Application of Poisson state-space models and shared frailty models for multistage processes surveillance

Abstract

There are many applications in actual multistage processes with Poisson data. Control charts are an essential tool for monitoring quality variables in multistage processes. On the other hand, it is not straightforward to adjust a quality variable for the effect of all influential covariates, and ignoring latent variables introduces unobserved heterogeneity which diminishes the detection power of a monitoring scheme. Hence, the present paper proposes two monitoring schemes namely, the GEWMA control chart based on a Poisson state-space model and the modified EWMA control chart based on a shared frailty model in which latent variables are considered in Phase II. In this regard, expectation – maximization and Bayesian algorithms are used to estimate the parameters of the proposed models. A comparison between the two proposed control charts demonstrates that the GEWMA control chart based on a Poisson state-space model performs better than the modified EWMA control chart using the frailty model. Then, comprehensive simulation experiments are conducted to evaluate the performance of the proposed GEWMA. The results show that it performs satisfactorily under different shifts in single and multiple stages. Also, this control chart helps well to identify the out-of-control stage. Finally, a real case in health-care related processes is used to appraise the performance of the proposed monitoring scheme in practice.

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