigmaQuality ImprovementSix SigmaStatisticsStatistics HelpStatistics in the NewsStatsWed, 29 Jun 2016 12:00:00 +0000http://blog.minitab.com/blog/understanding-statistics/those-10-simple-rules-for-using-statistics-theyre-not-just-for-researchEston MartzAre You Putting the Data Cart Before the Horse? Best Practices for Prepping Data for Analysis, ...
http://blog.minitab.com/blog/meredith-griffith/are-you-putting-the-data-cart-before-the-horse-best-practices-for-prepping-data-for-analysis%2C-part-1
<p>Most of us have heard a backwards way of completing a task, or doing something in the conventionally wrong order, described as “putting the cart before the horse.” That’s because a horse pulling a cart is much more efficient than a horse pushing a cart.</p>
<p><img alt="cart before horse" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/479b4fbd-f8c0-4011-9409-f4109cc4c745/Image/ec1fbea4785510ea0e0a9997c1669c68/cart_horse.png" style="margin: 10px 15px; float: right; width: 350px; height: 206px;" />This saying may be especially true in the world of statistics. Focusing on a statistical tool or analysis before checking out the condition of your data is one way you may be putting the cart before the horse. You may then find yourself trying to force your data to fit an analysis, particularly when the data has not been set up properly. It’s far more efficient to first make sure your <a href="http://blog.minitab.com/blog/understanding-statistics/the-single-most-important-question-in-every-statistical-analysis">data are reliable</a> and then allow your questions of interest to guide you to the right analysis.</p>
<p>Spending a little quality time with your data up front can save you from wasting a lot of time on an analysis that either can’t work—or can’t be trusted.</p>
<p>As a quality practitioner, you’re likely to be involved in many activities—establishing quality requirements for external suppliers, monitoring product quality, reviewing product specifications and ensuring they are met, improving process efficiency, and much more.</p>
<p>All of these tasks will involve data collection and statistical analysis with software such as Minitab. For example, suppose you need to perform a <a href="http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr">Gage R&R</a> study to verify your measurement systems are valid, or you need to understand how machine failures impact downtime.</p>
<p>Rather than jumping right into the analysis, you will be at an advantage if you take time to look at your data. Ask yourself questions such as:</p>
<ul>
<li>What problem am I trying to solve?</li>
<li>Is my data set up in a way that will be useful to answering my question?</li>
<li>Did I make any mistakes while recording my data?</li>
</ul>
<p>Utilizing process knowledge can also help you answer questions about your data and identify data entry errors. A focus on preparing and exploring your data prior to an analysis will not only save you time in the long run, but will help you obtain reliable results.</p>
<p>So then, where to begin with best practices for prepping data for an analysis? Let’s look no further than your data.</p>
Clean your data before you analyze it
<p>Let’s assume you already know what problem you’re trying to solve with your data. For instance, you are the area supervisor of a manufacturing facility, and you’ve been experiencing lower productivity than usual on the machines in your area and want to understand why. You have collected data on these machines, recording the amount of time a machine was out of operation, the reason for the machine being down, the shift number when the machine went down, and the speed of the machine when it went down.</p>
<p>The first step toward answering your question is to ensure your data are clean. Cleaning your data before you begin an analysis can save time by preventing rework, such as reformatting data or correcting data entry errors, after you’ve already begun the analysis. Data cleaning is also essential to ensure your analyses and results—and the decisions you make—are reliable.</p>
<p>With the latest update to Minitab<span style="line-height: 20.8px;">, an improved data import helps you identify and correct case mismatches, fix improperly formatted columns, represent missing data accurately and in a manner that is recognized by the software, remove blank rows and extra spaces, and more. When importing your data, you see a preview of your data as a reminder to ensure it’s in the best possible state before it finds its way into Minitab. This preview helps you spot mistakes you have made in your data collection, and automatically corrects mistakes you don’t notice or that are difficult to find in large data sets.</span></p>
<p><img alt="Data Import" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/dae6c7b7-fc22-4616-9d65-f04909c20ab1/Image/b1c679056c60ac2fa82f37e1f1de406b/data_import.jpg" style="width: 775px; height: 655px;" /></p>
