Percentile-based control chart design with an application to Shewhart X̅ and S² control charts

We present a method to design control charts such that in-control and out-of-control run lengths are guaranteed with prespecified probabilities. We call this method the percentile-based approach to control chart design. This method is an improvement over the classical and popular statistical design approach employing constraints on in-control and out-of-control average run lengths since we can ensure with prespecified probability that the actual in-control run length exceeds a desired magnitude. Similarly, we can ensure that the out-of-control run length is less than a desired magnitude with prespecified probability. Some numerical examples illustrate the efficacy of this design method.