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Control charts for the coefficient of variation

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Abstract

The coefficient of variation (CV) has received an extensive attention in quality control. The existing control charts for monitoring the two-sided changes in the CV do not consider the average run length (ARL) unbiased criterion. In practice, the practitioners prefer the ARL-unbiased control charts. This paper proposes an ARL-unbiased Shewhart-type control chart to monitor the two-sided shifts in the CV. Then an ARL-unbiased synthetic chart in which the conforming run length sub-chart only needs a lower control limit is proposed to improve the performance of the ARL-unbiased Shewhart-type chart. The comparison results show that the proposed synthetic chart outperforms the proposed ARL-unbiased control chart in terms of the ARL. The effects of the parameter estimation on the proposed charts are also studied. Finally, a real example is used to illustrate the proposed control charts.

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Acknowledgments

The authors thank the Editor, the Associate Editor and the reviewers for their detailed comments and suggestions, which considerably helped improve the manuscript. The work of Guo is sponsored by the National Social Science Foundation of China (Grant No. 14BTJ030). The work of Wang is supported by the National Natural Science Foundation of China (Grant No. 11371322), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY16G020003), Foundation of Ministry of Education of China (Grant No. 13YJC910005, 13YJC910010), Philosophy and Social Science Research Project in Zhejiang Province of China (Grant No. 13NDJC055YB), National Statistical Research Plan Project (Grant No. 2015LZ50) and Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics).

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  1. School of Statistics, Zhejiang Gongshang University, Hangzhou, People’s Republic of China

    Baocai Guo & Bing Xing Wang

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  1. Baocai Guo
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  2. Bing Xing Wang
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Correspondence to Bing Xing Wang.

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Guo, B., Wang, B.X. Control charts for the coefficient of variation. Stat Papers 59, 933–955 (2018). https://doi.org/10.1007/s00362-016-0797-0

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  • DOI: https://doi.org/10.1007/s00362-016-0797-0

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