Using frailty models to account for heterogeneity in multistage manufacturing and service processes

Statistical process control has been widely applied to manufacturing and service operations with the aim of monitoring and improving the reliability of products. The existing monitoring procedures were introduced following the assumption that a single-stage process with independent quality characteristic is under consideration. However, in multistage processes with dependent variables, quality characteristics of interest should be optimally monitored only after they have been adjusted for the effect of influential covariates. In general, it is impossible to include all relevant covariates because measuring such values entails great financial costs. The neglect of such covariates results in having unobserved heterogeneity which dampens the detection ability of the monitoring procedure. The more complicated picture arises when the values corresponding to the reliability-related quality variable are censored due to the time and cost constraints. Thus, to deal with the effect of observed and unobserved covariates together with the censoring issue, the frailty and the proportional hazard models are used and some model-based monitoring schemes are devised. The surveillance procedures are proposed in both the presence and absence of a censoring mechanism. The performance analysis shows that the monitoring procedure based on the cumulative sum chart is superior in detecting shifts while the exponentially weighted moving average chart is effective in some cases. Copyright Springer Science+Business Media Dordrecht 2014