Design of Adaptive Control Charts for Monitoring Poisson Data Using Covariate Information and Regression Adjustment

ABSTRACT Adaptive control charts, widely used in manufacturing or nonmanufacturing fields where the quality characteristic of a process or product follows a Poisson distribution, were often directly designed based on the Poisson distribution, while ignoring other helpful information (such as environmental factors) in the process. Due to the impact of many unavoidable and objective factors on the final result, in addition, the in‐control mean value of the Poisson process may not be constant in the actual situation (such as the content of chemical components in the blood of healthy individuals). To this end, this work makes use of covariate information and regression adjustment to develop an adaptive control chart for monitoring Poisson data based on a Poisson regression model. This work first designs three time‐varying smoothing parameters using covariate information and studies the performances of the proposed charts with three time‐varying smoothing parameters from the perspective of known parameters. In practice, however, the parameters are unknown. Hence, the impact of the in‐control data size on the performance of the proposed charts is studied when the parameters are unknown. Next, the out‐of‐control performance of the proposed chart is compared with that of other existing charts using the metric of average run length. The results show that the proposed chart performs the best. Finally, the implementation of the proposed chart is illustrated by a real example.