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The geometric CUSUM chart with sampling inspection for monitoring fraction defective

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  • Patrick Bourke

Abstract

The detection of an upward shift in the fraction defective of a repetitive process is considered using the geometric CUSUM. This CUSUM makes use of the information provided by the run-lengths of non-defective items between successive defective items, and was initially developed for the case of 100% inspection. This paper considers the geometric CUSUM under sampling inspection, and emphasizes that the pattern of sampling inspection can be quite haphazard without causing any difficulty for the operation of the CUSUM. Two separate mechanisms for the occurrence of a shift are considered. Methods for evaluating zero-state and steady-state ARL are presented for both 100% inspection and sampling inspection. Parameter choice is also considered, and recommendations made. Comparisons with some np -charts are provided.

Suggested Citation

  • Patrick Bourke, 2001. "The geometric CUSUM chart with sampling inspection for monitoring fraction defective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 951-972.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:8:p:951-972
    DOI: 10.1080/02664760120076643
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    References listed on IDEAS

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    1. Kenneth W. Kemp, 1962. "The Use of Cumulative Sums for Sampling Inspection Schemes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 11(1), pages 16-31, March.
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    Cited by:

    1. Patrick Bourke, 2006. "The RL2 chart versus the np chart for detecting upward shifts in fraction defective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-15.
    2. Patrick Bourke, 2002. "A continuous sampling plan using CUSUMs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(8), pages 1121-1133.
    3. Zhang C. W. & Xie M. & Goh T. N., 2005. "On Cumulative Conforming Type of Control Charts for High Quality Processes Under Sampling Inspection," Stochastics and Quality Control, De Gruyter, vol. 20(2), pages 205-222, January.
    4. Qu, Liang & Wu, Zhang & Khoo, Michael B.C. & Castagliola, Philippe, 2013. "A CUSUM scheme for event monitoring," International Journal of Production Economics, Elsevier, vol. 145(1), pages 268-280.
    5. Fang Yen Yen & Khoo Michael Boon Chong & Lee Ming Ha, 2013. "Synthetic-Type Control Charts for Time-Between-Events Monitoring," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-13, June.
    6. Wu, Zhang & Luo, Hua & Zhang, Xiaolan, 2006. "Optimal np control chart with curtailment," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1723-1741, November.

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