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Take It Easy: Create a Run Chart

Ever make a task harder than it needs to be? Last night my son wanted to get a toy from a shelf in the closet that was a little beyond his reach. I watched as he tried to jump up and grab it.  Next, he started climbing the shelves (a quick word from me stopped that approach). Then he tried jumping several more times. Finally he said "I give up."

That's when I suggested he use the stepladder, which had been just inside the closet the whole time. 

Statistics can be like that. We can focus on the complexities of an analysis, but lose sight of the practical question we're trying to answer. If we step back and look at all of the available tools, sometimes there's a simpler way to get the information we need. 

When seeking to improve quality, you often look for processes with unusual variation so you can identify what's causing the variation, then control it. A process is in control when only natural variation affects the output. That's the idea behind control charts, and Minitab makes it easy to create a wide variety of control charts depending on what type of data you're looking at.

But step back a second. Some variation is a natural part of any process, and in the quality world we're concerned only about that unusual, "special cause" variation. You can use a simple tool -- the run chart -- to see if special causes are influencing your process. A run chart can't tell you everything that a control chart can, but if a run chart suggests a process is already under control, perhaps you can find a process in more urgent need of improvement! 

What Is a Run Chart?

A run chart displays how your process data changes over time, and can reveal evidence of special cause variation that creates recognizable patterns. 

Minitab's run chart plots individual observations in the order they were collected, and draws a horizontal reference line at the median. Minitab also performs two tests that provide information on non-random variation due to trends, oscillation, mixtures, and clustering -- patterns that suggest the variation observed is due to special causes.

Creating a Run Chart

It's very easy to make a run chart in Minitab. Let's say you work for a company that makes radon detectors. To make sure that detectors using a certain kind of membrane measure the amount of radiation consistently, you test 20 devices (in groups of 2) in an experimental chamber. You record the amount of radiation each device measured after every test. 

You decide to create a run chart as a first step in evaluating the variation in your measurements. (Want to follow along? Open the worksheet RADON.MTW included with Minitab's sample data sets.) 

In Minitab, choose Stat > Quality Tools > Run Chart to bring up the dialog box below. When your data are in one column, enter the data column in Single column. In Subgroup size, enter a subgroup size or column of subgroup indicators. For this data, you enter "Membrane" in Single column, and enter "2" for Subgroup size

Run Chart Dialog Box

When you click OK, Minitab creates the following graph: 

Run Chart Example

Interpreting the Run Chart

The black points on the run chart represent the individual values, while the red points connected with a line represent the subgroup means. Visually, it looks like there's some unusual variation happening for tests 3, 4, and 5.  This is confirmed in the data for the normality tests: the p-values for mixtures, trends, and oscillation look fine, but the test for clustering is significant at the 0.05 level.

 Because the p-value for the cluster test (p = 0.022) is less than the alpha value of 0.05, you can conclude that special causes are affecting your process, and you should investigate possible sources. Clusters can be evidence of sampling or measurement problems, but you'll need to collect more data to be sure.

In this case, the run chart detected unusual variation, so you'll need to dig deeper to find out what's going on with your data. But if the chart hadn't shown variation, you could be more confident about the accuracy of your membrane detectors and dedicate your time to improving a process that might be more problematic. 

Either way, creating a run chart is a good, easy step to take toward the goal of eliminating special cause variation. It sure beats jumping and grabbing!  

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Comments

Name: Rajiv • Saturday, April 20, 2013

This is very helpful.It helped me understand the significance of Run chart and what to infer if the P


Name: annie • Tuesday, December 17, 2013

Can you please help me on what kind of chart should i use to determine which machine provides a good measurement?
Note : it doesn't have any specification or reference value.


Name: Eston • Tuesday, December 17, 2013

Hi Annie - It sounds like you might want to do an measurement systems analysis rather than use a control chart for this. A Type 1 gage study might work, see Minitab Help or check out this blog post for more details about this method: http://blog.minitab.com/blog/statistics-and-quality-improvement/gummi-bear-measurement-systems-analysis-type-1-gage-study
Hope this helps!
Eston


Name: jesse • Wednesday, February 19, 2014

i havent used tab in a lil while but am having a difficult time this morning trying to get a specific chart to come out which in my head sounds and seem like the easiest chart in the world, so I am hoping to find some asistance please - I want a run chart or scatterplot that has categories or groups on the Y axis and the item on the X axis - basically I want to compare when an item comes inot the office to when it begins to be worked with the Y axis being days of the week - for example item 1 might have come into the office on Monday but not have started to be worked on until Wednesday - so for the column where item one is there would be the start of both my lines with one line beginning on Monday and other on Wednesday - The thought is that the day of the week an item comes into the office matters in when it gets worked on


Name: Eston • Wednesday, February 19, 2014

Hi Jesse - thanks for the question. I'm thinking there are a couple of ways a graph like that could be created; how long a period of time do you want to show -- for instance, would an item come in on a Monday and possibly not be worked on until the NEXT Monday? Or would the scale of the graph be 1 week, i.e. just 7 or 5 days?


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