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CUSUM from a Bayesian perspective
Andreou, Maria Z.; Athens University of Economics and Business, Department of Statistics; Tsiamyrtzis, Panagiotis
The basic purpose of this thesis is to study the Classic Cumulative Sum method of Statistical Process Control (SPC), from a Bayesian prism. We consider the hypothesis testing problem of two possible models. Model under H0 will be the model of the in control situation and model under H1 will be the model of the out of control situation for a process. We wish to decide whether the model under H1, has been more plausible than the model under 𝐻0, or not. In other words, we want to decide whether a process has gone from an in control to an out of control situation. The CUSUM charting is designed to detect small but persistent shifts of a process’ characteristic as soon as possible, giving the optimal in control Average Run Length for a particular shift. From a Bayesian point of view, we consider the hypothesis testing problem as a decision theory problem, and using Bayes test theorem, we construct the Bayesian CUSUM. Due to the optimality properties of CUSUM (Moustakides (1986)), we aim to prove that the two forms are equivalent, thus, the Bayesian CUSUM we have constructed will be an optimal scheme for detecting a persistent shift in a process’ characteristic.