Steady state analysis of three process monitoring procedures in quality control.

摘要

Control charts are a popular tool in statistical quality control and are used to maintain current control of industrial manufacturing processes. In this dissertation, the economic behavior of three control policies--the X-bar chart, the exponentially weighted moving average (EWMA) chart, and the Bayes' procedure--is analyzed. In controlling a process that tends to shift from an in-control state into an out-of-control state, every control policy is faced with a trade-off between providing too many false alarms and allowing an out-of-control state to go undetected for too long. It is shown that for a broad class of control policies, the continuous operation of a policy can be characterized by an ergodic Markov process. The steady state distribution of the characterizing Markov process is shown to be sufficient for determining the expected cost per unit time incurred by the policy under a linear cost function. The process failure mechanism is explicitly incorporated into the study distinguishing it from many of the conditional analyses available in the statistical quality control literature.; A complete analysis is provided for the X-bar chart. A method for obtaining optimal chart parameters is also developed. The steady state distributions for the EWMA chart and the Bayes' procedure are obtained through simulation. It is seen that the Bayes' procedure is uniformly better than the other two control charts. The sensitivity of the performance of the various charts to the parameters of the manufacturing process is examined. Some salient features of the analysis are: (a) it makes minimal assumptions, (b) it is computationally intensive, and (c) the resulting tools have a high visual appeal.; It is hoped that the results of this study will significantly aid in the economic design of control charts. This work also creates a framework for comparing other types of control charts using a steady state economic approach.