<p><em>Minitab offers a data import dialog that helps you quickly clean and format your data before importing into the software, ensuring your data are trustworthy and allowing you to get to your analysis sooner.</em></p>
<p><span style="line-height: 20.8px;">If you’d rather copy and paste your data from Excel, Minitab will ensure you paste your data in the right place. For instance, if your data have column names and you accidentally paste your data into the first row of the worksheet, your data will all be formatted as text—even when the data following your column names are numeric! With </span>Minitab<span style="line-height: 20.8px;">, you will receive an alert that your data is in the wrong place, and Minitab will automatically move your data where it belongs. This alert ensures your data are formatted properly, preventing you from running into the problem during an analysis and saving you time manually correcting every improperly formatted column.</span></p>
<p><img alt="Copy Paste Warning" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/dae6c7b7-fc22-4616-9d65-f04909c20ab1/Image/5df941ffaa491a0072261aef075a19d6/copy_paste_warning.jpg" style="width: 431px; height: 299px;" /></p>
<p><em>Pasting your Excel data in the first row of a Minitab worksheet will trigger this warning, which safeguards against improperly formatted columns.</em></p>
<p><span style="line-height: 1.6;">This is only the beginning! Minitab makes it quick and painless to begin exploring and visualizing your data, offering more insights and ease once you get to the analysis. If you’d like to learn additional best practices for prepping your data for any analysis, stay tuned for my next post where I’ll offer tips for exploring and drawing insights from your data!</span></p>
Data AnalysisStatisticsWed, 30 Mar 2016 14:05:00 +0000http://blog.minitab.com/blog/meredith-griffith/are-you-putting-the-data-cart-before-the-horse-best-practices-for-prepping-data-for-analysis%2C-part-1Meredith GriffithGage R&R Metrics: What Do They All Mean?
http://blog.minitab.com/blog/starting-out-with-statistical-software/gage-rr-metrics%3A-what-do-they-all-mean
<p>When you analyze a Gage R&R study in <a href="http://www.minitab.com/products/minitab/">statistical software</a>, your results can be overwhelming. There are a lot of statistics listed in Minitab's Session Window—what do they all mean, and are they telling you the same thing?</p>
<p>If you don't know where to start, it can be hard to figure out what the analysis is telling you, especially if your measurement system is giving you some numbers you'd think are good, and others that might not be. I'm going to focus on three different statistics that are often confused when <span><a href="http://blog.minitab.com/blog/meredith-griffith/fundamentals-of-gage-rr">reading Gage R&R output</a></span>. </p>
<p>The first thing to look at is the %Study Variation and the %Contribution.</p>
<p style="margin-left: 40px;"><img alt="gage r&R output" src="https://cdn2.content.compendiumblog.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/f7e1af57-c25e-4ec3-a999-2166d525717e/Image/be2a9d9d311b9fad9b00eacdd73abff5/gage2.png" style="width: 618px; height: 404px;" /></p>
<p>You could look at either of them, as they are both telling you the same thing, just in a different way. By definition, the %Contribution for a source is 100 times the variance component for that source divided by the Total Variation variance component. This calculation has the benefit of making all of your sources of variability add up to 100%, which can make things easy to interpret.</p>
<p>The %Study Variation does not sum up to 100% like %Contribution, but it does have other benefits. %Contribution is based on the variance component that is specific to the values you observed in your study, not what the population of values might be. In contrast, the %Study Variation, by taking 6*standard deviation, extrapolates out over the entire population of values (based on the observed values, of course).</p>
<p>The bottom line is that both % Study Variation and %Contribution are telling you, in simple terms, about the percentage of variation in your process attributable to that particular source. </p>
<p>What about %Tolerance? What does <em>that </em>allow us to look at? While %StudyVar and %Contribution compare the variation from a particular source to the total variation, the %Tolerance compares the amount of variation from a source to a specified tolerance spread. This can lead to seemingly conflicting results, such as getting a low %StudyVar while having a high %Tolerance. In this case, your gage system may be introducing low levels of variability compared to other sources, but the amount of variation is still too much based on your spec limits. The %Tolerance column may be more important to you in this case, as it's more specific to your actual product and its spec limits. </p>
