Multiobjective Optimization; Genetic Algorithm; Economic Statistical Design; Control Charts
Abstract :
[en] Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, by a statistical criterion, an economic criterion or a joint economic-statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed above is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this paper, we explore multi objective models as an alternative for the methods listed above. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well known industrial problem and compare optimal multi objective designs to economic designs, statistical designs, economic statistical designs and heuristic designs.
Disciplines :
Mathematics
Author, co-author :
Faraz, Alireza ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Saniga, Erwin; Department of Business Administration, University of Delaware, Newark, Delaware 19716, USA
Language :
English
Title :
Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an application to Xbar and S2 charts
Duncan AJ,. The economic design of X ̄ charts used to maintain current control of a process. Journal of the American Statistical Association 1956; 51: 228-242.
Feigenbaum AV,. Total Quality Control. New York: McGraw-Hill, 1961.
Ishikawa K,. Guide to Quality Control. Asian Productivity Organization: Tokyo, 1976.
Juran IM, Gryna FM Jr, Bingham RS Ir,. Quality Control Handbook. New York: McGraw-Hill, 1974.
Lorenzen TJ, Vance LC,. The economic design of control charts: A unified approach. Technometrics 1986; 28: 3-11.
Montgomery DC,. The economic design of control charts: A review and literature survey. Journal of Quality Technology 1980; 12: 75-87.
Svoboda L,. The economic design of control charts: A review and literature survey (1979-1989). In Statistical Process Control in Manufacturing, JB Keats, DC Montgomery, (eds). Marcel Dekker: New York, 1991.
Ho C, Case KE,. Economic design of control charts: A literature review for 1981-1991. Journal of Quality Technology 1994; 26: 39-53.
Saniga EM,. Economic statistical control chart designs with an application to X ̄ and R charts. Technometrics 1989; 31: 313-320.
Saniga EM,. Joint statistical design of X ̄ and R control charts. Journal of Quality Technology 1991; 23: 156-162.
Faraz A, Saniga E,. Economic and Economic Statistical Design of Hotelling's T2 Control Chart with double warning lines. Quality and Reliability Engineering International 2011; 27 (2): 125-139. DOI: 10.1002/qre.1095.
Woodall WH,. Weaknesses of the economical design of control charts. Technometrics 1986; 28: 408-409.
Saniga EM,. Economic Design of Control Charts. In Encyclopedia of Statistics in Quality and Reliability, F Ruggeri, R Kenett, FW Faltin, (eds). John Wiley and Sons Ltd: Chichester, UK, 2007; 590-595.
Del Castillo E, Mackin P, Montgomery DC,. Multiple-criteria optimal design of X control charts. IIE Transactions 1996; 28: 467-474.
Celano G, Fichera S,. Multi-objective Economic Design of an Xbar control chart. Computers and Industrial Engineering 1999; 37: 129-132.
Linderman K, Love TE,. Economic and economic statistical design for MEWMA control charts. Journal of Quality Technology 2000; 32 (4): 410-417.
Montgomery DC,. Introduction to Statistical Quality Control. John Wiley: New York, 2003.
Holland JH,. Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press, 1975.
Schaffer JD,. Multiple objective optimization with vector evaluated genetic algorithms. In Proceedings of the international conference on genetic algorithm and their applications, 1985.
Fonseca CM, Fleming PJ,. Multiobjective genetic algorithms. In: IEE colloquium on Genetic Algorithms for Control Systems Engineering (Digest No. 1993/130), 28 May 1993. London, UK: IEE; 1993.
Konak A, Coit DW, Smith AE,. Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering and System Safety 2006; 91: 992-1007.
Faraz A, Kazemzadeh RB, Saniga, E,. Economic and Economic Statistical Design of Hotelling's T2 Control Chart with Variable Sample Sizes. Journal of Statistical Computation and Simulation 2009; 80 (12): 1299-1316. DOI: 10.1080/00949650903062574.
Faraz A, Heuchenne C, Saniga E,. Optimal T2 Control Chart with a Double Sampling Scheme-An Alternative to the MEWMA Chart. Quality and Reliability Engineering International 2011; DOI: 10.1002/qre.1268.