Phase II monitoring of linear profiles with random explanatory variable under Bayesian framework

Linear profiles monitoring have been successfully implemented in many industrial applications. The design structures of control charts for profiles monitoring are mostly based on two major classifications namely Classical and Bayesian. This study investigates the novel Bayesian exponentially weighted moving average and multivariate exponentially weighted moving average control charts for the monitoring of linear profiles, when explanatory variable(s) are random. The informative priors of normal and inverse gamma; and Bramwell, Holdsworth, Pinton (BHP) and Levy distributions are considered as conjugate and non-conjugate priors respectively. The proposed Bayesian schemes are evaluated using different run length characteristics. The schemes are also validated with simulation study and real-world data sets. The outcomes demonstrate that the Bayesian methods perform effectively better than the competing methods. The specified values of hyper-parameters are selected carefully after elicitation and sensitivity analysis of hyper-parameters. It has been observed that careful consideration is required while selecting the priors and possible values of hyper-parameters. The selection of appropriate priors and corresponding hyper-parameters comes up with efficient control structures which provide tangible benefits.