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 in practice, needs derive decision limit threshold that will guarantee preset false alarm tolerance, very difficult task when parameters are unknown and their estimate sequentially updated. Utilizing Bayesian framework PRC, we provide theoretic allow decision-making threshold, based on which along PRC closed-form monitoring scheme permit its straightforward application real-life practice. An enhancement simulation study evaluates robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, binomial) illustrate implementation Technical details, algorithms, R-codes reproducing illustrations provided as supplementary material.