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Normal Distribution

Blog posts and articles about the role of the normal distribution in statistics, data analysis, and quality improvement.

If you have a process that isn’t meeting specifications, using the Monte Carlo simulation and optimization tool in Companion by Minitab can help. Here’s how you, as a chemical technician for a paper products company, could use Companion to optimize a chemical process and ensure it consistently delivers a paper product that meets brightness standards. The brightness of Perfect Papyrus Company’s new... Continue Reading
In Parts 1 and 2 of Gauging Gage 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... Continue Reading

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by Kevin Clay, guest blogger In transactional or service processes, we often deal with lead-time data, and usually that data does not follow the normal distribution. Consider a Lean Six Sigma project to reduce the lead time required to install an information technology solution at a customer site. It should take no more than 30 days—working 10 hours per day Monday–Friday—to complete, test and... Continue Reading
Welcome to the Hypothesis Test Casino! The featured game of the house is roulette. But this is no ordinary game of roulette. This is p-value roulette! Here’s how it works: We have two roulette wheels, the Null wheel and the Alternative wheel. Each wheel has 20 slots (instead of the usual 37 or 38). You get to bet on one slot. What happens if the ball lands in the slot you bet on? Well, that depends... Continue Reading
As a person who loves baking (and eating) cakes, I find it bothersome to go through all the effort of baking a cake when the end result is too dry for my taste. For that reason, I decided to use a designed experiment in Minitab to help me reduce the moisture loss in baked chocolate cakes, and find the optimal settings of my input factors to produce a moist baked chocolate cake. I’ll share the... Continue Reading
by Matthew Barsalou, guest blogger.  The old saying “if it walks like a duck, quacks like a duck and looks like a duck, then it must be a duck” may be appropriate in bird watching; however, the same idea can’t be applied when observing a statistical distribution. The dedicated ornithologist is often armed with binoculars and a field guide to the local birds and this should be sufficient. A... Continue Reading
T'was the season for toys recently, and Christmas day found me playing around with a classic, the Etch-a-Sketch. As I noodled with the knobs, I had a sudden flash of recognition: my drawing reminded me of the Empirical CDF Plot in Minitab Statistical Software. Did you just ask, "What's a CDF plot? And what's so empirical about it?" Both very good questions. Let's start with the first, and we'll... Continue Reading
In my last post on DMAIC tools for the Define phase, we reviewed various graphs and stats typically used to define project goals and customer deliverables. Let’s now move along to the tools you can use in Minitab Statistical Software to conduct the Measure phase. Measure Phase Methodology The goal of this phase is to measure the process to determine its current performance and quantify the problem.... Continue Reading
by Matthew Barsalou, guest blogger The great Dr. Seuss tells of Mr. Plunger, who is the custodian at Diffendoofer School on the corner of Dinkzoober and Dinzott in the town of Dinkerville. The good Mr. Plunger “keeps the whole school clean” using a supper-zooper-flooper-do. Unfortunately, Dr. Seuss fails to tell us where the supper-zooper-flooper-do came from and if the production process was... Continue Reading
The language of statistics is a funny thing, but there usually isn't much to laugh at in the consequences that can follow when misunderstandings occur between statisticians and non-statisticians. We see these consequences frequently in the media, when new studies—that usually contradict previous ones—are breathlessly related, as if their findings were incontrovertible facts. Similar, though less... Continue Reading
As we enter late December, snow is falling here on the East Coast of the United States. The official start to winter is on December 21, 2016, but it’s certainly not uncommon to see snowflakes flying before this date. If you live in the U.S., you know the winter of 2015 was one for the record books. In fact, more than 90 inches of snow fell in Boston in the winter of 2015! Have you ever wondered how... Continue Reading
If you’re familiar with Lean Six Sigma, then you’re familiar with DMAIC. DMAIC is the acronym for Define, Measure, Analyze, Improve and Control. This proven problem-solving strategy provides a structured 5-phase framework to follow when working on an improvement project. This is the first post in a five-part series that focuses on the tools available in Minitab Statistical Software that are most... Continue Reading
by Matt Barsalou, guest blogger I know that Thanksgiving is always on the last Thursday in November, but somehow I failed to notice it was fast approaching until the Monday before Thanksgiving. This led to frantically sending a last-minute invitation, and a hunt for a turkey. I live in Germany and this greatly complicated the matter. Not only is Thanksgiving not celebrated, but also actual turkeys... Continue Reading
In Part 1 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.  The common data... Continue Reading
Statistical inference uses data from a sample of individuals to reach conclusions about the whole population. It’s a very powerful tool. But as the saying goes, “With great power comes great responsibility!” When attempting to make inferences from sample data, you must check your assumptions. Violating any of these assumptions can result in false positives or false negatives, thus invalidating... Continue Reading
So the data you nurtured, that you worked so hard to format and make useful, failed the normality test. Time to face the truth: despite your best efforts, that data set is never going to measure up to the assumption you may have been trained to fervently look for. Your data's lack of normality seems to make it poorly suited for analysis. Now what? Take it easy. Don't get uptight. Just let your data... Continue Reading
See if this sounds fair to you. I flip a coin. Heads: You win $1.Tails: You pay me $1. You may not like games of chance, but you have to admit it seems like a fair game. At least, assuming the coin is a normal, balanced coin, and assuming I’m not a sleight-of-hand magician who can control the coin. How about this next game? You pay me $2 to play.I flip a coin over and over until it comes up heads.Your... Continue Reading
Back when I used to work in Minitab Tech Support, customers often asked me, “What’s the difference between Cpk and Ppk?” It’s a good question, especially since many practitioners default to using Cpk while overlooking Ppk altogether. It’s like the '80s pop duo Wham!, where Cpk is George Michael and Ppk is that other guy. Poofy hairdos styled with mousse, shoulder pads, and leg warmers aside, let’s... Continue Reading
Here is a scenario involving process capability that we’ve seen from time to time in Minitab's technical support department. I’m sharing the details in this post so that you’ll know where to look if you encounter a similar situation. You need to run a capability analysis. You generate the output using Minitab Statistical Software. When you look at the results, the Cpk is huge and the histogram in... Continue Reading
In my last post, we took the red pill and dove deep into the unarguably fascinating and uncompromisingly compelling world of the matrix plot. I've stuffed this post with information about a topic of marginal interest...the marginal plot. Margins are important. Back in my English composition days, I recall that margins were particularly prized for the inverse linear relationship they maintained with... Continue Reading