Developing a univariate approach to phase-I monitoring of fuzzy quality profiles

Abstract: In many real-world applications, the quality of a process or a particular product can be characterized by a functional relationship called profile. A profile builds the relationships between a response quality characteristic and one or more explanatory variables. Monitoring the quality of a profile is implemented to understand and to verify the stability of this functional relationship over time. In some real applications, a fuzzy linear regression model can represent the profile adequately where the response quality characteristic is fuzzy. The purpose of this paper is to develop an approach for monitoring process/product profiles in fuzzy environment. A model in fuzzy linear regression is developed to construct the quality profiles by using linear programming and then fuzzy individuals and moving-range (I-MR) control charts are developed to monitor both intercept and slope of fuzzy profiles to achieve an in-control process. A case study in customer satisfaction is presented to show the application of our approach and to express the sensitivity analysis of parameters for building a fuzzy profile.

How to cite this paper

 Noghondarian, K & Ghobadi, S. (2012). Developing a univariate approach to phase-I monitoring of fuzzy quality profiles.International Journal of Industrial Engineering Computations , 3(5), 829-842.

Refrences

Amiri, A., Eyvazian, M., Zou, C. & Noorossana, R. (2012). A parameters reduction method for monitoring multiple linear regression profiles. International Journal of Advanced Manufacturing Technology, 58(5-8), 621-629.

Azadeh, A., Saberi, M. & Seraj, O. (2010). An integrated fuzzy regression algorithm for energy consumption estimation with non-stationary data: A case study of Iran. Energy , 35, 2351–2366.

Chang, Y. & Ayyub, B. M. (2001). Fuzzy regression methods- a comparative assessment. Fuzzy Sets and Systems, 119, 187–203.

Chen, C.T. (2001). A fuzzy approach to select the location of the distribution center. Fuzzy Sets and Systems, 118, 65-73.

Chen, S. & Nembhard, H.B. (2011). High-dimensional control chart for profile monitoring. Quality and Reliability Engineering International, 27(4), 451–464.

Croarkin, C. & Varner, R. (1982). Measurement assurance for dimensional measurements on integrated-circuit photomasks. NBS Technical Note 1164. US Department of Commerce, Washington, D.C.

Erginel, N. (2008). Fuzzy individual and moving range control charts with ?-cuts. Journal of Intelligent & Fuzzy Systems, 19, 373–383.

Eyvazian, M., Noorossana, R., Saghaei, A. & Amiri, A. (2011). Phase II monitoring of multivariate multiple linear regression profiles. Quality and Reliability Engineering International, 27(3), 281-296.

Gupta, S., Montgomery, D. C. & Woodall, W. H. (2006). Performance Evaluation of Two Methods for Online Monitoring of Linear Calibration Profiles. International journal of Production Research, 44, 1927-1942.

Hojati, M., Bector, C.R. & Smimou, K. (2005), A Simple method for computation of fuzzy linear regression. European Journal Of Operational Research, 166(1), 172-184.

Hosseinifard, S.Z., Abdollahian, M. & Zeephongsekul, P. (2011). Application of artificial neural networks in linear profile monitoring. Expert Systems with Applications, 38(5), 4920-4928.

Jensen, W. A., Birch, J. B. & Woodall, W. H. (2008). Monitoring Correlation Within Linear Profiles Using Mixed Models. Journal of Quality Technology, 40, 167-183.

Kang, L. & Albin, S. L. (2000). On-Line Monitoring When the Process Yields a Linear Profile. Journal of Quality Technology, 32, 418-426.

Kim, K., Mahmoud, M.A. & Woodall, W. H. (2003). On the monitoring of linear profiles. Journal of Quality Technology, 35, 317-328.

Mahmoud, M.A., Parker, P.A., Woodall, W.H. & Hawkins, D.M. (2007). A change point method for linear profile data. Quality and Reliability Engineering International, 23(2), 247–268.

Mahmoud, M. A. & Woodall, W. H. (2004). Phase I monitoring of linear profiles with calibration application. Technometrics, 46, 380-391.

Montgomery, D.C. (2005). Introduction to statistical quality control. Wiley, New York.

Noorossana, R., Eyvazian, M., Amiri, A. & Mahmoud M. A. (2010). Statistical Monitoring of Multivariate Multiple Linear Regression Profiles in Phase I with Calibration Application. Quality and Reliability Engineering International, 26(3), 291-303.

Noorossana, R., Eyvazian, M. & Vaghefi, S. A. (2010). Phase II monitoring of multivariate simple linear profiles. Computers and Industrial Engineering, 58, 563-570.

Noorossana, R., Vaghefi, A. & Dorri, M. (2011). Effect of non-normality on the monitoring of simple linear profiles. Quality and Reliability Engineering International, 27(4), 425–436.

Noorossana, R., Amiri, A. , Vaghefi, S. A. & Roghanian, E. (2004). Monitoring Quality Characteristics Using Linear Profile. Proceedings of the 3rd International Industrial Engineering Conference, Tehran, Iran, 246-255.

Noorossana, R. Amiri & A. Soleimani, P. (2008). On the Monitoring of Auto-correlated Linear Profiles. Communications in Statistics, Theory and Methods, 37, 425-442.

Noorossana, R., Eyvazian, M. & Vaghefi, A. (2011). Phase II monitoring of multivariate simple linear profiles. Quality and Reliability Engineering International, 27(3), 281-296.

Noorossana, R., Eyvazian, M., Amiri, A. & Mahmoud, M.A. (2010). Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application. Quality and Reliability Engineering International, 26(3), 291-303.

Ozelkan, E.C. & Duckstein, L. (2000), Multi-objective fuzzy regression: A general framework. Computers and Operation Research, 27, 635-652.

Saghaei, A., Mehrjoo M. & Amiri A. (2009). A CUSUM-based method for monitoring simple linear profiles. International Journal of Advanced Manufacturing Technology, 45,1252–1260.

Savic, D.A. & Pedrycz, W. (1991). Evaluation of fuzzy linear regression models. Fuzzy Sets and Systems, 39, 51-63.

Sridevi, B. & Nadarajan, R. (2009). Fuzzy Similarity Measure for Generalized Fuzzy Numbers. International Journal of Open Problems in Computer Science and Mathematics, 2(2), 240-253.

Tanaka, H., Uejima, S. & Asai, K. (1982). Linear regression analysis with fuzzy model. IEEE Transactions Systems, Man, and Cybernetics, 12, 903-907.

Walker, E. & Wright, S. (2002). Comparing Curves Using Additive Models. Journal of Quality Technology, 34, 118-129.

Wang, H.F. & Tsaur, R.C. (2000 a). Insight of a fuzzy regression model. Fuzzy Sets and Systems, 112, 355–69.

Wang, H.F. & Tsuar, R.C. (2000 b). Resolution of fuzzy regression model. European Journal of Operational Research, 126, 637–50.

Zhang, J., Li, Z. & Wang, Z. (2009). Control Chart Based on Likelihood Ratio for Monitoring Linear Profiles. Computational Statistics and Data Analysis, 53, 1440-1448.

Zhu, J. & Lin, D.K.J. (2010). Monitoring the Slopes of Linear Profiles. Quality Engineering, 22(1), 1-12.

Zou, C., Zhang, Y. & Wang, Z. (2006). Control Chart Based on Change-Point Model for Monitoring Linear Profiles. IIE Transactions, 38, 1093-1103.

Zou, C., Ning, X. & Tsung, F. (2012). LASSO-based multivariate linear profile monitoring. Annals of Operations Research, 192(1), 3-19.