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Using an XBar and s Chart to Compare Samples from Different Applications

Authors: Marilyn & Robert Hart

Q: How do I use a control chart to compare measurement data taken from samples from different applications?

A: The Xbar and s control chart is an excellent way to compare both the average (mean) and the variability (standard deviation) of samples from different applications in order to compare their performance. This is called the use of rational subgroups, rather than the time-order of data usually associated with control charts. Since there are typically few subgroups involved, subgroups of at least 25 measurements are recommended.

Example:
It is desirable to compare the performance of two shifts making similar product. Fifty measurements from each of the two shifts are taken to be analyzed on an Xbar & s chart. Since only two subgroups are being used, it is desirable to use 1.5 sigma limits to keep the alpha risk in the desired range (close to 0.07). (See the previous month's Quality Practice Tips.) The resulting Xbar & s chart is shown in Figure 1. The s chart is out of control which means that the difference in s between the two shifts is statistically significant. Note that this is similar to hypothesis testing on the means (and variances) or analysis of variance in classical statistics.

Figure 1. Xbar & s Chart, 1.5-Sigma Limits