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Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location

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  • Chenglong Li
  • Amitava Mukherjee
  • Qin Su
  • Min Xie

Abstract

Traditionally, a cost-efficient control chart for monitoring product quality characteristic is designed using prior knowledge regarding the process distribution. In practice, however, the functional form of the underlying process distribution is rarely known a priori. Therefore, the nonparametric (distribution-free) charts have gained more attention in the recent years. These nonparametric schemes are statistically designed either with a fixed in-control average run length or a fixed false alarm rate. Robust and cost-efficient designs of nonparametric control charts especially when the true process location parameter is unknown are not adequately addressed in literature. For this purpose, we develop an economically designed nonparametric control chart for monitoring unknown location parameter. This work is based on the Wilcoxon rank sum (hereafter WRS) statistic. Some exact and approximate procedures for evaluation of the optimal design parameters are extensively discussed. Simulation results show that overall performance of the exact procedure based on bootstrapping is highly encouraging and robust for various continuous distributions. An approximate and simplified procedure may be used in some situations. We offer some illustration and concluding remarks.

Suggested Citation

  • Chenglong Li & Amitava Mukherjee & Qin Su & Min Xie, 2016. "Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7259-7273, December.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:24:p:7259-7273
    DOI: 10.1080/00207543.2016.1173254
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    References listed on IDEAS

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    1. Giovanna Capizzi & Guido Masarotto, 2009. "Bootstrap-based design of residual control charts," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 275-286.
    2. Changsoon Park, 2013. "Economic design of charts when signals may be misclassified and the bounded reset chart," IISE Transactions, Taylor & Francis Journals, vol. 45(4), pages 436-448.
    3. Teyarachakul, Sunantha & Chand, Suresh & Tang, Jen, 2007. "Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap," European Journal of Operational Research, Elsevier, vol. 178(2), pages 472-481, April.
    4. Franco, Bruno Chaves & Celano, Giovanni & Castagliola, Philippe & Costa, Antonio Fernando Branco, 2014. "Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies," International Journal of Production Economics, Elsevier, vol. 151(C), pages 121-130.
    5. Nenes, George, 2011. "A new approach for the economic design of fully adaptive control charts," International Journal of Production Economics, Elsevier, vol. 131(2), pages 631-642, June.
    6. Lee, Pei-Hsi & Torng, Chau-Chen & Liao, Li-Fang, 2012. "An economic design of combined double sampling and variable sampling interval X¯ control chart," International Journal of Production Economics, Elsevier, vol. 138(1), pages 102-106.
    7. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2539-2561.
    8. Jun Li & Xin Zhang & Daniel R. Jeske, 2013. "Nonparametric multivariate CUSUM control charts for location and scale changes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 1-20, March.
    9. Amitava Mukherjee & Rudra Sen, 2015. "Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes," International Journal of Production Research, Taylor & Francis Journals, vol. 53(14), pages 4414-4445, July.
    10. Qiu, Peihua & Li, Zhonghua, 2011. "Distribution-free monitoring of univariate processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1833-1840.
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    Cited by:

    1. Reza Pourtaheri, 2022. "Economic Statistical Design for Three-level Control Charts with Variable Sample Size," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 130-145, May.

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