Design and properties of the predictive ratio cusum (PRC) control charts

In statistical process control/monitoring (SPC/M), memory-based control charts aim to detect small/medium persistent parameter shifts. When a phase I calibration is not feasible, self-starting methods have been proposed, with the predictive ratio cusum (PRC) being one of them. To apply such methods in practice, one needs to derive the decision limit threshold that will guarantee a preset false alarm tolerance, a very difficult task when the process parameters are unknown and their estimate is sequentially updated. Utilizing the Bayesian framework in PRC, we will provide the theoretic framework that will allow to derive a decision-making threshold, based on false alarm tolerance, which along with the PRC closed-form monitoring scheme will permit its straightforward application in real-life practice. An enhancement of PRC is proposed, and a simulation study evaluates its robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, and binomial) illustrate its implementation in practice. Technical details, algorithms, and R-codes reproducing the illustrations are provided as supplementary material.