Cause-Selecting Charts Based on Proportional Hazards and Binary Frailty Models

Monitoring the reliability of products in both the manufacturing and service processes is of main concern in today’s competitive market. To this end, statistical process control has been widely used to control the reliability-related quality variables. The so-far surveillance schemes have addressed processes with independent quality characteristics. In multistage processes, however, the cascade property must be effectively justified which entails establishing the relationship among quality variables with the purpose of optimal process monitoring. In some cases, measuring the values corresponding to specific covariates is not possible without great financial costs. Subsequently, the unmeasured covariates impose unobserved heterogeneity which decreases the detection power of a control scheme. The complicated picture arises when the presence of a censoring mechanism leads to inaccurate recording of the process response values. Hence, frailty and Cox proportional hazards models are employed and two regression-adjusted monitoring procedures are constructed to effectively account for both the observed and unobserved influential covariates in line with a censoring issue. The simulation-based study reveals that the proposed scheme based on the cumulative sum control chart outperforms its competing procedure with smaller out-of-control average run length values.