[en] The economic and statistical merits of a multiple variable sampling intervals (MVSI) scheme are studied. The problem is formulated as a double-objective optimization problem with the adjusted average time to signal as the statistical objective and the expected cost per hour as the economic objective. Bai and Lee’s [2] economic model is considered. Then we find the Pareto-optimal designs in which the two objectives are minimized simultaneously by using the non-dominated sorting genetic algorithm. Through an illustrative example, the advantages of the proposed approach is shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.
Disciplines :
Business & economic sciences: Multidisciplinary, general & others
Author, co-author :
Faraz, Alireza ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Seif, Asghar; Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
Sadeghifar; Department of Statistics, Bu-Ali Sina University, Hamedan, Iran
Language :
English
Title :
Evaluation of the Economic Statistical Design of the Multivariate T2 Control Chart with Multiple Variable Sampling Intervals Scheme: NSGA-II Approach
Publication date :
June 2015
Journal title :
Journal of Statistical Computation and Simulation
ISSN :
0094-9655
eISSN :
1563-5163
Publisher :
Taylor & Francis Ltd, Abingdon, United Kingdom
Volume :
85
Issue :
12
Pages :
2442-2455
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Hotelling, H., Multivariate quality control – illustrated by the air testing of sample bombsights (1947) Techniques of statistical analysis, pp. 111-184. , Eisenhart C., Hastay M.W., Wallis W.A., (eds), New York: MacGraw-Hill
Jackson, J.E., Multivariate quality control (1985) Comm Statist Theory Methods, 14, pp. 2657-2688
Alt, F.B., Multivariate quality control (1985) The encyclopedia of statistical sciences, , New York: John Wiley
Mason, R.L., Young, J.C., (2002) Multivariate statistical process control with industrial applications, , Philadelphia, PA: ASASIAM
Fuchs, C., Kenett, R.S., (1998) Multivariate quality control, theory and applications, , NewYork: Marcel Dekker
Mason, R.L., Tracy, N.D., Young, J.C., A practical approach for interpreting multivariate T2 control chart signals (1997) J Qual Technol, 29, pp. 396-406
Lowry, C.A., Montgomery, D.C., A review of multivariate control charts (1995) IIE Trans, 27, pp. 800-810
Duncan, A.J., The economic design of X charts used to maintain current control of a process (1956) J Amer Statist Assoc, 51, pp. 228-242
Woodall, W.H., Weaknesses of the economical design of control charts (1986) Technometrics, 28, pp. 408-409
Saniga, E.M., Economic statistical control chart designs with an application to X and R charts (1989) Technometrics, 31, pp. 313-320
Montgomery, D.C., Woodall, W.H., A discussion on statistically based process monitoring and control (1997) J Qual Technol, 29, pp. 121-162
Taylor, H.M., Markovian sequential replacement processes (1965) Ann Math Stat, 36, pp. 13-21
Chen, Y.K., Economic design of variable sampling interval T2 control charts – a hybrid Markov chain approach with genetic algorithms (2007) Expert Syst Appl, 33, pp. 683-689
Chao, Y.C., Chun, H.C., Chung, H.C., Economic design of variable sampling intervals T2 control charts using genetic algorithms (2006) Expert Syst Appl, 30, pp. 233-242
Faraz, A., Saniga, E., Kazemzade, R.B., Economic and economical statistical design of Hotelling's T2 control chart with two-state adaptive sample size (2009) J Stat Comput Simul
Chen, Y.K., Economic design of variable T2 control chart with the VSSI sampling scheme (2009) Qual Quant
Faraz, A., Kazemzadeh, R., Parsian, A., Moghadam, M.B., On the advantages of economically designed Hotelling's T2 control chart with variable sample sizes and sampling intervals (2012) Qual Quant, 46, pp. 39-53
Faraz, A., Saniga, E., Economic and economic statistical design of Hotelling's T2 control chart with double warning lines (2011) Qual Reliab Eng Int, 27, pp. 125-139
Torabian, M., Moghadam, M.B., Faraz, A., economically designed Hotelling's T2 control chart using VSICL scheme (2010) Arab J Sci Eng, 35, pp. 251-263
Seif, A., Moghadam, M.B., Faraz, A., Heuchenne, C., Statistical merits and economic evaluation of T2 control charts with the VSSC scheme (2011) Arab J Sci Eng, 36, pp. 1461-1470
Seif, A., Faraz, A., Heuchenne, C., Saniga, E., Moghadam, M.B., A modified economicstatistical design of T2 control chart with variable sample sizes and control limits (2011) J Appl Stat, 38, pp. 2459-2469
Costa, A.F.B., Rahim, M.A., (2001) J Appl Stat, 28, pp. 875-885. , Economic design of charts with variable parameters: the Markov chain approach
Faraz, A., Heuchenne, C., Saniga, E., Optimal T2 control chart with double sampling scheme – an alternative to the MEWMA chart (2012) Qual Reliab Eng Int, 28, pp. 751-760
Faraz, A., Saniga, E., Multiobjective genetic algorithm approach to the economic statistical design of control charts with an application to Xbar and S2 charts (2013) Qual Reliab Eng Int, 29, pp. 407-415
Faraz, A., Heuchenne, C., Saniga, E., Costa, A.F.B., Double-objective economic statistical design of the VP T2 control chart: Wald's identity approach (2014) J Stat Comput Simul, 84, pp. 2123-2137
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II (2002) IEEE Trans. Evol Comput, 6, pp. 184-197
Bai, D.S., Lee, K.T., (1998) Int J Prod Econ, 54, pp. 57-64. , An economic design of variable sampling interval control charts
Reynolds, M.R., Jr., Arnold, J.C., Optimal one-side Shewhart control chart with variable sampling intervals (1989) Sequential Anal, 8, pp. 51-77
Schaffer, J.D., (1985) Multiple objective optimization with vector evaluated genetic algorithms, , In: Proceedings of the International Conference on Genetic Algorithm and their Applications
Horn, J., Nafpliotis, N., (1993) Multiobjective optimization using the niched genetic algorithm, , Technical Report IIIiGAI Report 93005, University of Illinoisat Urbana-Champaign, Urbana, IL
Zitzler, E., Thiele, L., Multiobjective optimization using evolutionary algorithms – a comparative case study (1998) Parallel problem solving from nature-PPSN V, , Eiben A.E., (ed), Berlin: Sprinter
