Gradient analysis of Markov-type control schemes and its applications

Abstract

This paper presents formulas for gradients of the Average Run Length (ARL) and other Run Length characteristics by control scheme parameters, in the context of Markov Chain approach to analysis of Markov-type control schemes. We illustrate use of these formulas in several problems related to control charting, including (a) design of control schemes, (b) inference on Run Length characteristics based on Phase-1 data and (c) performance analysis for highly complex input data distributions.

KEYWORDS:

• Average run length
• Detection
• Monitoring
• Statistical process control

Acknowledgments

I am grateful to the Editors and the Referees, whose work helped to improve substantially the quality of this article.