Melis ZEYBEK

Confidence Interval based Quality Improvement for Non-normal Responses

Robust parameter design is an effective tool to determine the optimal operating conditions of a system.Because of its practicability and usefulness, the widespread applications of robust design techniquesprovide major quality improvements. The usual assumptions of robust parameter design are that normallydistributed experimental data and no contamination due to outliers. Optimizing an objective functionunder the normality assumption for a skewed data in dual-response modeling may result in misleading fitand operating conditions located far from the optimal values. This creates a chain of degradation in theproduction phase, e.g., poor quality products. This paper focuses on skewed experimental data. Theproposed approach is constructed on the confidence interval of the process mean which makes the systemmedian unbiased for the mean using the skewness information of the data. The response modeling of themidpoint of the interval is proposed as a location performance response. The main advantages of theproposed approach are that it gives a robust solution due to the skewed structure of the experimental datadistribution and does not need any transformation which causes any loss of information in estimation ofthe mean response. The procedure and the validity of the proposed approach are illustrated on a popularexample, the printing process study.

PDF

___

Taguchi, G. Introduction to Quality Engineering: Designing Quality into Products and Processes; Asian Productivity Organization: Tokyo, 1986.
Box, GEP. 1985. Discussion of off-line quality control, parameter design, and the Taguchi method. Journal of Quality Technology; 17: 198-206.
Vining, GG, Myers RH. 1990. Combining Taguchi and response surface philosophies: A dual response approach. Journal of Quality Technology; 22(1): 38-45.
Box, GEP, Wilson, KB. 1951. On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society; 13: 1-45.
Del Castillo, E, Montgomery, DC. 1993. A nonlinear programming solution to the dual response problem. Journal of Quality Technology; 25: 199-204.
Lin, DKJ, Tu, W. 1995. Dual response surface. Journal of Quality Technology; 27(1):34-39.
Copeland, KA, Nelson, PR. 1996. Dual response optimization via direct function minimization. Journal of Quality Technology; 28(1): 331-336.
Köksoy, O, Doganaksoy, N. 2003. Joint optimization of mean and standard deviation in response surface experimentation. Journal of Quality Technology; 35(3): 239-252.
Shoemaker, AC, Tsui, KL, Wu, CFJ. 1991. Economical experimentation methods for robust parameter design. Technometrics; 33: 415-427.
Lucas, JM. 1994. How to achieve a robust process using response surface methodology. Journal of Quality Technology; 26(4): 248-260.
Zeybek, M, Köksoy, O. 2016. Optimization of correlated multi-response quality engineering by the upside-down normal loss function. Engineering Optimization; 48: 1419-1431.
Zeybek, M. 2018. Process capability: A new criterion for loss function–based quality improvement. Süleyman Demirel University Journal of Natural and Applied Sciences; 22: 470-477.
Elsayed, EA, Chen, A. 1993. Optimal levels of process parameters for products with multiple characteristics. Journal of Production Research; 31(5):1117-1132.
Tan, MHY, Ng, SH. 2009. Estimation of the mean and variance response surfaces when the means and variances of the variables are unknown. IIE Transactions; 41(11): 942-956.
Quyang, L, Ma, Y, Byun, JH, Wang, J, Tu Y. 2016. An interval approach to robust design with parameter uncertainty. International Journal of Production Research; 54(11): 3201- 3215.
Miro-Quesada, G, DelCastillo, E, Peterson, PP. 2004. A Bayesian approach for multiple response surface optimization in the presence of noise variables. Journal of Applied Statistics; 31(3): 251-270.
Bisgaard, S, Fuller, H. 1994. Analysis of factorial experiments with defects or defectives as the response. Quality Engineering; 7(2):429-443.
Box, G, Fung, C. 1994. Is Your Robust Design Procedure Robust?. Quality Engineering; 6(3): 503–514.
Nelder, JA, Lee, Y. 1991. Generalized linear models for the analysis of Taguchi-type experiments. Applied Stochastic Models and Data Analysis; 7:107-120.
Myers, WR, Brenneman, WA, Myers, RH. 2005. A dual response approach to robust parameter design for a generalized linear model. Journal of Quality Technology; 37:130-138.
Boylan, GL, Cho, BR. 2013. Comparative studies on the high-variability embedded robust parameter design from the perspective of estimators. Computers and Industrial Engineering; 64: 442-452.
Zeybek, M, Köksoy, O. 2018. The effects of gamma noise on quality improvement. Communications in Statistics-Simulation and Computation; 48: 1-15.
Johnson, JN. 1978. Modified t tests and confidence intervals for asymmetrical populations. Journal of the American Statistical Association; 73 (363): 536-544.
Boukezzoula, R, Galichet, S, Bisserier, A. 2011. A Midpoint– Radius approach to regression with interval data. International Journal of Approximate Reasoning; 52: 1257-1271.
Köksoy, O. 2006. Multiresponse robust design: Mean square error (MSE) criterion. Applied Mathematics and Computation; 175: 1716-1729.
Ding, R, Lin, DKJ, Wei, D. 2004. Dual-response surface optimization: A weighted MSE approach. Quality Engineering; 16(3):377-385.
Box, GEP, Draper, NR. Empricial model-building and response surface; John Wiley & Sons, New York, NY, 1987.
Oyeyemi, GM. 2004. Treatment of non-normal responses from designed experiments. Journal of the Nigerian Statistical Association; 17: 8-19.