Modelling of unexpected shift in SPC

Abstract

Optimal statistical process control (SPC) requires models of both in-control and out-of-control process states. Whereas a normal distribution is the generally accepted model for the in-control state, there is a doubt as to the existence of reliable models for out-of-control cases. Various process models, available in the literature, 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 SPC technique and should substantially affect the model. The developed stochastic model yields a Laplace distribution of a process mean. An alternative approach, based on the Information theory, also results in a Laplace distribution. Real-data tests confirm the applicability of a Laplace distribution for the parts industry and show that the distribution parameter is mainly controlled by the SPC sample size.

Keywords:

• Control charts
• Markov chain
• mixture distribution
• information distance

Acknowledgements

The authors thank Dr P. Grabov, Advanced Logistics Developments Ltd, for his help in creating a database and for constructive and meaningful discussion. The authors also wish to thank Dr. B. Yoskovich, TAAS, who provided the control chart data.