Conway-Maxwell-Poisson profile monitoring with rk-Shewhart control chart: a comparative study

Abstract

A control chart is an essential tool in Statistical Quality Control for monitoring the production process. It provides a visual means of identifying process irregularities. In this study, we focus on the Shewhart control chart based on the rk-deviance residuals, namely rk-Shewhart control charts to examine the Conway–Maxwell–Poisson (COM-Poisson) profile, which is used to model the count data with varying degrees of dispersion. The primary goal of this study is to identify the biasing parameter that produces the best result among newly presented biasing parameters developed based on existing ones. It provides a short overview of the COM-Poisson distribution, its modeling, and rk parameter estimation in the case of multicollinearity, as well as the construction of the deviance-residual-based Shewhart chart. To evaluate the performance of the rk-Shewhart, we conduct an analysis using a real-life data set, considering various shift sizes. By employing different biasing parameters, we examine the effectiveness of the rk-Shewhart control chart. The performance evaluation outcomes of the rk-Shewhart charts are compared to the ML-deviance-based Shewhart chart and within themselves based on the biasing parameters. The results demonstrate the advantage of the rk-Shewhart charts over the ML-deviance-based control chart in detecting out-of-control signals. Among the considered biasing parameters, the rk-Shewhart chart utilizing the adjusted biasing parameter k_4 shows the best performance based on the ARL metric.