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Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time

Author

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  • F L Chen

    (National Tsing Hua University)

  • C H Yeh

    (National Tsing Hua University)

Abstract

This paper proposes an approach which simultaneously considers the properties of cost and quality based on the Burr distribution to determine three parameters (including sample size, sampling interval between successive samples, and the control limits) when an x-bar chart monitors a manufacturing process with Weibull failure characteristic and non-normal data. Also, the cost model of Banerjee and Rahim (1988) is used as the objective function, and the probability density function of the Burr distribution is applied to derive the statistical constraints of economic statistical design of the x-bar control charts for non-normal data. The example of Banerjee and Rahim (1988) is adopted to indicate the solution procedure and sensitivity analyses. Meanwhile, the design parameters of the x-bar control charts can be obtained through the grid search method. The results show that an increase of skewness coefficient (α3) results in a slight decrease for sample size (n), but is robust to the control limit width (L). Also, an increase of kurtosis coefficient (α4) leads to a wider control limit width.

Suggested Citation

  • F L Chen & C H Yeh, 2011. "Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 750-759, April.
    • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:4:d:10.1057_jors.2010.36
    DOI: 10.1057/jors.2010.36
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    References listed on IDEAS

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    1. Hajaj Al-Oraini & M. A. Rahim, 2003. "Economic statistical design of x ¥ control charts for systems with gamma ( 5 ,2) in-control times," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(4), pages 397-409.
    2. Chen, Huifen & Cheng, Yuyen, 2007. "Non-normality effects on the economic-statistical design of charts with Weibull in-control time," European Journal of Operational Research, Elsevier, vol. 176(2), pages 986-998, January.
    3. M. A. Rahim & P. K. Banerjee, 1993. "A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 787-809, October.
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    Cited by:

    1. Wook-Yeon Hwang, 2016. "Cluster-based artificial contrasts for inhomogeneously distributed data with an indicator variable," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5045-5055, September.
    2. 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.
    3. M. A. Pasha & M. Bameni Moghadam & M. A. Rahim, 2020. "Effects of non-normal quality data on the integrated model of imperfect maintenance, early replacement, and economic design of $${\bar{X}}$$ X ¯ -control charts," Operational Research, Springer, vol. 20(4), pages 2519-2536, December.

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