Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 27, No. 10 (October 2014) 1591-1600   

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  MULTI-OBJECTIVE ECONOMIC-STATISTICAL DESIGN OF CUMULATIVE COUNT OF CONFORMING CONTROL CHART
 
A. Sherbaf Moghaddam, A. Amiri and M. Bashiri
 
( Received: February 26, 2014 – Accepted: June 26, 2014 )
 
 

Abstract    Cumulative Count of Conforming (CCC) charts are utilized for monitoring the quality characteristics in high-quality processes. Executive cost of control charts is a motivation for researchers to design them with the lowest cost. Usually in most researches, only one objective named cost function is minimized subject to statistical constraints, which is not effective method for economic-statistical design of control charts. In this paper, a multi-objective model for the economic-statistical design of the CCC control chart is developed. Then, multi-objective evolutionary algorithm (NSGA-II) for obtaining the Pareto optimal solution of the model is proposed. A numerical example is applied to illustrate the effectiveness of the proposed model. This model leads to lower cost and smaller probability of Type I and Type II errors, compared with economic model. In addition, a sensitivity analysis is done to investigate the effect of input parameters on the best solutions of the proposed model.

 

Keywords    Statistical Process Control, Cumulative Count of Conforming Charts, High-Quality Processes, Multi-Objective Economic-Statistical Design, NSGA-II Algorithm

 

چکیده    نمودار هاي کنترل CCC براي پايش مشخصه هاي كيفي در فرآيندهاي با كيفيت بالا به كار برده مي شوند. هزينه عملياتي نمودارهاي كنترل به عنوان محركي براي محققان در طراحي نمودارها با كمترين هزينه مي باشد. در بسياري از پژوهش ها، تابع هزينه به عنوان يك تابع هدف با در نظر گرفتن محدودیتهای آماری مينيمم مي شود كه اين رويكرد موثري در طراحي اقتصادي-آماري نمودارهاي كنترل نمي‏باشد.در اين مقاله، يك مدل چند هدفه براي طراحي اقتصادي-آماري نمودار كنترل CCC توسعه داده شده است. سپس الگوريتم تكاملي چندهدفه (NSGA-II) براي بدست آوردن جواب بهينه پارتو مدل پيشنهاد شده است. براي نشان دادن اثر مدل پيشنهادي، از يك مثال عددي استفاده شده است. اين مدل اقتصادي- آماري پيشنهادي منجر به هزينه كمتر و احتمالات خطاي نوع اول و دوم كوچكتر در مقايسه با مدل اقتصادي مي شود. همچنین آناليز حساسيتي براي بررسي اثر پارامترهاي ورودي روي بهترين جواب هاي مدل پيشنهاد شده انجام شده است.

References   

1.     Calvin, T., "Quality control techniques for" zero defects"", Components, Hybrids, and Manufacturing Technology, IEEE Transactions on,  Vol. 6, No. 3, (1983), 323-328.

2.     Goh, T., "A control chart for very high yield processes", Quality Assurance,  Vol. 13, No. 1, (1987), 18-22.

3.     Lucas, J.M., "Control scheme for low count levels", Journal of Quality Technology,  Vol. 21, No. 3, (1989), 199-201.

4.     Glushkovsky, E.A., "Onlinegcontrol chart for attribute data", Quality and Reliability Engineering International,  Vol. 10, No. 3, (1994), 217-227.

5.     Xie, M. and Goh, T., "The use of probability limits for process control based on geometric distribution", International Journal of Quality & Reliability Management,  Vol. 14, No. 1, (1997), 64-73.

6.     Chan, L., Lai, C., Xie, M. and Goh, T., "A two-stage decision procedure for monitoring processes with low fraction nonconforming", European Journal of Operational Research,  Vol. 150, No. 2, (2003), 420-436.

7.     Weiler, H., "On the most economical sample size for controlling the mean of a population", The Annals of Mathematical Statistics, (1952), 247-254.

8.     Duncan, A.J., "The economic design of x charts used to maintain current control of a process", Journal of the American Statistical Association,  Vol. 51, No. 274, (1956), 228-242.

9.     Lorenzen, T.J. and Vance, L.C., "The economic design of control charts: A unified approach", Technometrics,  Vol. 28, No. 1, (1986), 3-10.

10.   McWilliams, T.P., "Economic, statistical, and economic-statistical x chart designs", Journal of Quality Technology,  Vol. 26, No. 3, (1994), 227-238.

11.   Surtihadi, J. and Raghavachar, M., "Exact economic design of x charts for general time in-control distributions", The International Journal Of Production Research,  Vol. 32, No. 10, (1994), 2287-2302.

12.   Montgomery, D.C., Torng, J.-C., COCHRAN, J.K. and LAWRENCE, F.P., "Statistically constrained economic design of the ewma control chart", Journal of Quality Technology,  Vol. 27, No. 3, (1995), 250-256.

13.   Simpson, J.R. and Keats, J.B., "Sensitivity study of the cusum control chart with an economic model", International Journal of Production Economics,  Vol. 40, No. 1, (1995), 1-19.

