Continuous Markovian Model for Unexpected Shift in SPC

Various process models for discrete manufacturing systems (parts industry) can be treated as bounded discrete-space Markov chains, completely characterized by the original in-control state and a transition matrix for shifts to an out-of-control state. The present work extends these models by using a continuous-state Markov chain, incorporating non-random corrective actions. These actions are to be realized according to the statistical process control (SPC) technique and should substantially affect the model. The developed stochastic model yields Laplace distribution of a process mean. Real-data tests confirm its applicability for the parts industry and show that the distribution parameter is mainly controlled by the SPC sample size.