Economic statistical design of non-uniform sampling scheme X bar control charts under non-normality and Gamma shock using genetic algorithm

This paper presented an approach which simultaneously considered the properties of cost and quality based on the Burr distribution and the non-unifampling scheme. The objective was to determine three parameters, namely, sample size, sampling interval between successive samples, and control limits, when an X bar chart monitors a manufacturing process with Gamma (@l, 2) failure characteristic and non-normal data. The design parameters of the X bar control charts can be obtained through the genetic algorithm (GA) method. An example was also adopted to indicate the solution procedure and sensitivity analyses. The results show that an increase of skewness coefficient (@a"3) results in a slight decrease for sample size (n) while an increase of kurtosis coefficient (@a"4) leads to a wider control limit width.

[1]  M. A. Rahim,et al.  Economic design of x -control charts under Weibull shock models , 1988 .

[2]  Barrie M. Baker,et al.  A genetic algorithm for the vehicle routing problem , 2003, Comput. Oper. Res..

[3]  Chung-Ho Chen,et al.  Economic design of variable sampling intervals T2 control charts using genetic algorithms , 2006, Expert Syst. Appl..

[4]  Guoqiang Zhang,et al.  Economic statistical design of x ¯ control charts for systems with Weibull in-control times , 1997 .

[5]  K. R. Baker,et al.  Two Process Models in the Economic Design of an X Chart , 1971 .

[6]  Erwin M. Saniga,et al.  Economic Statistical Control-Chart Designs With an Application to and R Charts , 1989 .

[7]  M. A. Rahim,et al.  A generalized model for the economic design of ??control charts for production systems with increasing failure rate and early replacement , 1993 .

[8]  Douglas C. Montgomery,et al.  Statistically constrained economic design of the EWMA control chart , 1995 .

[9]  Steven A. Yourstone,et al.  Non‐Normality and the Design of Control Charts for Averages* , 1992 .

[10]  Anikó Ekárt,et al.  Genetic algorithms in computer aided design , 2003, Comput. Aided Des..

[11]  Denis Royston Towill,et al.  Genetic algorithm optimisation of a class of inventory control systems , 2000 .

[12]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[13]  H. A. Knappenberger,et al.  Minimum Cost Quality Control Tests , 1969 .

[14]  Kyu-Yeul Lee,et al.  An improved genetic algorithm for facility layout problems having inner structure walls and passages , 2003, Comput. Oper. Res..

[15]  M. A. Rahim,et al.  Economic statistical design of X control charts for systems with gamma(λ, 2) in-control times , 2002 .

[16]  Genichi Taguchi.  System Of Experimental Design: Engineering Methods To Optimize Quality And Minimize Costs , 1987 .

[17]  M. A. Girshick,et al.  A BAYES APPROACH TO A QUALITY CONTROL MODEL , 1952 .

[18]  M. A. Rahim.  JOINT DETERMINATION OF PRODUCTION QUANTITY, INSPECTION SCHEDULE, AND CONTROL CHART DESIGN , 1994 .

[19]  William H. Woodall,et al.  Weaknesses of The Economic Design of Control Charts , 1986 .

[20]  Huifen Chen,et al.  Non-normality effects on the economic-statistical design of X charts with Weibull in-control time , 2007, Eur. J. Oper. Res..

[21]  Y.-K. Chen,et al.  An evolutionary economic-statistical design for VSI X control charts under non-normality , 2003 .

[22]  Cheng-Lung Huang,et al.  A GA-based feature selection and parameters optimizationfor support vector machines , 2006, Expert Syst. Appl..

[23]  Jesuk Ko,et al.  A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling , 2003, Comput. Oper. Res..

[24]  Antonio Fernando Branco Costa,et al.  Joint economic design of x and R charts under Weibull shock models , 2000 .

[25]  M. A. Rahim,et al.  A dynamic economic model for an x¯-control chart design , 1997 .

[26]  M. A. Rahim,et al.  Economic statistical design of x ¥ control charts for systems with gamma ( 5 ,2) in-control times , 2003 .

[27]  Thomas P. McWilliams,et al.  Economic, Statistical, and Economic-Statistical X̄ Chart Designs , 1994 .

[28]  Mikkel T. Jensen,et al.  Generating robust and flexible job shop schedules using genetic algorithms , 2003, IEEE Trans. Evol. Comput..

[29]  Fei-Long Chen,et al.  ECONOMIC DESIGN OF CONTROL CHARTS WITH BURR DISTRIBUTION FOR NON-NORMAL DATA UNDER WEIBULL FAILURE MECHANISM , 2006 .

[30]  Chao-Yu Chou,et al.  Joint Economic Design of Variable Sampling Intervals (X) and R Charts Using Genetic Algorithms , 2006 .

[31]  Chao-Yu Chou,et al.  Economic-statistical design of X ¥ charts for non-normal data by considering quality loss , 2000 .

[32]  Chung-Ho Chen,et al.  Economic design of X charts for non-normally correlated data , 2001 .

[33]  A. Goel,et al.  An Algorithm for the Determination of the Economic Design of -Charts Based on Duncan's Model , 1968 .

[34]  Isaac N. Gibra.  Economically Optimal Determination of the Parameters of np-Control Charts , 1971 .

[35]  M. A. Rahlm.  Economic model of chi-CHART under non-normality and measurement errors , 1985, Comput. Oper. Res..

[36]  Kenneth E. Case,et al.  The economic design of a dynamic X control chart , 1989 .

[37]  Gábor Renner.  Genetic algorithms in CAD , 2003, Comput. Aided Des..

[38]  Chao-Yu Chou,et al.  Economic design of variable sampling intervals EWMA charts with sampling at fixed times using genetic algorithms , 2008, Expert Syst. Appl..

[39]  Pupong Pongcharoen,et al.  Determining optimum Genetic Algorithm parameters for scheduling the manufacturing and assembly of complex products , 2002 .

[40]  M. A. Rahim.  Economic design of X control charts assuming Weibull in-control times , 1993 .

[41]  Erwin M. Saniga,et al.  Economic-Statistical Design of X̄ and R or X̄ and S Charts , 2001 .

[42]  Mohamed Ben-Daya,et al.  A generalized economic model for joint determination of production run, inspection schedule and control chart design , 1998 .

[43]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

[44]  Chao-Yu Chou,et al.  Economic-statistical design of multivariate control charts for monitoring the mean vector and covariance matrix , 2003 .

[45]  Yan-Kwang Chen,et al.  Economic design of variable sampling interval T , 2007, Expert Syst. Appl..