ECONOMIC AND ECONOMIC-STATISTICAL DESIGN OF FRS BAYESIAN CONTROL CHART USING MONTE CARLO METHOD AND ARTIFICIAL BEE COLONY ALGORITHM (ABC)

Abstract

In this paper, instead of traditional statistics, the Bayesian statistic has been considered incontrol charts based on economic and economic-statistical design. Due to the fact that this statistic does nothave any speciŞed distribution, the Monte Carlo method and artiŞcial bee colony (ABC) algorithm have beenutilized in order to obtain design optimum parameters (sample size, sampling interval and control limit). Thestudy indicates that the Bayesian statistic performance of control charts can be effective in this optimizationproblem. In addition, Numerical and comparison section are presented to support this proposition

Keywords

• Artificial Bee colony (ABC) Algorithm, Bayesian Control Chart, Economic-statistical Design, Monte Carlo Method.

References

1. Banerjee, P. K., and Rahim, M. A. (1988). Economic design of X-bar control charts under Weibull shock models, Technometrics, 30, 407-414.
2. Calabrese, J. M. (1995). Bayesian Process Control for Attributes,Management Science, 41, 637-645.
3. Costa, A. F. B., and Rahim, M. A. (2001). Economic design of X-bar charts with variable parameters: the Markov chain approach,Journal of Applied Statistics, 28/7, 875-885.
4. Duncan, A. J. (1956). The economic design of X-bar charts used to maintain current control of a process,
5. Journal of the American Statistical Association, 51, 228242.
6. Duncan, A. J. (1971). The economic design of 2 charts where there is a multiplicity of assignable causes,
7. Journal of the American Statistical Association, 66, 107-121. Eckles, J. E. (1968). Optimum maintenance with incomplete information, Operational Research, 16, 1067.
8. Faraz, A., Saniga, E., and Kazemzadeh, R. B. (2009). Economic and Economic Statistical Design ofT2

9. Control Chart with two-adaptive Sample Sizes, Journal of Statistical Computation and Simulation, 80, 1316.
10. Girshick, M. A., and Rubin, H. (1952), A Bayes approach to a quality control model,Annals of Mathe- matical Statistics, 23, 114–125.
11. Karaboga, D. (2005). An Idea Based On Honey Bee Swarm For Numerical Optimization, TR-06, October
12. Karaboga, D., and Akay, B. (2009). A comparative study of ArtiŞcial Bee Colony algorithm, Applied
13. Mathematics and Computation, 214, 108-132. Karaboga, D., and Basturk, B. (2007). A powerful and efficient algorithm for numerical function opti- mization: artiŞcial bee colony (ABC) algorithm, J. Glob Optim, 39, 459-471.
14. Karaboga, D., and Basturk, B. (2008). On the performance of artiŞcial bee colony (ABC) algorithm,
15. Applied Soft Computing, 8, 687-697. Lorenzen, T. J., and Vance, L. C. (1986). The economic design of control charts: a uni?ed approach, Technometrics, 28, 3-10.
16. Maikis, V. (2009). Multivariate Bayesian process control for a Şnite production run, European Journal of Operational Research, 194, 795–806.
17. Prabhu, S. S., Mongomery, D. C., and Runger, G. C. (1997).Economic-statistical design of an adaptive
18. X-bar chart, Int. J. Production Economics, 49, 1–15. Ross, S. M. (1970). Applied Probability Models with Optimization Applications, Holden-Day, San Fran- cisco.
19. Saniga, E. M. (1989). Economic statistical control chart designs with an application to X-bar and R charts, Technometrics, 31, 313-320.
20. Tagaras, G. (1994). A Dynamic Programming Approach to the Economic Design of X-bar Charts, IIE Transactions, 26/3, 48–56.
21. Tagaras, G. (1996). Dynamic Control Charts for Finite Production Runs, European Journal of Opera- tional Research, 91, 38-55.
22. Tagaras, G., and Nikolaidis, Y. (2002). Comparing the Effectiveness of Various Bayesian X-bar Control
23. Charts, Operations Research, 50, 878-888. Taylor, H. M. (1965). Markovian sequential replacement processes, Annals of Mathematical Statistics, , 13-21.
24. Taylor, H. M. (1967). Statistical Control of a Gaussian Process, Technometrics, 9, 29–41.
25. Yang, S. F., and Rahim, M. A. (2005). Economic statistical process control for multivariate quality characteristics under Weibull shock model, Int. J. Production Economics, 98, 215-226.
26. Zhang, G., and Berardi, V. (1997). Economic statistical design of X-bar control charts for systems with
27. Weibull in-control times, Computers and Industrial Engineering, 32, 575-586.