Process capability: A New Criterion for Loss Function–Based Quality Improvement

Year 2018, Volume: 22 Issue: Special, 470 - 477, 05.10.2018

Melis Zeybek

Abstract

Response surface methodology (RSM) – the method most preferred by quality engineers – is a natural and effective tool to achieve the desired process quality. Most of the current literature on process quality does not focus on information relating to how much better or worse a process is and also the degree of the process performance. On the other hand, although the process performance criteria are able to predict process capability, they cannot provide significant information relating to the process quality in terms of rate of rejects and losses. Therefore, this paper takes into account these two concepts and defines a criterion based on the process capability indices for the upside-down normal loss function (UDNLF). The proposed approach determines the optimal settings of a given process by minimizing the expected UDNLF which is defined in terms of and indices. The proposed procedure and its merits are illustrated on the basis of an example.

Keywords

Robust design, Response surface methodology; Loss function; Process capability indices

References

• [1] Taguchi, G. 1986. Introduction to Quality Engineering: Designing Quality into Products and Processes. Asian Productivity Organization, Tokyo,p. 191.
• [2] Spiring, F. 1993. The reflected normal loss function. Canadian Journal of Statistics. 21(1), 321-330.
• [3] Spiring, F., Yeung, A. 1998. A general class of loss functons with industrial applications. Journal of Quality Technology, 32(2), 152-162.
• [4] Drain, D.C., Gough, A.M. 1996. Applications of the upside-down normal loss function. IEEE Transactions on Semiconductor Manufacturing, 9, 143–145.
• [5] Box, G.E.P., Wilson, K.B. 1951. On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, 13, 1-45.
• [6] Vining, G.G., Myers R.H. 1990. Combining Taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology, 22(1), 38-45.
• [7] Del Castillo, E., Montgomery, D.C. 1993. A nonlinear programming solution to the dual response problem. Journal of Quality Technology, 25, 199-204.
• [8] Lin, D.K.J., Tu, W. 1995. Dual response surface. Journal of Quality Technology, 27(1), 34-39.
• [9] Köksoy, O., Fan, S.S. 2012. An upside-down normal loss function-based method for quality improvement. Engineering Optimization, 44, 935–945.
• [10] Shoemaker, A.C., Tsui, K.L., Wu, C.F.J. 1991. Economical experimentation methods for robust parameter design. Technometrics, 33, 415-427.
• [11] Lucas, J.M. 1994. How to achieve a robust process using response surface methodology. Journal of Quality Technology, 26(4), 248-260.
• [12] Copeland, K.A., Nelson, P.R. 1996. Dual response optimization via direct function minimization. Journal of Quality Technology, 28 (1), 331-336.
• [13] Kim, K., Lin, D.K.J. 1998. Dual response surface optimization: a fuzzy modeling approach. Journal of Quality Technology, 30, 1–10.
• [14] Köksoy, O., Doganaksoy, N. 2003. Joint optimization of mean and standard deviation in response surface experimentation. Journal of Quality Technology, 35(3), 239-252.
• [15] Köksoy, O. 2006. Multiresponse robust design: Mean square error (MSE criterion). Applied Statistics and Computation, 175, 1716-1729.
• [16] Zeybek, M., Köksoy, O. 2016. Optimization of correlated multiresponse quality engineering by the upside-down normal loss function. Engineering Optimization, 48, 1419-1431.
• [17] Tekindal M.A., Bayrak H., Ozkaya B., Yavuz G., 2012. Box-Behnken experimental design in factorial experiments: the importance of bread for nutrition and health. Turkish Journal of Field Crops, 17, 115-123.
• [18] Tekindal M.A., Bayrak H., Ozkaya B., Yavuz Y. 2014. Second-order response surface method: factorial experiments an alternative method in the field of agronomy. Turkish Journal Of Field Crops, 19, 35-45.
• [19] Bayrak, H., Özkaya, B., Tekindal, M.A. 2010. Birinci derece faktoriyel denemelerde verimlilik için optimum noktalarin belirlenmesi: bir uygulama. Türkiye Klinikleri Biyoistatistik Dergisi, 2, 18-26.
• [20] Chan, L.K., Cheng, S.W., Spiring, F. 1988. A new measure of process capability. Journal of Quality Technology, 20(3),162-175.
• [21] Pearn, W.L., Kotz, S., Johnson N.L. 1992. Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24, 216-231.
• [22] Spiring, F.A. 1997. A unifying approach to process capability indices. Journal of Quality Technology, 29, 49-58.
• [23] Zhang, B., Ni, J. 2007. Relative probability index C_rp: an alternative process capability index.
• Quality Engineering, 14(2), 267-278.
• [24] Noorossana, R., Alemzad, H. 2003. Quality improvement through multiple response optimization. Technecal Note, 16(1), 49-57.
• [25] Wu, H. 2004. An exploitation of target costing techniques in quality management. International Journal of Applied Science and Engineering, 2(2), 189-196.
• [26] Ch’ng, C.K., Quah S.H., Low, H.C. 2004. Index C_pm^* in Multiple Response Optimization. Quality Engineering, 17(1), 165-171.
• [27] Plante, R.D. 2001. Process capability: a criterion for optimizing multiple product and process design. IEE Transactions, 33(6), 497-509.
• [28] Jeang, A., Tsai, S.W., Li, H.C., Hsieh, C.K. 2002. A computer model for time-based tolerance design with response surface methodology. International Journal of Computer Integrated Manufacturing, 15(2), 97-108.
• [29] Abbasi B., Niaki S.T.A. 2010. Estimating process capability indices of multivariate nonnormal processes. International Journal of Advanced Manufacturing Technology, 50, 823-830.
• [30] Jahan A., Ismail, M.Y., Noorossana, R. 2010. Multi response optimization in design of experiments considering capability index in bounded objectives method. Journal of Scientific & Industrial Research, 69, 11-16.
• [31] Mondal S.C. 2013. Process capability-a surrogate measure of process robustness: a case study. International Journal of Quality & Reliability Management, 33(1), 90-106.
• [32] Myers, R.H, Montgomery, D.C., Anderson-Cook, C.M. 2009. Response surface methodology: process and product optimization using designed experiments., Wiley Series in Probability and Statistics, 3rd ed., p. 1247.
• [33] Luner, J. 1994. Achieving continuous improvement with the dual response approach: A demonstration of the Roman catapult. Quality Engineering, 6 (4), 691–705.
• [34] Ardakani, M.K., Noorossana, R. 2008. A new optimizaiton criterion for robust parameter design-target is best . The International Journal of Advanced Manufacturing Technology, 38, 851-859.
• [35] Ding, R., Lin, D.K.J., Wei, D. (2004), Dual response surface optimizaiton: a weighted MSE approach. Quality Engineering, 16(3), 377-385.
• [36] Ames, A.E., Mattucci, N., MacDonald, S., Szonyi, G., Hawkins, D.M. 1997. Quality loss functions for optimizaiton across multiple response surfaces. Journal of Quality Technology, 29(3).