On Designing the Phase II Bayesian CUSUM Control Charts for Monitoring the Process Mean Under Guaranteed In‐Control Performance

ABSTRACT Bayesian control charts have received much attention in statistical process control. In this paper, two types of Phase II CUSUM charts based on the predictive distribution, namely the predictive ratio CUSUM (PRC) chart and the simplified PRC (SPRC) chart, are constructed for detecting small and moderate shifts in the normal process mean under the guaranteed in‐control performance (GICP) design. Two cases are considered: Case I with an unknown mean and known standard deviation, and Case II with both unknown mean and standard deviation. Extensive simulation studies show that the proposed PRC and SPRC charts offer advantages over their frequentist counterparts when the Phase I reference sample is small or when prior information is available. Finally, a real example is provided to illustrate the applicability and effectiveness of the proposed charts.