A side-sensitive group runs median control chart with measurement errors

Abstract

The Shewhart median (denoted as ) chart can be used in place of the Shewhart chart for detecting mean shifts when outliers are present because the sample mean is easily affected by outliers. However, the Shewhart median chart is slow in detecting small and moderate mean shifts. In this study, the side-sensitive group runs median (called SSGR ) chart is proposed to enhance the speed of the Shewhart median chart in detecting small and moderate mean shifts. Additionally, by adopting a linear covariate error model, the effect of measurement errors on the performance of the SSGR chart is studied. The average run length (ARL) and standard deviation of the run length (SDRL) criteria are used as performance measures, for cases with and without measurement error. The Markov chain method is used to compute the ARL and SDRL values of the SSGR and competing charts. Performance analyses show that the SSGR chart surpasses the synthetic chart for detecting all shift sizes but for detecting small shifts, the exponentially weighted moving average (EWMA) chart performs better than the SSGR chart. Finally, the application of the SSGR chart is described with an example.