Optimization of experiments where some responses are profiles. (Otimização de experimentos com variáveis de resposta descritas por perfis.) (Portuguese. English summary) Zbl 1257.90114
Summary: In multiresponse experiments (MREs) the same experimental unit is evaluated with respect to more than one response simultaneously. Optimization of MREs involves determining the point in the design region where responses perform best with respect to given criteria. Utility functions are used to transform responses outcomes at each experimental treatment into performance measures. In this paper, we investigate MREs where some response outcomes are profiles rather than individual values. A functional response gives one or more profiles as observed outcomes at each experimental treatment, and the objective is to identify the outcome that is closest to a target profile. We propose the use of the Hausdorff Distance, a similarity metric from the field of image recognition, in combination with a desirability function to obtain a utility function that gives the distance of a functional response outcome to its desired target.
References:
| [1] | Antony J., Multiple response optimization using Taguchi methodology and neuro-fuzzy based model, Journal of Manufacturing Technology Management 17 (7) pp 908– (2006) · doi:10.1108/17410380610688232 |
| [2] | Belogay E., Calculating the Hausdorff distance between curves, Information Processing Letters 64 pp 17– (1997) · Zbl 1337.68265 · doi:10.1016/S0020-0190(97)00140-3 |
| [3] | Berni R., Planning and Optimization of a Numerical Control Machine in a Multiple Response Case, Quality and Reliability Engineering International 22 pp 517– (2006) · doi:10.1002/qre.758 |
| [4] | Biles W.E., A response surface method for experimental optimization of multiresponse processes, Industrial Engineering Chemistry, Process Design and Development 14 pp 152– (1975) · doi:10.1021/i260054a010 |
| [5] | Cardot H., Functional linear model, Statistics & Probability Letters 45 pp 11– (1999) · Zbl 0962.62081 · doi:10.1016/S0167-7152(99)00036-X |
| [6] | Castagliola P., Monitoring of Batch Processes with Varying Durations Based on the Hausdorff Distance, International Journal of Reliability, Quality and Safety Engineering 13 (3) pp 213– (2006) · doi:10.1142/S0218539306002227 |
| [7] | Ch’ng C.K., Index in multiresponse optimization, Quality Engineering 17 pp 161– (2005) |
| [8] | Chang S., A multiple-objective decision-making approach for assessing simultaneous improvement in die life and casting quality in a die-casting process, Quality Engineering 7 pp 371– (1994) · doi:10.1080/08982119408918790 |
| [9] | Cheng C.B., Neuro-fuzzy and genetic algorithm in multiple response optimization, Computers and Mathematics with Applications 44 pp 1503– (2002) · Zbl 1044.90094 · doi:10.1016/S0898-1221(02)00274-2 |
| [10] | Cornell J.A., Experiments with mixtures: designs, models, and analysis of mixture data (1990) · Zbl 0732.62069 |
| [11] | Del Castillo E., Modified desirability functions for multiple response optimization, Journal of Quality Technology 28 pp 337– (1996) |
| [12] | Del Castillo E., Multiresponse process optimization via constrained confidence regions, Journal of Quality Technology 28 pp 61– (1996) |
| [13] | Derringer G., Simultaneous optimization of several response variables, Journal of Quality Technology 12 pp 214– (1990) |
| [14] | Elsayed E.A., Optimal levels of process parameters for products with multiple characteristics, International Journal of Production Research 31 pp 1117– (1993) · doi:10.1080/00207549308956778 |
| [15] | Ferraty F., Nonparametric functional analysis: Theory and practice (2006) · Zbl 1119.62046 |
| [16] | Fogliatto F.S., A hierarchical approach to optimizing descriptive analysis multiresponse experiments, Journal of Sensory Studies 14 pp 443– (1999) · doi:10.1111/j.1745-459X.1999.tb00127.x |
| [17] | Fogliatto F.S., A hierarchical method for evaluating products with quantitative and sensory characteristics, IIE Transactions 33 pp 1081– (2001) · doi:10.1080/07408170108936898 |
| [18] | Fogliatto F.S., An AHP-based procedure for sensory data collection and analysis in quality and reliability applications, Food Quality & Preference 14 pp 375– (2003) · doi:10.1016/S0950-3293(03)00006-5 |
| [19] | Fogliatto F.S., Variance of predicted response as an optimization criterion in multiresponse experiments, Quality Engineering 12 pp 523– (2000) · doi:10.1080/08982110008962618 |
