ARL-Design of S Charts with k-of-k Runs Rules

Abstract

The standard S chart signals an out-of-control condition when one point exceeds a control limit. It can be augmented with runs rules to improve its performance in detecting assignable causes. A commonly used rule signals when k consecutive points exceed a control limit. This rule can be used alone or to supplement the standard chart. In this article we derive ARL expressions for charts with the k-of-k runs rule. We show how to design S charts with this runs rule, compare their ARL performance, and make a control chart recommendation when it is important to monitor for both increases and decreases in process dispersion.

Keywords:

• Average run length
• Markov chain
• Runs rules
• Warning limit

Mathematics Subject Classification:

• 62P30
• 90C90

Acknowledgment

The work of César A. Acosta-Mejía is supported by the Asociación Mexicana de Cultura.