Discussion
Suppose two control charts have the same in-control average run length (ARL). Then which of the following is true ?
Answer: B
The true statement is The charts can be compared using out-of-control ARL.
Matching the in-control ARL makes two charts equally prone to false alarms. The fair comparison is then how quickly each detects a real shift, that is, which has the smaller out-of-control ARL for the shifts of interest. This is how Shewhart, CUSUM and EWMA charts are usually compared.
Equal in-control ARLs do not mean equal performance: a CUSUM chart detects small shifts much faster than a Shewhart chart with the same in-control ARL. Charts can of course be designed to share an in-control ARL, and ARL comparisons apply to charts for variability as well as for the mean.
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