| [20] | Fung C.P., Multi-response optimization in friction properties of PBT composites using Taguchi method and principal components analysis, Journal of Materials Processing Technology 170 pp 602– (2005) · doi:10.1016/j.jmatprotec.2005.06.040 |
| [21] | Govaerts B., Analysing the results of a designed experiment when the response is a curve: Methodology and application in metal injection moulding, Quality and Reliability Engineering International 21 pp 509– (2005) · doi:10.1002/qre.737 |
| [22] | Harrington Jr E.C., The desirability function, Industrial Quality Control 21 pp 494– (1965) |
| [23] | Hsieh K.L., Optimization of multiple quality responses involving qualitative and quantitative characteristics in IC manufacturing using neural networks, Computers in Industry 46 pp 1– (2001) · doi:10.1016/S0166-3615(01)00091-4 |
| [24] | Huttenlocher D.P. pp 340– (1990) |
| [25] | Huttenlocher D.P., Comparing images using the Hausdorff distance, IEEE Transactions on Pattern Analysis and Machine Intelligence 15 pp 850– (1993) · doi:10.1109/34.232073 |
| [26] | Jeong M.K., Wavelet-based SPC procedure for complicated functional data, International Journal of Production Research 44 (4) pp 729– (2006) · Zbl 1095.62136 · doi:10.1080/00207540500222647 |
| [27] | Kang L., On-line monitoring when the process yields a linear profile, Journal of Quality Technology 32 (4) pp 418– (2000) |
| [28] | Khuri A.I., Simultaneous optimization of multiple responses represented by polynomial regression functions, Technometrics 23 pp 363– (1981) · Zbl 0492.62067 · doi:10.1080/00401706.1981.10487681 |
| [29] | Khuri A.I., Response Surfaces, 2. ed. (1996) · Zbl 0953.62073 |
| [30] | Kim K., On the monitoring of linear profiles, Journal of Quality Technology 35 pp 317– (2003) |
| [31] | Kim K.J., Dual response surface optimization: a fuzzy modeling approach, Journal of Quality Technology 30 pp 1– (1998) |
| [32] | Kim K.J., Optimization of multiple responses considering both location and dispersion effects, European Journal of Operational Research 169 pp 133– (2006) · Zbl 1083.90520 · doi:10.1016/j.ejor.2004.06.020 |
| [33] | Ko Y.H., A new loss function-based method for multiresponse optimization, Journal of Quality Technology 37 pp 50– (2005) |
| [34] | Kros J.F., Comparing methods for the multi-response design problem, Quality and Reliability Engineering International 17 pp 323– (2001) · doi:10.1002/qre.404 |
| [35] | Kulkarni M.S., Multiple response optimization for improved machined surface quality, Journal of Materials Processing Technology 141 pp 174– (2003) · doi:10.1016/S0924-0136(02)01017-8 |
| [36] | León N.A., A pragmatic approach to multiresponse problems using loss functions, Quality Engineering 9 pp 213– (1996) · doi:10.1080/08982119608919037 |
| [37] | León R.V., Performance measures independent of adjustment: an explanation and extension of Taguchi’s signal-to-noise ratios, Technometrics 29 pp 253– (1987) · Zbl 0664.62103 · doi:10.1080/00401706.1987.10488231 |
| [38] | Li J., Medium optimization by combination of response surface methodology and desirability function: an application in glutamine production, Appl Microbiol Biotechnol 74 pp 563– (2007) · doi:10.1007/s00253-006-0699-5 |
| [39] | Lin J.L., The use of grey-fuzzy logic in the optimization of the manufacturing process, Journal of Materials Processing Technology 160 pp 9– (2005) · doi:10.1016/j.jmatprotec.2003.11.040 |
| [40] | Lind E.E., Fitting yield and cost response surfaces, Chemical Engineering Progress 56 pp 62– (1960) |
| [41] | Logothetis N., Characterizing and optimizing multiresponse processes by the Taguchi method, Quality and Reliability Engineering International 4 pp 159– (1988) · doi:10.1002/qre.4680040211 |
| [42] | Lu D., International Journal of Production Research 40 pp 1613– (2002) · doi:10.1080/00207540210122202 |
| [43] | Manohar R.S., Effect of emulsifiers, fat level and type on the rheological characteristics of biscuit dough and quality of biscuits, Journal of the Science of Food and Agriculture 79 pp 1223– (1999) · doi:10.1002/(SICI)1097-0010(19990715)79:10<1223::AID-JSFA346>3.0.CO;2-W |
| [44] | Manteiga W.G., Statistics for functional data, Computational Statistics & Data Analysis 51 pp 4788– (2007) · Zbl 1162.62338 · doi:10.1016/j.csda.2006.10.017 |
| [45] | Montgomery D.C., Using statistically designed experiments for process development and improvement, Robotics and Computer Integrated Manufacturing 16 pp 55– (2000) · doi:10.1016/S0736-5845(99)00057-5 |