14.   Collani, E.V. and Drager, K., "A simplied economic design of control charts for monitoring the nonconforming probability", Journal of Economic Quality Control,  Vol. 10, (1995), 231-247.

15.   Xie, M., Tang, X. and Goh, T., "On economic design of cumulative count of conforming chart", International Journal of Production Economics,  Vol. 72, No. 1, (2001), 89-97.

16.   Zhang, C.W., Xie, M. and Goh, T.N., "Economic design of cumulative count of conforming charts under inspection by samples", International Journal of Production Economics,  Vol. 111, No. 1, (2008), 93-104.

17.   Woodall, W.H., "Weaknesses of the economic design of control charts", Technometrics,  Vol. 28, No. 4, (1986), 408-409.

18.   Saniga, E.M., "Economic statistical control chart with an application to x-bar and r charts", Technometrics,  Vol. 31, No. 3, (1989), 313-320.

19.   Evans, G.W. and Emberton, G.R., "Bicriterion design of process control charts", International Journal of Production Economics,  Vol. 22, No. 2, (1991), 141-150.

20.   Castillo, E.D., Mackin, P. And Montgomery, D.C., "Multiple-criteria optimal design of x control charts", IIE Transactions,  Vol. 28, No. 6, (1996), 467-474.

21.   Celano, G. and Fichera, S., "Multi-objective economic design of an x control chart", Journal of Computers & Industrial Engineering,  Vol. 37, No. 1, (1999), 129-132.

22.   Zarandi, M.H.F., Alaeddini, A., Turksen, I.B. and Ghazanfari, M., A neuro-fuzzy multi-objective design of shewhart control charts, in Analysis and design of intelligent systems using soft computing techniques., Springer. (2007) 842-852.

23.   Chen, Y.-K. and Liao, H.-C., " Multi-criteria design of an X control chart ", Computers & Industrial Engineering,  Vol. 46, No. 4, (2004), 877-891.

24.   Asadzadeh, S. and Khoshalhan, F., " Multiple-objective design of an X control chart with multiple assignable causes ", The International Journal of Advanced Manufacturing Technology,  Vol. 43, No. 3-4, (2009), 312-322.

25.   Amiri, A., Mogouie, H. and Doroudyan, M.H., "Multi-objective economic-statistical design of mewma control chart", International Journal of Productivity and Quality Management,  Vol. 11, No. 2, (2013), 131-149.

26.   Amiri, A., Bashiri, M., Maleki, M.R. and Sherbaf Moghaddam, A., "Multi-objective markov based economic-statistical design of ewma control chart using nsga-ii and moga algorithms", To appear in International Journal of Multicriteria Decision Making,  (2014).

27.   Bashiri, M., Amiri, A., Doroudyan, M.H. and Asgari, A., "Multi-objective genetic algorithm for economic-statistical design of xbar control chart", Scientia Iranica,  Vol. 20, No. 3, (2013), 909-918.

28.   Bashiri, M., Amiri, A., Asgari, A. and Doroudyan, M.H., "A multiple objective efficient design of np control charts using data envelopment analysis", International Journal of Engineering-Transactions C: Aspects,  Vol. 26, No. 6, (2013), 587-588.

29.   Safaei, A.S., Kazemzadeh, R.B. and Niaki, S.T.A., "Multi-objective economic statistical design of x-bar control chart considering taguchi loss function", The International Journal of Advanced Manufacturing Technology,  Vol. 59, No. 9-12, (2012), 1091-1101.

30.   Fonseca, C.M. and Fleming, P.J., "Genetic algorithms for multiobjective optimization: Formulationdiscussion and generalization", in ICGA. Vol. 93, (1993), 416-423.

31.   Deb, K., "Multi-objective optimization using evolutionary algorithms, John Wiley & Sons,  Vol. 16,  (2001).

32.   Niaki, S.A., Houshmand, A. and Moeinzadeh, B., "On the performance of a multivariate control chart in multistage environment", International Journal of Engineering,  Vol. 14, No. 1, (2001), 49-64.

33.   Niaki, S. and Moeinzadeh, B., "A multivariate quality control procedure in multistage production systems", International Journal of Engineering Transactions A Basics,  Vol. 10, No. 4, (1997), 191-208.

34.   Niaki, S.T.A., Abbasi, B. and Arkat, J., "A generalized linear statistical model approach to monitor profiles", International Journal of Engineering Transactions A Basics,  Vol. 20, No. 3, (2007), 233-242.

35.   Keramatpour, M., Niaki, S., Khedmati, M. and Soleymanian, M., "Monitoring and change point estimation of ar (1) autocorrelated polynomial profiles", International Journal of Engineering-Transactions C: Aspects,  Vol. 26, No. 9, (2013), 933-942.

36.           Abdella, G., Yang, K. and Alaeddini, A., "Effect of location of explanatory variable on monitoring polynomial quality profiles", International Journal of Engineering-Transactions A: Basics,  Vol. 25, No. 2, (2012), 131-140                             .       





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