A double sampling scheme for process variability monitoring

Abstract

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes a standardized asymmetric exponentially weighted moving average (EWMA) variance chart with a double sampling scheme (SDS EWMA-AV chart) for monitoring process variability. We further explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using the proposed SDS EWMA-AV chart. The performance of the SDS EWMA-AV chart and that of the single sampling EWMA variance (SS EWMA-V) chart are then compared, with the former showing superior out-of-control detection performance versus the latter. We also compare the out-of-control variance detection performance of the proposed chart with those of nonparametric variance charts, the nonparametric Mood variance chart (NP-M chart) with runs rules, and the nonparametric likelihood ratio-based distribution-free EWMA (NLE) chart and the combination of traditional EWMA (CEW) and the SS EWMA-V control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi-square, and exponential distributions. Comparison results show that the proposed chart always outperforms the NP-M with runs rules, the NLE, CEW, and the SS EWMA-V control charts. We hence recommend employing the SDS EWMA-AV chart. Finally, a numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed variability control chart. © 2017 John Wiley & Sons, Ltd.