| [46] | Mukherjee I., Optimal process design of two-stage multiple responses grinding processes using desirability functions and metaheuristic technique, Applied Soft Computing 8 pp 402– (2008) · doi:10.1016/j.asoc.2007.02.005 |
| [47] | Murphy T.E., A review of robust design methods for multiple responses, Research in Engineering Design 15 pp 201– (2005) · doi:10.1007/s00163-004-0054-8 |
| [48] | Myers R.H., Response surface techniques for dual response surfaces, Technometrics 15 pp 301– (1973) · Zbl 0265.62022 · doi:10.1080/00401706.1973.10489044 |
| [49] | Myers R.H., Response surface alternatives to the Taguchi robust parameter design approach, The American Statistician 46 pp 131– (1992) |
| [50] | Myers R.H., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2. ed. (2002) · Zbl 1161.62393 |
| [51] | Nair V.N., Analysis of functional responses from robust design studies, Journal of Quality Technology 34 pp 355– (2002) |
| [52] | Ortiz F., A genetic algorithm approach to multiple-response optimization, Journal of Quality Technology 36 pp 432– (2004) |
| [53] | Pasamontes A., Optimization by means of responses surface of an analytical sequence using a sequential injection system, Talanta 68 pp 1617– (2006) · doi:10.1016/j.talanta.2005.08.033 |
| [54] | Pasandideh S.H.R., Multi-response simulation optimization using genetic algorithm within desirability function framework, Applied Mathematics and Computation 175 (1) pp 366– (2006) · Zbl 1088.65060 · doi:10.1016/j.amc.2005.07.023 |
| [55] | Pignatiello Jr J.J., Strategies for robust multiresponse quality engineering, IIE Transactions 25 pp 5– (1993) · doi:10.1080/07408179308964286 |
| [56] | Plante R.D., Process capability: a criterion for optimizing multiple response product and process design, IIE Transactions 33 pp 497– (2001) · doi:10.1080/07408170108936849 |
| [57] | Quesada G.M., A dual-response approach to the multivariate robust parameter design problem, Technometrics 46 pp 176– (2004) · doi:10.1198/004017004000000220 |
| [58] | Raiman L.B., The development and implementation of multivariate cost of poor quality loss function, IMSE Working Paper pp 92– (1992) |
| [59] | Ramsay J.O., Functional data analysis, 2. ed. (2005) · Zbl 1079.62006 |
| [60] | Ribeiro J.L., A case study on process optimization using the gradient loss function, International Journal of Production Research 33 pp 3233– (1995) · Zbl 0912.90076 · doi:10.1080/00207549508904871 |
| [61] | Ribeiro J.L., Minimizing manufacturing and quality costs in multiresponse optimization, Quality Engineering 13 pp 559– (2001) · doi:10.1080/08982110108918686 |
| [62] | Shah H.K., Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions, Quality Engineering 16 pp 387– (2004) · doi:10.1081/QEN-120027941 |
| [63] | Shen Q., Diagnostics for linear models with functional responses, Technometrics 49 (1) pp 26– (2007) · doi:10.1198/004017006000000444 |
| [64] | Siegel I.H., Index-Number Differences: Geometric Means, Journal of the American Statistical Association 37 (218) pp 271– (1942) · doi:10.1080/01621459.1942.10500636 |
| [65] | Taguchi G., Introduction to quality engineering: designing quality into products and processes (1986) |
| [66] | Tribus M., An alternative view of the Taguchi approach, Quality Progress 22 pp 46– (1989) |
| [67] | Tyan J.C., Multiple response optimization in a fully automated FAB: an integrated tool and vehicle dispatching strategy, Computers & Industrial Engineering 46 pp 121– (2004) · doi:10.1016/j.cie.2003.11.003 |
| [68] | Vining G.G., A compromise approach to multiresponse optimization, Journal of Quality Technology 30 pp 309– (1998) |
| [69] | Williams J.D., Statistical Monitoring of Nonlinear Product and Process Quality Profiles, Quality and Reliability Engineering International 23 pp 925– (2007) · doi:10.1002/qre.858 |
| [70] | Wu F.C., Optimization of correlated multiple quality characteristics using desirability function, Quality Engineering 17 pp 119– (2005) |
| [71] | Wurl R.C., A comparison of mutiresponse optimization: sensitivity to parameter selection, Quality Engineering 11 pp 405– (1999) · doi:10.1080/08982119908919257 |
| [72] | Yang Y., Solving a multiresponse simulation-optimization problem with discrete variables using a multiple-attribute decision-making method, Mathematics and Computers in Simulation 68 pp 9– (2005) · Zbl 1108.93305 · doi:10.1016/j.matcom.2004.09.004 |
| [73] | Yum B., On Parameter Design Optimization Procedures, Quality and Reliability Engineering International 7 pp 39– (1991) · doi:10.1002/qre.4680070110 |
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