Integrated model for determining the optimal initial settings of the process mean and the optimal production run assuming quadratic loss functions

Chen and Chung (1996) addressed the problem of the joint determination of the optimal process mean and production run for an industrial process. Their study considered a product with an upper and a lower specification limit. The optimal process mean and optimal production run were obtained by balancing the profit of meeting and not meeting the specification limits. However, Chen and Chung did not consider the quality cost for the product within the specification limits. The present paper revisits the problem and incorporates the quality cost by introducing a Taguchi loss function for determining simultaneously the optimal process mean and production run. As per Chen and Chung, the present paper assumes a 100% inspection scheme. It also investigates the differences between Chen and Chung's approach and the Reward Theorem approach. A sample inspection scheme is also proposed. Numerical examples are provided to demonstrate the application of the model. A sensitivity analysis of the model is provided. Some new directions for further research are also outlined.

[1]  A.-B. Shaibu,et al.  Economic selection of optimal target values , 2000 .

[2]  Robert L. Schmidt,et al.  Economic selection of the mean and upper limit for a canning problem with limited capacity , 1991 .

[3]  Chandrasekhar Das.  Selection and evaluation of most profitable process targets for the control of canning quality , 1995 .

[4]  Isaac N. Gibra.  Optimal production runs of processes subject to systematic trends , 1974 .

[5]  Stephen M. Pollock,et al.  Determination of the Optimal Process Mean and the Upper Limit for a Canning Problem , 1988 .

[6]  S. Eilon,et al.  Controlling Production Processes Which are Subject to Linear Trends , 1963 .

[7]  Min Koo Lee,et al.  Determination of the optimal target values for a filling process when inspection is based on a correlated variable , 1994 .

[8]  T. P. M. Pakkala,et al.  DETERMINATION OF AN OPTIMAL SETTING AND PRODUCTION RUN USING TAGUCHI'S LOSS FUNCTION , 1999 .

[9]  Stephen M. Pollock,et al.  Cost Savings Due to Variance Reduction in a Canning Process , 1992 .

[10]  S.-L. Chen,et al.  Determination of the optimal production run and the most profitable process mean for a production process , 1996 .

[11]  Olle Carlsson.  Determining the most profitable process level for a production process under different sales conditions , 1984 .

[12]  Do Sun Bai,et al.  Optimal target values for a filling process when inspection is based on a correlated variable , 1993 .

[13]  M. A. Rahim,et al.  Joint determination of the optimum target mean and variance of a process , 2000 .

[14]  M. A. Rahim,et al.  Optimal control of a deteriorating process with a quadratic loss function , 2001 .

[15]  Lloyd S. Nelson,et al.  Best Target Value for a Production Process , 1978 .

[16]  George Tagaras,et al.  ECONOMIC ACCEPTANCE SAMPLING BY VARIABLES WITH QUADRATIC QUALITY COSTS , 1994 .

[17]  G. O. Wesolowsky,et al.  Optimal Control of a Linear Trend Process with Quadratic Loss , 1989 .

[18]  Bryan Dodson.  DETERMINING THE OPTIMAL TARGET VALUE FOR A PROCESS WITH UPPER AND LOWER SPECIFICATIONS , 1993 .

[19]  Samar K. Mukhopadhyay,et al.  Optimal process variance under Taguchi loss , 1995 .

[20]  M. A. Rahim,et al.  Joint determination of optimum variable and attribute target means , 1991 .

[21]  G. Taguchi.  Quality engineering in japan , 1985 .

[22]  Damodar Y. Golhar.  Determination of the Best Mean Contents for A "Canning Problem" , 1987 .

[23]  C.-H. Chen,et al.  Determining the Optimum Process Mean for a Poor Process , 2002 .

[24]  Viliam Makis.  Optimal tool replacement with asymmetric quadratic loss , 1996 .

[25]  Byung Rae Cho,et al.  DETERMINATION OF THE OPTIMAL PROCESS MEAN WITH THE CONSIDERATION OF VARIANCE REDUCTION AND PROCESS CAPABILITY , 2000 .

[26]  William G. Hunter,et al.  Determining the Most Profitable Target Value for a Production Process , 1977 .

[27]  Tarun Gupta,et al.  Determination of optimal lot sizing parameters and a controllable process mean for a production system , 1991 .

[28]  R. S. Lashkari,et al.  Optimal decision rules for determining the length of the production run , 1985 .

[29]  William G. Hunter,et al.  Economic Selection of Quality Manufactured Product , 1984 .

[30]  Angus Jeang,et al.  Optimal tool replacement with nondecreasing tool wear , 1992 .

[31]  P. K. Banerjee,et al.  Selection of the Most Economical Production Plan in a Tool-Wear Process , 1985 .

[32]  Douglas C. Montgomery,et al.  The use of statistical process control and design of experiments in product and process improvement , 1992 .

[33]  S. P. Ladany,et al.  Optimal set-up of a manufacturing process with unequal revenue from oversized and undersized items , 1995, Proceedings for Operating Research and the Management Sciences.

[34]  K. S. Al-Sultan,et al.  Variance reduction in a process with random linear drift , 1997 .

[35]  R. N. Kackar.  Taguchi’s Quality Philosophy: Analysis and Commentary , 1989 .

[36]  K. S. Al-Sultan,et al.  An extension of Rahim and Banerjee's model for a process with upper and lower specification limits , 1997 .

[37]  Chao-Yu Chou,et al.  Determining the Optimum Process Mean Under the Bivariate Quality Characteristics , 2003 .

[38]  D. C. Bettes.  Finding an Optimum Target Value in Relation to a Fixed Lower Limit and an Arbitrary Upper Limit , 1962 .

[39]  Jirarat Teeravaraprug,et al.  Designing the optimal process target levels for multiple quality characteristics , 2002 .

[40]  A. Raouf,et al.  Optimal production run for a process having multilevel tool wear , 1988 .

[41]  Mohsen A. Jafari,et al.  The optimum target value for single filling operations with quality sampling plans , 1991 .

[42]  Joyendu Bhadury,et al.  Joint Economic Selection of Target Mean And Variance , 2002 .

[43]  Kwei Tang,et al.  Joint determination of process mean, production run size and material order quantity for a container-filling process , 2000 .

[44]  Kwei Tang,et al.  Determination of the optimal process mean when inspection is based on a correlated variable , 1993 .

[45]  Chao-Yu Chou,et al.  Determining the Optimum Manufacturing Target Based on an Asymmetric Quality Loss Function , 2002 .

[46]  P. K. Banerjee,et al.  Optimal production run for a process with random linear drift , 1988 .

[47]  Viliam Makis,et al.  Optimal replacement of a tool subject to random failure , 1995 .

[48]  F. J. Arcelus,et al.  Optimal Production Run for a Normally Distributed Quality Characteristic Exhibiting Non-Negative Shifts in Process Mean and Variance , 1982 .