The Principle of Mathematical Induction Applied to the Generalized Model for the Economic Design of X-Control Charts

DOI: 10.4236/ojapps.2012.24035   PDF   HTML     4,565 Downloads   8,687 Views   Citations


Rahim and Banerjee [1] developed a general model for the optimal design of x-control charts. The model minimizes the expected cost per unit time. The heart of the model is a theorem that derives the expected total cost and the expected cycle length. In this paper an alternative simple proof for the theorem is provided based on mathematical induction.

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M. Seliaman and S. Duffuaa, "The Principle of Mathematical Induction Applied to the Generalized Model for the Economic Design of X-Control Charts," Open Journal of Applied Sciences, Vol. 2 No. 4, 2012, pp. 236-240. doi: 10.4236/ojapps.2012.24035.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. A. Rahim and P. K. Banerjee, “A Generalized Model for the Economic Design of -Control Charts for Production Systems with Increasing Failure Rate and Early Replacement,” Naval Research Logistics, Vol. 40, No. 6, 1993, pp. 787-809. doi:10.1002/1520-6750(199310)40:6<787::AID-NAV3220400605>3.0.CO;2-4
[2] D. C. Montgomery, “The Economic Design of Control Charts: A Review and Literature Survey,” Journal of Quality Technology, Vol. 12, No. 2, 1980, pp. 75-87.
[3] D. Patel, “Economic Design of Control Chart,” B. Tech Thesis, National Institute of Technology, Rourkela, 2009.
[4] R.-C. Wang and C.-H. Chen, “Economic Statistical NpControl Chart Designs Based on Fuzzy Optimization,” International Journal of Quality & Reliability Management, Vol. 12, No. 1, 1995, pp. 82-92. doi:10.1108/02656719510076276
[5] Y.-S. Chen and Y.-M. Yang, “An Extension of Banerjee and Rahim’s Model for Economic Design of Moving Average Control Chart for a Continuous Flow Process,” European Journal of Operational Research, Vol. 143, No. 3, 2002, pp. 600-610. doi:10.1016/S0377-2217(01)00341-1
[6] I. N. Gibra, “Economically Optimal Determination of the Parameters of X-Control Chart,” Management Science, Vol. 17, No. 9, 1971, pp. 635-646.
[7] E. M. Saniga, “Economic Statistical Control-Chart Designs with an Application to X and R Charts,” Technometrics, Vol. 31, No. 3, 1989, pp. 313-320.
[8] A. J. Duncan, “The Economic Design of -Control Charts Used to Maintain Current Control of a Process,” Journal of the American Statistics Association, Vol. 51, 1956, pp. 228-242.
[9] P. K. Banerjee and M. A. Rahim, “Economic Design of -Control Charts under Weibull Shock Models,” Technometrics, Vol. 30, No. 4, 1998, pp. 407-414.

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