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Probability distribution of CUSUM charting statistics
Wenpo Huang1; Lianjie Shu2; Junjie Cao3; Kwok-Leung Tsui3
2016-04-02
Source PublicationIIE Transactions (Institute of Industrial Engineers)
ISSN15458830 0740817X
Volume48Issue:4Pages:324-332
Abstract

In parallel to the conventional study of the distribution of the first time to signal, this paper investigates the probability distribution of the article Cumulative Sum (CUSUM) charting statistics based on a recurrence relationship. The probability distribution of the CUSUM statistic can not only provide statistical significance of observations against the null hypothesis of being in control but also facilitate the analysis of the CUSUM chart in the steady-state scenario. Both the conditional case (CUSUM chart without restarting) and the cyclical case (CUSUM chart with restarting) are considered. It is shown that the distribution of CUSUM charts both with and without restarting approaches a stationary distribution, independent of their initial values. We also show that the null steady-state distribution of the unbounded CUSUM chart previously reported in the literature is a special case of this article as the control limit approaches infinity.

KeywordIntegral Equation Run Length Statistical Process Control Steady-state
DOI10.1080/0740817X.2015.1067736
URLView the original
Indexed BySCIE
Language英语
WOS Research AreaEngineering ; Operations Research & Management Science
WOS SubjectEngineering, Industrial ; Operations Research & Management Science
WOS IDWOS:000372450100002
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Document TypeJournal article
CollectionDEPARTMENT OF ACCOUNTING AND INFORMATION MANAGEMENT
Affiliation1.Antai College of Economics and Management,Shanghai Jiao Tong University,,Shanghai,China
2.Faculty of Business Administration,University of Macau,,Macao
3.Department of Systems Engineering and Engineering Management,City University of Hong Kong,,Kowloon Tong,Hong Kong
Recommended Citation
GB/T 7714
Wenpo Huang,Lianjie Shu,Junjie Cao,et al. Probability distribution of CUSUM charting statistics[J]. IIE Transactions (Institute of Industrial Engineers),2016,48(4):324-332.
APA Wenpo Huang,Lianjie Shu,Junjie Cao,&Kwok-Leung Tsui.(2016).Probability distribution of CUSUM charting statistics.IIE Transactions (Institute of Industrial Engineers),48(4),324-332.
MLA Wenpo Huang,et al."Probability distribution of CUSUM charting statistics".IIE Transactions (Institute of Industrial Engineers) 48.4(2016):324-332.
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