Analysis of CUSUM and Other Markov-type Control Schemes by Using Empirical Distributions

Abstract

The run-length distribution of a cumulative sum control scheme, when the underlying distribution of the incoming observations is unknown, is discussed. Given a sample of size n from this distribution, the estimators related to various characteristics of the run length can be obtained by using the empirical cdf instead of the true cdf in the standard analysis procedure. The article discusses the properties of the resulting point estimators, as well as interval estimators obtained by using resampling techniques. Applications of the technique for the purpose of design and analysis of control schemes are also discussed. The proposed methodology can be easily adapted for other Markov-type control schemes.

KEY WORDS:

• Control charts
• Markov chains
• Resampling techniques
• Run length