Two Sets of Runs Rules for the Chart

ABSTRACT

To increase the performance for detecting small shifts, control charts are used with runs rules. The Western Electrical Handbook (1956) suggests runs rules to be used with the Shewhart chart. In this article, we review the performance of two sets of runs rules. The rules of one set signal if k succesive points fall beyond a limit. The rules of the other set signal if k out of k + 1 consecutive points fall beyond a different limit. We suggest runs rules from these sets. They are intended to be used with a modified Shewhart chart, a chart with 3.3 σ limits. We find that for small shifts all suggested charts have improved performance than the Shewhart chart. For large shifts they have comparable performance.

KEYWORDS:

• average run length
• control limit
• Markov chain
• runs rules
• warning limit