 |
 |
 |
 |
 |
 |
Sains Malaysiana 53(4)(2024):
http://doi.org/10.17576/jsm-2024-5304-15
Dual Response Surface Optimization Based on Skill
Scores
(Pengoptimuman Permukaan Tindak Balas Dwi Berdasarkan Skor Kemahiran)
AGAH KOZAN, MELIS ZEYBEK
& ELIF KOZAN*
Department
of Statistics, Faculty of Science, Ege University,
Turkey
Diserahkan: 12 April 2023/Diterima: 14 Mac 2024
Abstract
The popular formulations of dual-response
optimization are
constructed on minimizing a function of bias and
system variability. This study provides an opportunity to evaluate the dual
response surface (DRS) problem from a different perspective by adapting two new
terms such that internal and external
quality forecasts. The background of the proposed approach focuses on
the relationship between internal and external quality forecasts and discusses
the DRS problem in regards of skill
scores by defining a model quality criterion. Skill is the relative accuracy of the
forecast and defines a correspondence between forecast of interest and
reference forecasts. The reference
forecast does not require any knowledge or modelling; thus, it is an unskilled
forecast. In this context, skill score is a measure of this relative
improvement and widely used in evaluating the performance of operational and
experimental forecasts. An alternative version of mean square error
(MSE) which is reconstructed by skill scores and model quality criterion is
proposed as an objective function for the DRS problem. Integrating the
relationship between internal and external quality forecasts into such a
response function can improve the effectiveness and cooperation of the applied
technique. The proposed approach has a flexible structure and provides decision
makers alternative solutions for different values of the model quality
criterion. The proposed procedure is discussed by conducted a simulation study
and demonstrated in an engineering process.
Keywords: Dual response
optimization; mean square error; model quality criterion; robust parameter
design; skill scores
Abstrak
Formulasi popular pengoptimuman gerak balas dual dibina untuk meminimumkan fungsi bias dan kebolehubahan sistem. Kajian ini memberi peluang untuk menilai masalah permukaan gerak balas dual (DRS) dari perspektif yang berbeza dengan menyesuaikan dua istilah baharu seperti ramalan kualiti dalaman dan luaran. Latar belakang pendekatan yang dicadangkan memfokuskan pada hubungan antara ramalan kualiti dalaman dan luaran dan membincangkan masalah DRS dalam hal skor kemahiran dengan mentakrifkan kriteria kualiti model. Kemahiran ialah ketepatan relatif ramalan dan mentakrifkan perpadanan antara ramalan kepentingan dan ramalan rujukan. Ramalan rujukan tidak memerlukan sebarang pengetahuan atau pemodelan; oleh itu, ia adalah ramalan yang tidak mahir. Dalam konteks ini, skor kemahiran adalah ukuran peningkatan relatif ini dan digunakan secara meluas dalam menilai prestasi ramalan operasi dan uji kaji. Versi alternatif bagi ralat min kuasa dua (MSE) yang dibina semula oleh skor kemahiran dan kriteria kualiti model dicadangkan sebagai fungsi objektif untuk masalah DRS. Mengintegrasikan hubungan antara ramalan kualiti dalaman dan luaran ke dalam fungsi tindak balas sedemikian boleh meningkatkan keberkesanan dan kerjasama teknik yang digunakan. Pendekatan yang dicadangkan mempunyai struktur yang fleksibel dan menyediakan penyelesaian alternatif pembuat keputusan untuk nilai yang berbeza bagi kriteria kualiti model. Prosedur yang dicadangkan dibincangkan dengan menjalankan kajian simulasi dan ditunjukkan dalam proses kejuruteraan.
Kata kunci: Kriteria kualiti model; pengoptimuman gerak balas dual; ralat min kuasa dua; reka bentuk parameter teguh; skor kemahiran
RUJUKAN
Baba, I.,
Midi, H., Ibragımov, G. & Rana, S. 2022. A
new optimization scheme for robust design modeling with unbalanced data. Sains Malaysiana 51(5): 1577-1586.
