Designs of control charts with supplementary runs rules

Authors:
Sheng Zhang;Zhang Wu
Affiliations:
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore 639798;School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore 639798
Venue:
Computers and Industrial Engineering
Year:
2005

Citing 2
Cited 1

Exact results for shewhart control charts with supplementary runs rules

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Abstract

This article studies the designs of the control charts with the supplementary runs rules (zone rules). It also investigates, compares and ranks 15 resultant control charts based on steady-state Average Run Length (ARL) that is evaluated by computer simulation. The in-control ARL"0 values of the charts are made equal to the users' specified value. Numerous insights and new findings have been discovered, including: (1) The optimization technique can considerably improve the performance of the control charts with runs rules; (2) Some combinations of runs rules that exclude the basic Shewhart X@? chart have excellent performance, especially when sample size is small; (3) The relative effectiveness (ranking) of the charts is significantly influenced by the sample size and the required in-control ARL"0, and incorporating the X@? chart with runs rules is effective only when the sample size is small; (4) The steady-state ARL of the charts with runs rules differs from the conventional zero-state ARL to some degree. Finally, the proposed design algorithm and the results of some studies provide the quality practitioners with a systematic approach to design the control charts with runs rules and to predict their performance in a production setting.