基于主成分分析的函数型产品质量特性的优化方法研究

摘要/Abstract

摘要：

针对质量特性为轮廓（Profile）的输出响应的优化问题展开研究，提出一种基于主成分分析的双响应曲面法和满意度函数相结合的函数响应优化方法。将Profile的每个观测点看成一个独立响应，将Profile问题转化为多响应问题。求得多个观测点的均值和方差的满意度函数值，通过主成分分析法，将多个观测点的均值和方差的满意度函数值转化为主成分综合得分，并将这两者的加权和作为最终的优化指标。本文所提方法可以有效解决观测点之间存在的相关性的问题，并且优化过程同时考虑到每个观测点响应的均值和方差影响。实例证明，该方法简单易行，优化结果满意。

关键词: 函数响应, 主成分分析, 双响应曲面法, 满意度函数

Abstract:

A method is presented to optimize the profile based on functional response optimization method combining the dual response surface method with the satisfaction function based on principal component analysis. The response value of each observation point is treated as an independent response. The Profile has been as multiresponse optimization problem of nominalthebest type. First, desirability function is used to measure the mean and variance for each observed point. Finally, the principal component analysis (PCA) is adopted to derive the overall performance index (OPI) for multiple response which is the weighted sum of principal values of both the desirability values of mean and variance for each observed point. A methodology is utilized for optimizing the problem of correlated observed points while involving the simultaneous optimization of the process mean and variance. Examples show that the method is simple, with satisfactory optimization results.

Key words: functional response, principal component analysis, dual response surface method, desirability function approach

许静, 何桢, 陈喆芝, 袁蓉. 基于主成分分析的函数型产品质量特性的优化方法研究[J]. 工业工程.

XU Jing HE Zhen CHEN Zhezhi YUAN Rong. A Study of Optimizing Functional Response Problems Based on Principal Component Analysis[J]. Industrial Engineering Journal .

参考文献

1］MONTGOMERY D C. Design and Analysis of Experiments［M］.John Wiley & Sons，2009.
［2］FOGLIATTO F S.Multiresponse optimization of products with functional quality characteristics［J］.Quality and Reliability Engineering International,2008,24(8):927-939.
［3］GELFAND I M，FOMIN S V .Calculus of variations.Englewood Cliffs，NJ：Prentice Hall，1963.
［4］TAGUCHI G．Introduction to Quality Engineering： Designing Quality into Products and Processes［M］. Tokyo：Asian Productivity Organization，1986.
［5］MILLER A.Analysis of parameter design experiments for signal-response systems［J］. Journal of Quality Technology，2002，34(2)： 139-151.
［6］MCCASKEY S D，TSUI K L.Analysis of functional response design experiments［J］.International Journal of Quality Technology，1997，35（6）：1561-1574.
［7］MILLER A， WU C F J.Parameter design for signalresponse systems：a different look at taguchi′s dynamic parameter design［J］. Statistical Science，1996，11(2)： 122-136.
［8］WU C F J，HAMADA M. Experiments，Planning， Analysis and Parameter Design Optimization［M］.New York，NY：John Wiley & Sons，2000.
［9］DIGGLE P, HEAGERTY P, LIANG KY, Zeger S. Analysis of Longitudinal Data［M］. Oxford University Press: London, UK, 2013:5.
［10］FAN J, ZANG J T. Twostep estimation of functional linear models with application to longitudinal data［J］. Journal of the Royal Statistical Society, Series B: Statistical Methodology 2000; 62:303-322. DOI: 10.1111/1467-9868.002336.
［11］FITZMAURICE G M，LAIRD N M，WARE J H.Applied Longitudinal Analysis［M］. Hoboken，NJ：John Wiley & Sons，2004.
［12］KIM K, MAHMOUD MA, WOODALL WH. On the monitoring of linear profiles［J］. Journal of Quality Technology 2003; 35(3):317-328.
［13］QIU P, ZOU C, WANG Z. Nonparametric profile monitoring by mixed effects modeling［J］. Technometrics 2010; 52:265277. DOI: 10.1198/TECH.2010.08188
［14］NOOROSSANA R, SAGHAEI A, AMIRI A. Statistical Analysis of Profile Monitoring［J］. John Wiley & Sons: Hoboken, NJ, 2011.

［15］NAIR V N，TAM W ，YE K Q. Analysis of functional responses from robust design studies［J］.Journal of Quality Technology，2002，34（4):355-370.
［16］PEARSON K. On lines and planes of closes fit to a systems of points in space［J］.Philosophica Magazine,1901,2(11): 559-572.
［17］HOTELLING H .Analysis of a complex of statistical varia-bles into principal components［J］.Journal of Educational Psyc-hology, 1933,24(6):417-414.
［18］LIAO H C.Multiresponse optimization using weighted pri-ncipal component［J］.The International Journal of Adva-nced Manufacturing Technology,2006,27(7):720-725.
［19］DERRINGER G C,SUICH R.Simultaneous optimization of sev- eral response variables［J］.Journal of Quality Technology, 1980,12(4):214-219.
［20］MYERS R H, CARTER W H.Response surface techniques for dual response systems［J］. Technometrics,1973,15(2):301-317.
［21］VINING G G,MYERS R H.Combining taguchi and response surface philosophies:a dual response approach［J］. Journal of Quality Technology, 1990,22(1):38-45.
［22］LIND K J,TU W.Dual response surface optimization［J］.Jo- urnal of quality Technology,1995,27(1):34-39.
［23］KAREN A F C,NELSON P P.Dual response optimization via direct function minimization［J］. Journal of Quality Tech-nology,1996,28(2):34-38.
［24］QUESADA G M,CASTILLO E D,PETERSON J J. A Bayesian app-roach for multiple response surface optimization in the p-resence of noise variables.Journal Applied Statistics, 2004, 31(3):251-270.
［25］HE Zhen,WANG Jing,PARK S H.Robust optimization for m- ultiple responses using response surface methodology［J］. Applied Stochastic Models in Business and Industry,2010, 26(2):157-171.
［26］杨方,高齐圣,于增顺.多响应问题的稳健性设计优化［J］. 工业工程,2010,13（3）:43-46.
YANG Fang, GAO Qiaheng, YU Zengshun.Robust design optimization of multi-response proplems［J］.Industrial Engineering Journal,2010,13(3):43-46.
［27］GOHEL M,AMIN A.Formulation optimization of controlled release diclofenac Sodium microspheres using factorial d-esign［J］.Journal of controlled release,1998,51(2/3):115-122.
［28］GOETHALS P,ARAGON L,CHO B R.Experimenta investigations of estimated response surface function with different mea- sures.International Journal of Experimental Design and P-rocess Optimization,2009,1(2/3):123-163.

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