<p>So, a short summary:</p>
<p><strong>%Contribution: </strong>The percentage of variation due to the source compared to the total variation, but with the added benefit that all sources will sum to 100%</p>
<p><strong>%StudyVar:</strong> The <span style="line-height: 20.8px;">percentage of variation due to the source compared to the total variation, but with the added benefit of extrapolating beyond your specific data values. </span></p>
<p><strong>%Tolerance:</strong> The percentage of variation due to the source compared to your specified tolerance range.</p>
<p>The %StudyVar is perhaps more reliant on having a good quality study and can be used when your goal is improving the measurement system. On the other hand %Tolerance can be used when the focus is on the measurement system being able to do it’s job and classify parts as in or out of spec.</p>
<p>Each of these statistics provide valuable information, and how you weigh each of these largely depends on what you're looking to get out of your study.</p>
Lean Six SigmaProject ToolsQuality ImprovementMon, 21 Mar 2016 12:00:00 +0000http://blog.minitab.com/blog/starting-out-with-statistical-software/gage-rr-metrics%3A-what-do-they-all-meanEric HeckmanImproving Recycling Processes at Rose-Hulman, Part III
http://blog.minitab.com/blog/real-world-quality-improvement/improving-recycling-processes-at-rose-hulman-part-iii
<p><img alt="" src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/fa7a4559e547be217d5fa38f61c978c1/landfill.jpg" style="float: right; width: 350px; height: 253px; margin: 10px 15px;" />In previous posts, I discussed the results of a recycling project done by Six Sigma students at Rose-Hulman Institute of Technology last spring. (If you’re playing catch up, you can read <a href="http://blog.minitab.com/blog/real-world-quality-improvement/a-little-trash-talk3a-improving-recycling-processes-at-rose-hulman" target="_blank">Part I</a> and <a href="http://blog.minitab.com/blog/real-world-quality-improvement/a-little-trash-talk%3A-improving-recycling-processes-at-rose-hulman%2C-part-ii" target="_blank">Part II</a>.)</p>
<p>The students did an awesome job reducing the amount of recycling that was thrown into the normal trash cans across all of the institution’s academic buildings. At the end of the spring quarter (2014), 24% of trash cans (by weight) included recyclable items. At the beginning of that spring quarter, 36% of trash cans were recyclable items, so you can see that they were very successful in reducing this percentage!</p>
<p>The fall quarter (2015) brought a new set of Six Sigma students to Rose-Hulman who were just as dedicated to reducing the amount of recycling thrown into normal trash cans, and I want to cover their success in this post, as well as some of the neat statistical methods they used when completing their project.</p>
Fall 2015 goals
<p>This time around, the students wanted to at least maintain or improve on the percentage spring quarter (2014) students were able to achieve. They set out with a specific goal to reduce the amount of recycling in the trash to 20% by weight.</p>
<p>In order to further reduce the recyclables in the academic buildings in fall 2015, the standard “Define, Measure, Analyze, Improve, Control” (DMAIC) methodology of Six Sigma was once again implemented. The main project goal focused on standardizing the recycling process within the buildings, and their plan to reduce the amount of recyclables focused on optimizing the operating procedure for collecting recyclables in all academic building areas (excluding classrooms) where trash and recycling are collected.</p>
<p>Many of the same DMAIC tools that were used by spring 2014 students were also used here, including—<a href="http://support.minitab.com/quality-companion/3/help-and-how-to/run-projects/brainstorming/ct-tree/" target="_blank">Critical to Quality Diagrams</a>, <a href="http://support.minitab.com/quality-companion/3/help-and-how-to/run-projects/maps/process-map/" target="_blank">Process Maps</a>, <a href="http://blog.minitab.com/blog/real-world-quality-improvement/spicy-statistics-and-attribute-agreement-analysis" target="_blank">Attribute Agreement Analysis</a>, <a href="http://blog.minitab.com/blog/marilyn-wheatleys-blog/evaluating-a-gage-study-with-one-part-v2" target="_blank">Gage R&R</a>, Statistical Plots, <a href="http://blog.minitab.com/blog/adventures-in-software-development/risk-based-testing-at-minitab-using-quality-companions-fmea" target="_blank">FMEA</a>, <a href="http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-tutorial-and-examples" target="_blank">Regression</a>—among many others.</p>
Making and measuring improvements
