Evaluating the performance of variable scheme X-bar control chart: a Taguchi loss approach

The concept of loss function has been combined, with a numerous statistical decision models which require quality cost estimation. Moreover, estimation of the costs of non-conforming product is one of the most important inputs in economic design of control charts. Therefore, on the basis of Markov chain approach, this paper focused on extending control chart with variable schemes control charts by considering Taguchi’s quality loss function. Afterwards, control chart parameters are defined in such a way to minimise the cost of process monitoring via genetic algorithm. Sensitivity analysis on the different sizes of the process shift and the cost of rework or scrap a product and comparing the results unfold insights that will help the quality engineers in designing the most powerful plans for the process.

[1]  Seyed Taghi Akhavan Niaki,et al.  Multiobjective design of an S control chart for monitoring process variability , 2012 .

[2]  J. Douglas Barrett,et al.  Taguchi's Quality Engineering Handbook , 2007, Technometrics.

[3]  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..

[4]  S. M. Alexander,et al.  Economic design of control charts using the Taguchi loss function , 1995 .

[5]  Mohamed Limam,et al.  Economic Design of an Attribute np Control Chart Using a Variable Sample Size , 2011 .

[6]  Seyed Taghi Akhavan Niaki,et al.  Economic and economic-statistical designs of MEWMA control charts—a hybrid Taguchi loss, Markov chain, and genetic algorithm approach , 2010 .

[7]  Zhang Wu,et al.  Optimization design of control charts based on Taguchi's loss function and random process shifts , 2004 .

[8]  Eugenio K. Epprecht,et al.  ECONOMIC DESIGN OF A VP X CHART , 2001 .

[9]  George Tagaras A Survey of Recent Developments in the Design of Adaptive Control Charts , 1998 .

[10]  Shu-Ling Wang,et al.  Economic design of autoregressive moving average control chart using genetic algorithms , 2012, Expert Syst. Appl..

[11]  Yan-Kwang Chen Economic design of X̄ control charts for non-normal data using variable sampling policy , 2004 .

[12]  Hsu-Hwa Chang,et al.  Economic design of variable parameters X̄ control charts for processes with fuzzy mean shifts , 2008, J. Oper. Res. Soc..

[13]  Seyed Taghi Akhavan Niaki,et al.  A particle swarm optimization approach on economic and economic-statistical designs of MEWMA control charts , 2011 .

[14]  Dogan A. Serel,et al.  Economic design of EWMA control charts based on loss function , 2009, Math. Comput. Model..

[15]  Yau-Ren Shiau,et al.  Monitoring capability study and genetic economic design of X-bar control chart , 2006 .

[16]  Yee-Ming Chen,et al.  An Economic design for a variable-sampling-interval ${\bar{x}}$ control chart for a continuous-flow process , 2005 .

[17]  Seyed Taghi Akhavan Niaki,et al.  A hybrid Nelder–Mead simplex and PSO approach on economic and economic-statistical designs of MEWMA control charts , 2013 .

[18]  Alireza Faraz,et al.  Economic statistical design of a T2 control chart with double warning lines , 2011, Qual. Reliab. Eng. Int..

[19]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[20]  Antonio Fernando Branco Costa,et al.  X̄ charts with variable sample size , 1994 .

[21]  Alireza Faraz,et al.  A unification and some corrections to Markov chain approaches to develop variable ratio sampling scheme control charts , 2011 .

[22]  Herbert Moskowitz,et al.  Joint economic design of EWMA control charts for mean and variance , 2008, Eur. J. Oper. Res..

[23]  Thomas R. Rohleder,et al.  The economic design of an X̄ control chart recognizing process improvement , 1999 .

[24]  Elsayed A. Elsayed,et al.  An economic design of [xbar] control chart using quadratic loss function , 1994 .

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

[26]  Salih O. Duffuaa,et al.  Integration of Taguchi's loss function approach in the economic design of x¯‐chart , 2003 .

[27]  Akhavan Niaki Seyed Taghi,et al.  A Comparative Study of Four Evolutionary Algorithms for Economic and Economic-Statistical Designs of MEWMA Control Charts , 2011 .

[28]  Douglas C. Montgomery,et al.  Economic Design of T2 Control Charts to Maintain Current Control of a Process , 1972 .

[29]  이경택,et al.  An Economic Design of Variable Sampling Interval Χ Control Charts , 1995 .

[30]  Yan-Kwang Chen,et al.  Multi-criteria design of an X̄ control chart , 2004, Comput. Ind. Eng..

[31]  Yu Guo,et al.  Economic and statistical design of and S control charts using an improved multi-objective particle swarm optimisation algorithm , 2012 .

[32]  Chung-Ho Chen,et al.  Economic-Statistical Design of Multivariate Control Charts Using Quality Loss Function , 2002 .

[33]  M. A. Bakir,et al.  The optimization with the genetic algorithm approach of the multi-objective, joint economical design of the x and R control charts , 2004 .

[34]  Changsoon Park,et al.  Economic design of a variable sample size -chart , 1994 .

[35]  Feng-Chia Li,et al.  An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models , 2011 .

[36]  Marion R. Reynolds,et al.  Optimal one-sided shewhart control charts with variable sampling intervals , 1989 .

[37]  George Nenes,et al.  A new approach for the economic design of fully adaptive control charts , 2011 .

[38]  Seyed Taghi Akhavan Niaki,et al.  Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function , 2012 .

[39]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[40]  J. A. Nachlas,et al.  X charts with variable sampling intervals , 1988 .

[41]  Yu-Chang Lin,et al.  The variable sampling rate X̄ control charts for monitoring autocorrelated processes , 2008, Qual. Reliab. Eng. Int..

[42]  Herbert Moskowitz,et al.  Effect of quality loss functions on the economic design of process control charts , 1994 .

[43]  W. Edwards Deming,et al.  Out of the Crisis , 1982 .