Bayesian Monitoring of Linear Profiles Using DEWMA Control Structures With Random $X$

Abstract

The process structures of manufacturing industry are efficiently modeled using linear profiles. Classical and Bayesian set-ups are two well-appreciated schemes for designing control charts for the monitoring of process structures. Mostly in profiles monitoring the independent variables along with the process parameters are assumed fixed. There are manufacturing processes where these conditions may not hold. The advancement in technology and day-to-day changes in process structures caused the parametric uncertainty along with variability in explanatory variables. This paper considered the case of random $X$ and assumes different conjugate and non-conjugate priors to handle parametric uncertainty using double exponentially weighted moving average (DEWMA) control charts. Three univariate DEWMA charts are designed for the monitoring of $Y$ -intercepts, slopes, and error variances. The average run length criterion has been used to evaluate the proposed and competing charts. The wide spread relative study identifies that the proposed Bayesian DEWMA control charts are better than the competing charts based on early detection of out-of-control profiles, particularly for smaller value shifts. The Bayesian DEWMA charts using conjugate priors are the quickest in all as they take less sample points to show out-of-control profile. A case study has been considered to further justify the superiority of Bayesian DEWMA charts over competing charts.