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Economic statistical design of x ¥ control charts for systems with gamma ( 5 ,2) in-control times

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  • Hajaj Al-Oraini
  • M. A. Rahim

Abstract

In this paper, gamma ( 5 ,2) distribution is considered as a failure model for the economic statistical design of x ¥ control charts. The study shows that the statistical performance of control charts can be improved significantly, with only a slight increase in the cost, by adding constraints to the optimization problem. The use of an economic statistical design instead of an economic design results in control charts that may be less expensive to implement, that have lower false alarm rates, and that have a higher probability of detecting process shifts. Numerical examples are presented to support this proposition. The results of economic statistical design are compared with those of a pure economic design. The effects of adding constraints for statistical performance measures, such as Type I error rate and the power of the chart, are extensively investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:4:p:397-409
    DOI: 10.1080/0266476032000035430
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    References listed on IDEAS

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    1. Prabhu, Sharad S. & Montgomery, Douglas C. & Runger, George C., 1997. "Economic-statistical design of an adaptive chart," International Journal of Production Economics, Elsevier, vol. 49(1), pages 1-15, March.
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    Cited by:

    1. Ching-Hsin Wang & Feng-Chia Li, 2020. "Economic design under gamma shock model of the control chart for sustainable operations," Annals of Operations Research, Springer, vol. 290(1), pages 169-190, July.
    2. 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.
    3. 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.
    4. 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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