<p>The spring 2014 initiative added recycling bins to every classroom, which created a measurable improvement. The fall 2015 effort focused on improvement through <em>standardization of operation</em>. For example, many areas in the academic buildings suffer from random placement and arrangement of trash cans and recycling bins. The students thought standardization of bin areas (one trash, one plastic/aluminum recycling, and one paper recycling) would lessen the confusion of recycling, and clear signage and stickers on identically shaped trash cans and recycling bins would be better visual cues of where to place waste of both kinds.</p>
<p>For fall 2015, there were seven teams, and they were assigned different academic building floors (not including classrooms) and common areas. Unlike the spring 2014 data collection, the teams did not combine the trash from their assigned areas. They treated each recycling station as a unique data point.</p>
<p>After implementing the improvements to standardize the bins, the teams collected data for four days across twenty-nine total stations. Thus, there were a total of 116 fall 2015 improvement percentages. The fall 2015 students used the post-improvement percentage of recyclables in the trash from spring 2014 (24%) as their baseline for determining improvement in fall 2015.</p>
<p>The descriptive statistics for the percentage of recyclables (by weight) in the trash were as follows:</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/5c77690aaaff21d0b33eb5083f82074e/descriptive_stats.jpg" style="border-width: 0px; border-style: solid; width: 550px; height: 67px;" /></p>
<p>Below, the students put together a histogram and a boxplot of the data using <a href="http://www.minitab.com/products/minitab/features/" target="_blank">Minitab Statistical Software</a>. Over half of the stations (61 out of 116) had less than 5% of recyclables in the trash. Forty-six of the 116 recycling stations had no recyclables. The value of the third quartile (16.6%), meant that 75% of the stations had less than 16.6% recyclables. The descriptive statistics above showed that the sample mean was much larger than the sample median. The graphs confirmed that this must be the case because of the strong positively skewed shape of the data.</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/4e730181a9288e531ff9caf69a347dd0/histogram.jpg" style="border-width: 0px; border-style: solid; width: 624px; height: 206px;" /></p>
<p>Even though the 116 data points didn’t follow a normal distribution and there was a large mound of 0’s as part of the distribution from collection spots that had no recyclables, the students trusted that the <a href="http://blog.minitab.com/blog/understanding-statistics/how-the-central-limit-theorem-works" target="_blank">Central Limit Theorem</a> with a sample size of 116 would generate a sampling distribution of the means that was normally distributed. Because of the large sample size and unknown standard deviation, they used a <em>t</em> distribution to create a 95% confidence interval for the true mean percentage of recyclables in the trash for fall 2015.</p>
<p>Also using Minitab, they constructed the 95% confidence interval:</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/2ccf17f68f0055c32282c2020f2c9108/one_sample_t.jpg" style="border-width: 0px; border-style: solid; width: 423px; height: 48px;" /></p>
<p>The 95% confidence interval meant that the students were 95% certain that the interval [9.94, 18.22] contains the true mean percentage of recyclables in the trash for fall 2015. At an alpha level equal to 0.025, they were able to reject the null hypothesis, where H0: μ = 24% versus Ha: μ < 24%, because 24% was not contained in the two-sided 95% confidence interval. (Remember that 24% was the mean percentage of recyclables in trash after the spring 2014 improvement phase.) The null hypothesis for H0: μ = 20% versus Ha: μ < 20%, was rejected. This meant that they had met their goal to reduce the percentage of recyclables in the trash to below 20% for this project!</p>
Continuing to analyze the data
<p>The students also subgrouped their data by collection day. Each day consisted of data from 29 recycling stations. The comparative boxplots and individual value plots below show the percentage of recyclables in the trash across the four collection dates. (The horizontal dotted line in the boxplot is the mean from spring 2014’s post-improvement data.)</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/664e8bf0f443d278376e71a70817e727/ivp.jpg" style="border-width: 0px; border-style: solid; width: 624px; height: 207px;" /></p>
<p>Though all four collection days have sample means less than 24%, it’s obvious from the boxplots that the first three collection days are clearly below 24%, and the medians from all four days are less than 11%. The individual value plots reveal the large number of 0’s on each day, which represented collection spots that had no recyclables. Both graphs display the positively skewed nature of the data. Because of the positive skewness, each day’s mean is much larger than its median.</p>
How capable was the process?
