Creating Run Charts

Overview

We're going to learn how to create and interpret Run Charts. Specifically, by the end of this lesson, you'll know what a Run Chart is, as well as, how it can and should be used in harmony with the graphical analysis tool, prior to more advanced statistical analysis, such as hypothesis tests.

The first thing we should do once we are presented with new data is to complete a graphical analysis of our data. With this said, before we conduct more advanced statistical analysis, we have one more graphical analysis to complete.

Specifically, we need to create and analyze a Run Chart. A Run Chart tests for randomness and independence. With a Run Chart, we're able to actually verify statistically whether our data is in fact random. We do this by plotting our data points in sequential order much like a time series plot.

The measure of central tendency, either the mean or median, is drawn in and two different tests for randomness are conducted. Although no hypothesis or Ho for all Run Charts is that our data are random and the alternate hypothesis or Ha is that our data are not random.

If our data are random, we're able to continue with more advanced statistical analysis, but if our data are not random, we must take the time to understand what's going on since pressing on with non-random data can lead to inaccurate results and conclusions down the road.

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The first test examines the number of runs about the median. A run with this test is one or more consecutive points on the same side of the median.

In the graph above we see a run of five points on the same side of the median.

As you can see there are two specific results for this first test. We see a P-Value for clustering and a P-Value for mixtures. In this particular example, assuming we chose an alpha value of .05, we failed to reject the known hypothesis since the P- Values for both clusterings and mixtures are greater than .05. In other words, this data has passed the first statistical test.

Before we move to the second test, let's explore clustering and mixtures. First, clustering appears as a group of points together in one area of the chart. A cluster can be indicative of variation caused by poor sampling or measurement problems.

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You'll also notice that the P-Value for clustering is .005 well below our alpha value of .05, so since p is low Ho must go, meaning we reject the null hypothesis and conclude based on this sample data that our data are not random due to clustering.

Next, mixtures appear as an absence of data points near the center line. Notice in this example, very few of the data points fall near the mean.

Sometimes we see mixtures when dealing with a bimodal distribution such as when two different processes are combined. For example, we may produce the same parts with a different machine which could lead to a bimodal distribution.

Creating Run Charts GembaAcademy.com 3 Other things that can cause mixtures are changes in shift and variations in raw materials.

Notice how in the above example, our P-Value for mixtures is less than .05 so we reject the null hypothesis and conclude that our data are not random.

The second test Minitab runs focuses on the number of runs up or down. This test is based on the number of runs up or down increasing or decreasing.

A run with this test is one or more consecutive points in the same direction. A new run begins each time there's a change in the direction. The first thing this test checks for are trends which appear as an upward or downward drip in the data like we see here.

Creating Run Charts GembaAcademy.com 4 Now trends can be caused by many things such as a machine tool wearing out over time. Notice how in this example, the P-Value for trends is .001 much less than our alpha value of .05 meaning we reject the null hypothesis and conclude that our data are not random due to trends.

Finally, oscillations appear as rapid up and down fluctuations like we see in this example indicating process instability. The P-Value in this example is .009 meaning we'd reject the null hypothesis and conclude that our data are not random due to oscillations.

As an aside, you may have already noticed, but one minus the oscillations P-Value equals the P-Value for trends. Just like one minus the mixtures P-Value equals the P-Value for clustering since the values are mutually exclusive of one another.

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