Quantile-based control charts for poisson and gamma distributed data

Abstract

In terms of statistical process control (SPC), the probability distributions of the quality characteristics are critical in detecting changes in the process and product quality in manufacturing processes. Non-normally distributed output variables explained by input variables are common in real industries. The observation-based Shewhart control chart as well as the deviance residual-based Shewhart control chart has been applied to monitor the process mean of Poisson and Gamma distributed output variables explained by input variables. However, the observation-based quantile control charts have not been considered for them. Therefore, we propose the observation-based quantile control charts to monitor the process mean of Poisson and Gamma distributed output variables explained by input variables. Most significantly, with the simulation study and the semiconductor real example, we verify that the proposed observation-based adaptive quantile control chart outperforms the existing control charts for the non-homogeous process in terms of the out-of-control average run length for the detection of process mean shifts.