<p>Next, the students ran a <a href="http://blog.minitab.com/blog/real-world-quality-improvement/using-statistics-to-show-your-boss-process-improvements" target="_blank">process capability analysis</a> for the seven areas where trash was collected over four days:</p>
<p><img src="http://cdn.app.compendium.com/uploads/user/458939f4-fe08-4dbc-b271-efca0f5a2682/ccb8f6d6-3464-4afb-a432-56c623a7b437/Image/8f9b85a55164f9e957809a8be1eef1c0/process_cap.jpg" style="border-width: 0px; border-style: solid; width: 465px; height: 347px;" /></p>
<p>The process capability indices were Pp = 0.48 and Ppk = 0.42. (The Pp value corresponds to a 1.44 Sigma Level, while the Ppk value corresponds to a 1.26 Sigma Level.) Recall that the previous Ppk value after improvements in <a href="http://blog.minitab.com/blog/real-world-quality-improvement/a-little-trash-talk%3A-improving-recycling-processes-at-rose-hulman%2C-part-ii" target="_blank">spring 2014</a> was 0.22. The fall 2015 index is almost double that value!</p>
<p>The students knew that they still needed to account for the total weight of the trash and recyclables by calculating the percentage of recyclables per station. Some collection stations with the highest percentage of recyclables had the lowest total weight, while some stations with the lowest percentage of recyclables had the highest total weight. Instead of strictly using a capability index to indicate their improvement, they incorporated a <a href="http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-tutorial-and-examples" target="_blank">regression</a> model for the trash weight versus the total weight of trash and recyclables to show that the percentage of recyclables in the trash was less than 20%.</p>
<p>The 95% confidence interval for the true mean slope of the regression line was [0.856, 0.954]. The students were 95% certain that the trash weight was somewhere between 0.86 to 0.96 of the total weight of the collection. Hence, the recycling weight was between 0.046 and 0.114 of the total weight. This value is clearly below 20% with 95% confidence! From this, they were able to state through yet another type of analysis that there was a statistically significant improvement over the spring 2014 recycling project, and that they met their goal of reducing the percentage of recyclables in the trash to below 20%. Compared to the spring 2014 project where 24% of the trash was recyclables, the fall 2015 students saved <em>at least</em> 4% more recyclables from ending up in the local landfill!</p>
<p>For even more on this topic, be sure to check out Rose-Hulman student Peter Olejnik’s blog posts on how he and the recycling project team at the school used regression to evaluate project results:</p>
<p><a href="http://blog.minitab.com/blog/statistics-in-the-field/using-regression-to-evaluate-project-results%2C-part-1" target="_blank">Using Regression to Evaluate Project Results, part 1</a></p>
<p><a href="http://blog.minitab.com/blog/statistics-in-the-field/using-regression-to-evaluate-project-results%2C-part-2" target="_blank">Using Regression to Evaluate Project Results, part 2</a></p>
<p><em>Many thanks to Dr. Diane Evans for her contributions to this post!</em></p>
Data AnalysisFun StatisticsHypothesis TestingLean Six SigmaLearningSix SigmaStatisticsStatsFri, 08 May 2015 12:00:00 +0000http://blog.minitab.com/blog/real-world-quality-improvement/improving-recycling-processes-at-rose-hulman-part-iiiCarly Barry