Conditional Monte Carlo Gradient Estimation in Economic Design of Control Limits

Abstract

The economic approach to determining the optimal control limits of control charts requires estimating the gradient of the expected cost function. Simulation is a very general methodology for estimating the expected costs, but for estimating the gradient, straightforward finite difference estimators can be inefficient. We demonstrate an alternative approach based on smoothed perturbation analysis (SPA), also known as conditional Monte Carlo. Numerical results and consequent design insights are obtained in determining the optimal control limits for exponentially weighted moving average and Bayes charts. The results indicate that the SPA gradient estimators can be significantly more efficient than finite difference estimators, and that a simulation approach using these estimators provides a viable alternative to other numerical solution techniques for the economic design problem.