Steady-State Run Length Analysis of a Shewhart Quality Control Chart With Supplementary Runs Rules

Champ and Woodall (1987) introduced a technique for analyzing the run length distribution of a Shewhart control chart with supplementary runs rules. For charting procedures that can be represented as a Markov chain, Crosier (1986) suggested a technique for obtaining the cyclic steady-state distribution. We combine these two techniques to analyze the cyclic steady-state run length distribution of a Shewhart quality control chart supplemented with runs rules. Steady-state average run lengths are calculated and compared with those of the exponentially weighted moving average and cumulative sum charts. Some closed form expressions are given.