The Revised m-of-k Runs Rule

ABSTRACT

Sensitizing rules based on runs and scans are widely used to increase the sensitivity of the classical Shewhart control chart in detecting small process shifts. The use of these rules frequently results in a substantial reduction of the in-control average run length ARL and/or in a poor performance of the out-of-control average run length for moderate to large process shifts. To overcome these weaknesses, we introduce the revised m-of-k runs rule and we study the average run length performance of the Shewhart control chart supplemented with the revised runs rule. Our extensive numerical experimentation and the comparisons made with other competitive control charts reveal that the revised runs rule demonstrates an improved performance in the detection of small to moderate shifts while maintaining the same superiority for detecting large shifts.

KEYWORDS:

• average run length
• inner control limit
• Markov chain embedding technique
• outer control limit
• runs rule