On monitoring of linear profiles using Bayesian methods

• Bayesian methods show superiority in performance over classical methods.
• Conjugate priors are better than non-conjugate priors.
• Change of scale improves the performance of control charts for errors variance.
• Proposed scheme is efficient to detect small shifts.
• Proposed scheme is also superior to Roberts (1966) scheme.

In many industrial applications, the quality of a process or product is distinctly illustrated by a linear profile. Mostly, a linear profile is shaped or modeled through the usage of linear regression model. Classical and Bayesian set-ups are two possible ways of defining the design structure of a linear profile. This study proposes a fresh Bayesian approach by using different priors for monitoring the linear profiles of processes. In this research we constructed three novel univariate Bayesian EWMA control charts for the Y-intercepts, the slopes and the errors variance under phase II methods by using non-conjugate and conjugate priors. These control charts are used to monitor the Y-intercepts, the slope coefficients and increase in process standard deviations, respectively. This study confirmed that the Bayesian methods distinguish sustainable shifts in the process parameters superior than the competing methods. Moreover, the Bayesian control charting structures with conjugate priors provide better performance for monitoring the Y-intercepts and slopes than the one of non-conjugate priors, while both priors perform almost equivalently in case of errors variance. The individual and overall performance of control charts are evaluated by using (i.e., ARL, SDRL, and MDRL) and (i.e., EQL, RARL, and PCI), respectively. The practical example is considered as an illustration to justify the supremacy of proposed approach and recommendations are given for future perspective.