Application of Perturbation Analysis to the Design and Analysis of Control Charts

Abstract

The design of control charts in statistical quality control addresses the optimal selection of the design parameters such as the sampling frequency and the control limits; and includes sensitivity analysis with respect to system parameters such as the various process parameters and the economic costs of sampling. The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, particularly in the evaluation of performance measures such as average run length. In this paper, we apply perturbation analysis to derive gradient estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the technique on a simple Shewhart control chart and on a more complicated control chart that includes the exponentially- weighted moving average control chart as a special case.