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# Statistical Process Control Run Charts – Are They Still Relevant?

The Western Electric Company and Lloyd Nelson created elegant and simple rules.  These rules test whether a process is “out of control”.  These helped manufacturers for years to determine the degradation of their processes.  Statistical Process Control (SPC) uses these run charts to derive comfort that their process is stable. Really, violation of these rules actually tell you that you are out of control? My question is, how come we are still using run charts that test the assumption that our process is operating at three Sigma?

### What if our Process Runs at Five Sigma?

SPC asks this question: Is this test meaningful if you’re running at four Sigma or five Sigma or maybe even six Sigma?  The rules were devised when three Sigma was an acceptable tolerance. What good is it to look at a run chart now that processing capabilities are marching towards six Sigma?

The run charts are based on a probability that a point or set of points will exceed some threshold. As an example let’s look at the Lloyd Nelson Rule 1.  This rule states that the process is in an “out of control” state if a single point exceeds the Upper Control Limit, which is set at three Sigma. Since the rule does not specify how many points you test then there is a probability that if you test enough points, you will normally get a point that exceeds three Sigma even though the process is not out of control.

Let’s say that your process runs at five Sigma instead of three Sigma. Since that narrows the deviation of the data points and that the probability of a data point becomes much less likely to exceed the three Sigma boundary. Therefore, this diminishes the value of performing this test.

Since a five Sigma process has a much narrower distribution shouldn’t the boundary that we are testing against be narrower? Maybe a five Sigma process should test against an Upper Control Limit at two Sigma. You can analytically determine the probability that five Sigma process data points will exceed two Sigma.

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