A Double Sampling Scheme for Process Mean Monitoring

Abstract

Mean control charts are effective tools for detecting mean shifts of an interesting quality variable in both manufacturing processes and service processes. Much of the data in service industries come from processes exhibiting non-normal or unknown distributions. The commonly used Shewhart mean control charts, which depend heavily on the normality assumption, are not appropriately used here. This paper thus proposes an asymmetric EWMA mean chart with a double sampling scheme (DS EWMA-AM chart) for monitoring mean shifts of a process with variables data. Furthermore, we explore the sampling properties of the new mean monitoring statistics, and investigate the out-of-control detection performance of the proposed DS EWMA-AM chart using average run lengths. The detection performance of the DS EWMA-AM chart and that of the single sampling EWMA mean (SS EWMA-AM) chart are then compared, with the former showing superior out-of-control detection performance versus the latter. We also compare the out-of-control mean detection performance of the proposed chart with those of non-parametric mean control charts, like the likelihood ratio-based distribution-free NLE, CWE, SS EWMA-AM, the SL, the SU, and the VSS and double sampling and variable sampling interval $\overline X $ control charts by considering cases in which the critical quality characteristic presents normal, double exponential, uniform, chi-square, and exponential distributions, respectively. Comparison results show that the proposed control chart always outperforms the existing mean control charts. We hence recommend employing the DS EWMA-AM chart. A numerical example of a service system for a bank branch in Taiwan is used to illustrate the application of the proposed mean control chart. Finally, we give a discussion for future study.

Keywords

• Average run length
• control chart
• free-distribution
• process mean