A Comparison Study on Effectiveness and Robustness of Control Charts for Monitoring Process Mean and Variance

摘要

This article compares the effectiveness and robustness of nine typical control charts for monitoring both process mean and variance, including the most effective optimal and adaptive sequential probability ratio test (SPRT) charts. The nine charts are categorized into three types (the X type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and adaptive version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and adaptive charts are designed optimally in order to minimize an index average extra quadratic loss for the best overall performance. Moreover, the probability distributions of the mean shift δ_μ and standard deviation shift δ_σ are studied explicitly as the influential factors in a factorial experiment. The main findings obtained in this study include: (1) From an overall viewpoint, the SPRT-type chart is more effective than the CUSUM-type chart and X-type chart by 15 and 73%, respectively; (2) in general, the adaptive chart outperforms the optimal chart and basic chart by 16 and 97%, respectively; (3) the optimal CUSUM chart is the most effective fixed sample size and sampling interval chart and the optimal SPRT chart is the best choice among the adaptive charts; and (4) the optimal sample sizes of both the X charts and the CUSUM charts are always equal to one. Furthermore, this article provides several design tables which contain the optimal parameter values and performance indices of 54 charts under different specifications.