The Performance of <i>S</i> Control Charts for the Lognormal Distribution with Estimated Parameters

Control charts, one of the powerful tools in statistical process control (SPC), are widely used to monitor and detect out-of-control processes in the manufacturing industry. Many researchers have pointed out the effects of using estimated parameters on the average run length (ARL) performance metric. Most of the previous literature has studied the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL) to evaluate the performance of control charts. In this article, we study the performance of three S control charts, the Shewhart S-chart, the median absolute deviation (MAD) control chart, and the lognormal S control chart, for a lognormal distribution in terms of the AARL and SDARL. Simulation results indicate the sample size to reach the specified in-control ARL value is very large. The lognormal S control chart has a smaller SDARL value than the other two S-charts