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Anonymous
Most control charts assume the process mean does not change. Now what if we have a process with a time-varying mean? Or a time-varying variation? I’ve seen few articles about this topic. Is it just too hard or we already have useful tools for this problem?
Time-varying mean would certainly lead to an increase in the control limit range one would have to think. It would be interesting to see this in some form of statistical study to see how much it truly extends the range, definitely, variability correlated.
Control charts themselves can be used to determine if a process is out of control due to a mean shift. For instance if a xbar chart detected 7 points above the upper control limit then it is likely that a positive meanshit occurred. Different control charts have different sensitivities to small and large mean shifts. A good way to analyze if a certain control chart is effective in detecting a time based mean shift is to simulate the average run length in control and average run length out of control. You can actually use the Monte Carlo Simulation to test each chart on their effectiveness!
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