Efficient design and sensitivity analysis of control charts using Monte Carlo simulation

The design of control charts in statistical quality control addresses the o ptimal selection of the design parameters (such as the sampling frequency a nd the control Limits) and includes sensitivity analysis with respect to sy stem parameters (such as the various process parameters and the economic co sts of sampling). The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, espec ially in the evaluation of performance measures such as average run length. in this paper, we apply two gradient estimation procedures-perturbation an alysis and the Likelihood ratio/score function method-to derive estimators that can be used in gradient-based optimization algorithms and in sensitivi ty analysis when Monte Carlo simulation is employed. We illustrate the tech niques on a general control chart that includes the Shewhart chart and the exponentially-weighted moving average chart as special cases. Simulation ex amples comparing the estimators with each other and with "brute force" fini te differences demonstrate the possibility of significant variance reductio n in settings of practical interest.