¹Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Professor. Email: sindhuqau@gmail.com
²King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: riaz76qau@yahoo.com
³Riphah International University, Department of Basic Sciences, Islamabad, Pakistan. Professor. Email: aslamsdqu@yahoo.com
⁴Institute of Space Technology, Department of Applied Mathematics and Statistics, Islamabad, Pakistan. Professor. Email: zaheerqau77@gmail.com

This study deals with the cumulative charting technique based on a simple and a mixture of Rayleigh models. The respective charting schemes are referred as the SRCQC-chart and the MRCQC-chart. These are stimulated from existing statistical control charts in this direction i.e. the cumulative quantity control (CQC) chart, based on exponential and Weibull models, and the cumulative count control (CCC) chart, based on the simple geometric model. Another motivation for this study is the mixture cumulative count control (MCCC) chart based on the two component geometric model. The use of mixture cumulative quantity is an attractive approach for process monitoring. The design structure of the proposed control chart is derived by using the cumulative distribution function of simple, and two components of mixture distribution(s). We observed that the proposed charting structure is efficient in detecting the changes in process parameters. The application of the proposed scheme is illustrated using a real dataset.

Key words: Quality control, Inverse transformation method, Lossfunctions and bayes estimators, MRCQC-Chart, SRCQC-Char.

Este estudio trata con cartas de control acumuladas basadas en distribuciones Rayleigh y en mixturas de estas mismas. Las cartas se denominan SRCQC y MRCQC, respectivamente. Estas se fundamentan en cartas existentes como la carta de control de cantidades acumuladas (CQC), basada en modelos exponencial y Weibull en la carta de control de conteos acumulados (CCC), soportada en un modelo geométrico. Otra propuesta del estudio es la carta de control de mixtura de conteos acumulados (MCCC). Esta última es muy atractiva en procesos de monitoreo. La estructura de diseño de las cartas propuestas se deriva usando la función de distribución acumulada simple y la mixtura de dos distribuciones acumuladas. Se observa que las cartas propuestas son eficientes para detectar cambios en los parámetros del proceso. La aplicación del esquema propuesto es ilustrada usando un conjunto de datos reales.

Palabras clave: control de calidad, método de la transformación, función de pérdida, estimador bayesiano, carta MRCQC, carta SRCQC.

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References

1. Aslam, M. (2003), 'An application of prior predictive distribution to elicit the prior density', Journal of Statistical Theory and Applications 2(1), 70-83.         [ Links ]

2. Banjevic, D., Jardine, A. K. S., Makis, V. & Ennis, M. (2001), 'A control-limit policy and software for condition-based maintenance', INFOR 39, 32-50.         [ Links ]

3. Calvin, T. (1983), 'Quality control techniques for zero defects', IEEE Transactions on Components Hybrids and Manufacturing Technology 6(3), 323-328.         [ Links ]

4. Chan, L. Y., Lin, D. K. J., Xie, M. & Goh, T. N. (2002), 'Cumulative probability control charts for geometric and exponential process characteristics', International Journal of Production Research 40(1), 133-150.         [ Links ]

5. Chan, L. Y., Xie, M. & Goh, T. N. (2000), 'Cumulative quantity control charts for monitoring production processes', International Journal of Production Research 38(2), 397-408.         [ Links ]

6. Degroot, M. H. (1970), Optimal statistical decision, McGraw-Hill Inc.         [ Links ].

7. Grimshaw, S. D., Collings, B. J., Larsen, W. A. & Hurt, C. R. (2001), 'Eliciting factor importance in a designed experiment', Technometrics 43(2), 133-146.         [ Links ]

8. Jenkinson, D. J. (2005), The elicitation of probabilities a review of the statistical literature, BEEP working paper , University of Sheffield, United Kingdom.         [ Links ]

9. Leon, J. C., Vazquez-Polo, J. F. & Gonzalez, L. (2003), 'Environmental and resource economics', Kluwer Academic Publishers 26, 199-210.         [ Links ]

10. Majeed, M. Y., Aslam, M. & Riaz, M. (2012), 'Mixture cumulative count control chart for mixture geometric process characteristics', Quality & Quantity 26, 1-19.         [ Links ]

11. Mendenhall, W. & Hadar, R. J. (1958), 'Estimation of parameters of mixed exponentially distributed failure time distribution from censored life test data', Biometrika 45(3-4), 504-520.         [ Links ]

12. Montgomery, D. C. (2009), Introduction to Statistical Quality Control, 6 edn, John Wiley & Sons, New York.         [ Links ]

13. Norstrom, J. G. (1996), 'The use of precautionary loss functions in risk analysis', IEEE Transactions on Reliability 45(3), 400-403.         [ Links ]

14. O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. E., Garthwaite, P. H., Jenkinson, D. J., Oakley, J. E. & Rakow, T. (2006), Uncertain Judgements: Eliciting expert probabilities, John Wiley & Sons, New York.         [ Links ]

15. Quesenberry, C. P. (2007), SPC Methods for Quality Improvement, John Wiley & Sons, Toronto.         [ Links ]

16. Sun, F. B., Yang, J., del Rosario, R. & Murphy, R. (2001), A conditional-reliability control-chart for the post-production extended reliability-test, 'Proceedings Annual Reliability and Maintainability Symposium', p. 64-9.         [ Links ]

17. Xie, M. & Goh, T. N. (1992), 'Some procedures for decision making in controlling high yield processes', Quality and Reliability Engineering International 8(4), 355-360.         [ Links ]

18. Xie, M., Goh, T. N. & Kuralmani, V. (2000), 'On optimal setting of control limits for geometric chart', International Journal of Reliability Quality and Safety Engineering 7(1), 17-25.         [ Links ]

19. Xie, M., Goh, T. N. & Ranjan, P. (2002), 'Some effective control chart procedures for reliability monitoring', Reliability Engineering and System Safety 19(77), 143-150.         [ Links ]

20. Xie, M., Goh, T. N. & Tang, X. Y. (2000), 'Data transformation for geometrically distributed quality characteristics', Quality and Reliability Engineering International 16(1), 9-15.         [ Links ]

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