The application of proportional hazards and frailty models to multistage processes surveillance

Monitoring industrial and service processes with the purpose of improving the product reliability has been largely addressed in the literature. The surveillance procedures have been proposed with the concentration on single-stage processes with independent quality characteristics. However, the cascade property in multistage processes entails specific monitoring methods which take into account the dependency structure among quality variables in successive stages of a process. This is referred to as regression-adjustment that justifies the heterogeneity in the study population and thus leads to optimal monitoring of multistage processes. In general, it is not straightforward to adjust a quality variable for the effect of all influential covariates because measuring such covariates requires great financial cost and time effort or possibly one may have no prior information about such values. However, ignoring such covariates introduces unobserved heterogeneity which diminishes the detection power of a monitoring scheme. Moreover, the existence of a censoring mechanism results in having more complicated picture due to the inaccurate recording of some data. As a result, the proportional hazards and the frailty models are used to effectively account for both the observed and unobserved heterogeneity. Several monitoring procedures are devised which enable to justify the censoring issue as well. The comparison of the procedures reveals that the cumulative sum (CUSUM) control chart outweighs the competing counterparts.