Comparisons of some memory‐type control chart for monitoring Weibull‐distributed time between events and some new results

Abstract

AbstractMonitoring Weibull time between event (TBE) processes is essential to avoid deterioration of quality characteristics in various reliability analysis problems. Statistical process monitoring (SPM) charts are widely used to monitor the possible decreasing mean shift. For monitoring such data, many control charts have been proposed in the literature, such as the Weibull exponentially weighted moving average (EWMA) chart, the Weibull cumulative sum (CUSUM) chart, and Mixed EWMA–CUSUM (MEC) chart and Mixed Hybrid EWMA–CUSUM (MHEC) chart. The current investigation revisits their efficacy and compares them with a CUSUM chart based on the generally weighted moving average (GWMA) statistic, labelled as the Mixed GWMA–CUSUM (MGC) chart, to monitor the decreasing mean shift in Weibull TBEs processes. We offer some numerical results based on the Monte‐Carlo simulation, such as average run length (ARL), the standard deviation of the run length (SDRL) and the relative mean index (RMI). Our findings show that the MGC chart often outperforms the existing control charts in detecting small downward shifts. Finally, an illustrative example is given to display the application of the MGC chart for Weibulll data.