An algorithm for the properties of the integrated process control with bounded adjustments and EWMA monitoring

Abstract

An integrated process control (IPC) procedure is a scheme which simultaneously applies the engineering process control (EPC) and statistical process control (SPC) techniques to reduce the variation of a process. The EPC is performed by adjusting the process, which will continually wander away from the target by its inherent disturbances. The SPC is implemented by monitoring the process, which will be changed to an undesirable state by special causes. The wandering behaviour of the process is often well-fitted by an IMA(0,1,1) process and the occurrence of a special cause is considered to change the process level. For adjusting, the bounded adjustment scheme is used and for monitoring the EWMA chart is used. The performance of the IPC procedure is evaluated in terms of the expected cost per unit interval (ECU). In designing the IPC procedure for practical use, it is essential to derive its properties constituting the ECU, but no analytical solution has been known yet. As an alternative, an algorithm for calculation of the properties is derived by using a Markov chain approach when the process is in control and a Monte Carlo simulation when out of control.

Keywords:

• Integrated process control
• Expected cost per unit time
• Bivariate Markov chain
• Transition matrix
• Monte Carlo simulation

Acknowledgements

The author would like to thank the editor and the referees for their helpful comments. This work was supported by Korea Research Foundation Grant (KRF-2002-015-CS0005).