Box,
G.E.P. 1985. Discussion of “Off-line quality control, parameter design and the
Taguchi method”. Journal of Quality
Technology 17: 198-206.
Box, G.E.P.
& Draper, N.R. 1987. Empirical
Model-Building and Response Surfaces. Canada: John Wiley & Sons.
Box, G.E.P. & Wilson, K.B. 1951. On the
experimental attainment of optimum conditions. Journal of the Royal Statistical Society: Series B
(Methodological) 13(1): 1-38.
Copeland,
K.A. & Nelson, P.R. 1996. Dual response optimization via direct function
minimization. Journal of Quality
Technology 28(1): 331-336.
Del
Castillo, E. & Montgomery, D.C. 1993. A nonlinear programming solution to
the dual response problem. Journal of
Quality Technology 25: 199-204.
Del
Castillo, E., Colosimo, B.M. & Alshraideh, H. 2012. Bayesian modeling and optimization of
functional responses affected by noise factors. Journal of Quality Technology 44(2): 117-135.
Ding,
R., Lin, D.K.J. & Wei, D. 2004. Dual-response surface optimization: A
weighted MSE approach. Quality
Engineering 16(3): 377-385.
Edamo, M.L., Ukumo, T.Y., Lohani, T.K., Miranic, K.B. & Ayele, M.A.
2022(a). Flood inundation mapping under climate change scenarios in the Boyo watershed of Southern Ethiopia. Journal of Water and Climate Change 13: 3170-3178.
Edamo, M.L., Bushira, K.M., Ukumo, T.Y., Ayele, M.A., Alaro, M.A. & Borko, H.B. 2022(b). Effect of climate change on water
availability in Bilate catchment, Southern Ethiopia. Water Cycle 3: 86-99.
Gupta, H.V.,
Kling, H., Yilmaz, K.K. & Martinez, G.F. 2009. Decomposition of the mean
squared error and NSE performance criteria: Implications for improving
hydrological modelling. Journal of
Hydrology 377: 80-91.
Iqbal, A., Mondal, M.S., Khan, M.S.A., Hakvoort,
H. & Veerbeek, W. 2022. Flood propagation
processes in the Jamuna River Floodplain in Sirajganj. In Water Management: A View from
Multidisciplinary Perspectives, edited by Tarekul Islam, G.M., Shampa, S. & Chowdhury, A.I.A. Springer. pp. 45-67.
Kim,
K.J. & Lin, D.K.J. 1998. Dual response surface optimization: A fuzzy
modeling approach. Journal of Quality
Technology 30: 1-10.
Kim,
Y.J. & Cho, B.R. 2002. Development of priority-based robust design. Quality Engineering 14: 355-363.
Köksoy, O. 2006. Multiresponse robust design: Mean
square error (MSE criterion). Applied
Statistics and Computation 175: 1716-1729.
Köksoy, O. & Doganaksoy, N. 2003. Joint
optimization of mean and standard deviation in response surface
experimentation. Journal of Quality
Technology 35(3): 239-252.
Köksoy, O. & Fan, S.S. 2012. An upside-down normal loss function-based
method for quality improvement. Engineering
Optimization 44(8): 935-945.
Köksoy, O. & Yalcinoz, T. 2006. Mean square
error criteria to multi-response process optimization by a new genetic
algorithm. Applied Mathematics and
Computation 175: 1657-1674.
Lin,
D.K.J. & Tu, W. 1995. Dual response surface. Journal of Quality Technology 27(1):
34-39.
Li, H.,
Jiang, C., Choy, S., Wang, X., Zhang, K. & Zhu, D.A. 2022. Comprehensive
study on factors affecting the calibration of potential evapotranspiration
derived from the Thornthwaite Model. Remote Sensing 14(18): 4644.
Lizotte, D.J.,
Greiner, R. & Schuurmans, D. 2012. An
experimental methodology for response surface optimization methods. Journal of Global Optimization 52(4):
698-736.
