Simulating the average run length for cusum schemes using variance reduction techniques

Abstract

Some variance reduction techniques utilizing the total hazard are developed to estimate the average run lengths of the cumulative sum charts through simulation when the process follows a general probability distribution. Particularly, we propose the hazard estimator and the cycle estimator. Simulation results are shown for the exponential case and these estimators are compared with the raw simulation estimator. Applicability to multivariate CUSUM schemes is briefly discussed in the conclusion.

Keywords:

• cumulative sum
• average run length
• simulation
• total hazard
• control variate
• bootstrap method
• multivariate CUSUM