Conditional Monte Carlo Gradient Estimation in Economic Design of Control Limits

A major impediment to practitioner acceptance of the economic design approach to control charts is the complicated nature of the underlying optimization problem even under standard process assumptions. The economic approach to determining the optimal control limits requires estimating the derivatives of performance curves that are typically obtained via simulation. For this gradient estimation problem, finite difference estimators can be very inefficient, so we present an alternative approach based on smoothed perturbation analysis (SPA), also known as conditional Monte Carlo. Numerical results and consequent design insights obtained for the X̄-chart, the EWMA chart and the Bayes chart indicate that the SPA gradient estimators are significantly more efficient than the corresponding finite difference estimators.