The Revisedm-of-kRuns Rule Based on Median Run Length

Chun Kit Low · Michael B. C. Khoo · Wei Lin Teoh · Zhang Wu

30 citations0/0 files storedCommunications in Statistics - Simulation and Computation

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

Runs rules are used to increase the sensitivity of the Shewhart control chart in detecting small and moderate process mean shifts. Most of the charts incorporating runs rules are designed based on the average run length (ARL). It is known that the shape of the run length distribution changes according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control to approximately symmetric when the shift is large. Since the shape of the run length distribution changes with the magnitude of the shift in the mean, the median run length (MRL) provides a more meaningful explanation about the in-control and out-of-control performances of a control chart. In this article, we propose the design of the revised m-of-k runs rule based on MRL. In addition, the standard deviation of the run length (SDRL) of the revised m-of-k rule will also be studied. The revised m-of-k runs rule, suggested by Antzoulakos and Rakitzis (2008 Antzoulakos , D. L. , Rakitzis , C. A. ( 2008 ). The revised m-of-k runs rule . Quality Engineering 20 ( 1 ): 175 – 81 . [Google Scholar]), was originally designed based on ARL. The Markov chain technique is employed to obtain the MRLs. Compared with the standard chart, the MRL results show that the revised rules give better performances for small and moderate mean shifts, while maintaining the same sensitivity towards large mean shifts. The MRL results are in accordance with the results obtained by Antzoulakos and Rakitzis (2008 Antzoulakos , D. L. , Rakitzis , C. A. ( 2008 ). The revised m-of-k runs rule . Quality Engineering 20 ( 1 ): 175 – 81 . [Google Scholar]), where the rules are designed based on ARL.

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References

1992Introduction to Statistical Quality Control 1972An Approach to the Probability Distribution of Cusum Run Length 1959Control Charts and Stochastic Processes 1992Statistical Quality Design and Control: Contemporary Concepts and Methods 1993Statistical Quality Design and Control 2000Two Alternatives to the ShewhartXControl Chart 2007Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules 1983The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables

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2015A Study on EWMA charts with runs rules—the Markov chain approach 2016Optimal designs of multivariate synthetic |S| control chart based on median run length 2013Optimal Designs of the Median Run Length Based Double Sampling X Chart for Minimizing the Average Sample Size 2015On the Performance of Shewhart-type Synthetic and Runs-rules Charts Combined with an X¯ Chart 2020Optimal designs of the exponentially weighted moving average (EWMA) median chart for known and estimated parameters based on median run length

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