Midi, H.
& Aziz, N.A. 2019. High breakdown estimator for dual response optimization
in the presence of outliers. Sains Malaysiana 48(8):
1771-1776.
Murphy, A.H.
1988. Skill scores based on the mean square error and their relationships to
the correlation coefficient. Monthly
Weather Review 116: 2417-2424.
Murphy, A.H.
1993. What is a good forecast? An essay on the nature of goodness in weather
forecasting. Weather and Forecasting 8: 281-293.
Mushore, T.D., Mutanga, O. & Odindi, J.
2022. Estimating urban LST using multiple remotely sensed spectral indices and
elevation retrievals. Sustainable Cities and Society 78: 103623.
Nash, J.E.
& Sutcliffe, J.V. 1970. River flow forecasting through conceptual models.
Part I: A discussion of principles. Journal
of Hydrology 10: 282-290.
Nosratpour, R., Rahimzadegan, M. & Beikahmadi,
N. 2022. Introducing a merged precipitation satellite model using satellite
precipitation products, land surface temperature, and precipitable water vapor. Geocarto International 37(26): 11782-11812.
Park, C.
& Cho, B.R. 2003. Development of robust design under contaminated and
non-normal data. Quality Engineering 15(3): 463-469.
Robinson,
T.J., Wulff, S.S., Montgomery, D.S. & Khuri, A.I. 2006. Robust parameter design using generalized
linear mixed models. Journal of Quality
Technology 38: 65-75.
Shaibu, A.B. & Cho, B.R. 2009. Another view of dual response surface
modeling and optimization in robust parameter design. The International Journal of Advanced Manufacturing Technology 41:
631-641.
Shin,
S. & Cho, B.R. 2005. Bias-specified robust design optimization and
analytical solutions. Computers &
Industrial Engineering 48: 129-148.
Steenackers, G. & Guillaume, P. 2008. Bias-specified robust design
optimization: A generalized mean squared error approach. Computers & Industrial Engineering 54: 259-268.
Şen, Z. 2021. Model efficiency performance assessment
through a standard triangular diagram (STD). Modeling Earth Systems and Environment 7: 1193-1205.
Taguchi,
G. 1986. Introduction to Quality
Engineering: Designing Quality into Products and Processes. New York: Kraus
International Publications.
Tang,
L.C. & Xu, K. 2002. A unified approach for dual response surface
optimization. Journal of Quality
Technology 34(4): 437-447.
Truong,
N.K.V. & Shin, S. 2012. Development of a new robust design method based on
Bayesian perspectives. International
Journal of Quality Engineering and Technology 3(1): 50-78.
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.
Weglarczyk, S. 1998.
The interdependence and application of some statistical quality measures for
hydrological models. Journal of Hydrology 206: 98-103.
Wheatcroft, E. 2019.
Interpreting the skill score form of forecast performance metrics. International
Journal of Forecasting 35(2): 573-579.
Zeybek, M. 2020.
Interval robust design under contaminated and non-normal data, Communications in Statistics - Theory and
Methods 49: 5406-5418.
Zeybek, M. & Köksoy, O. 2020. The effects of gamma noise on quality
improvement. Communications in Statistics
– Simulation and Computation 49(7): 1783-1797.
Zeybek, M. 2018.
Nash-Sutcliffe efficiency approach for quality improvement. Journal of Applied Mathematics and Computation 2(11): 496-503.
Zeybek, M. & Köksoy, O. 2016. Optimization of correlated multi-response
quality engineering by the upside-down normal loss function. Engineering Optimization 48(8):
1419-1431.
Zeybek, M., Köksoy, O. & Robinson, T.J. 2020. A dual‐response
surface modeling approach for gamma robust design. Quality and Reliability Engineering International 36(3): 315-327.
*Pengarang untuk surat-menyurat;
email: elif.kozan@ege.edu.tr
|
|||
|
