Statistical process control based on gamma-frailty models for heterogeneous reliability observations

Abstract

The products are usually the result of the multistage processes in which the outgoing quality characteristics are controlled after the adjustment procedure has been done. However, in many cases, including all covariates is not possible. For instance, the tensile strength of threads is not only affected by the proportion of polyester to wool as the observed covariate, but also by the unobserved covariate called the maturity of fiber. Therefore, the main contribution of this paper is to combine the gamma frailty and accelerated failure time (AFT) models to control the reliability of products in the presence of observed and unobserved covariates. Three monitoring methods are proposed consequently. The results of simulation-based studies show that the CUSUM chart performs better than its competing counterparts. Moreover, the findings clearly reveal that the performance of the existing CUSUM charts in the literature deteriorates. Finally, a real case study has been thoroughly addressed.

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