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Data envelopment analysis approaches for solving the multiresponse problem in the Taguchi method

Published online by Cambridge University Press:  11 February 2009

Abbas Al-Refaie ,
Tai-Hsi Wu  and
Ming-Hsien Li
Abbas Al-Refaie
Affiliation:
Department of Industrial Engineering, University of Jordan, Amman, Jordan
Tai-Hsi Wu
Affiliation:
Department of Business Administration, National Taipei University, Taipei, Taiwan, Republic of China
Ming-Hsien Li
Affiliation:
Department of Industrial Engineering and Systems Management, Feng Chia University, Taichung, Taiwan, Republic of China
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Abstract

This research proposes a procedure for solving the multiresponse problem in the Taguchi method utilizing two data envelopment analysis (DEA) approaches, including comparisons of efficiency between different systems (CEBDS) and bilateral comparisons. In this procedure, each experiment in Taguchi's orthogonal array (OA) is treated as a decision-making unit (DMU) with the multiresponses as the inputs and outputs for all DMUs. For each factor of OA, the DMUs are divided into groups, each at the same factor level. Then, DMU's efficiency is separately evaluated by the CEBDS approach and the bilateral comparisons approach for each factor. The level efficiency, or the average of the efficiencies obtained by the CEBDS and the bilateral comparisons approaches for that factor level, is then used to determine the optimal factor levels for multiresponses. Three case studies are provided for illustration; in all, the proposed procedure provides the largest total anticipated improvements. Hence, it should be considered the most effective among all approaches applied in the case studies, including principal component analysis, DEA-based ranking approach, and others. In addition, the proposed procedure is more effective and requires less computational effort when the DMU's efficiency is evaluated by the bilateral comparisons approach instead of the CEBDS approach. In conclusion, the proposed procedure will provide great assistance to practitioners for solving the multiresponse problems in manufacturing applications on the Taguchi method.

Keywords

Data Envelopment AnalysisMultiresponse ProblemTaguchi Method
Type
Research Article
Information
AI EDAM , Volume 23 , Issue 2 , May 2009 , pp. 159 - 173
Copyright
Copyright © Cambridge University Press 2009

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References

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ABBREVIATIONS AND NOTATIONS

c

quality loss coefficient for NTB response

CEBDS

comparisons of efficiency between different systems

DEA

data envelopment analysis

DMU

decision making unit

DMUo

DMU to be individually evaluated on any trial be designated

E o

efficiency of DMUo

E o,k

efficiency of DMUo measured with respect to the DMUs of group k

f

number of factors to be studied in Taguchi's orthogonal array

I

index for DMU's input, that is, i = 1, … , m

j

index for a DMU, that is, j = 1, … , n

K

number of groups, that is, k = 1, … , K

L(y)

loss function for NTB response y

LTB

larger the better

n

number of experiment in OA

NTB

nominal the best

OA

orthogonal array

r

index for DMU's output, that is, r = 1, … , s

s 2

calculated replicates variance for NTB response

S/N

signal–noise ratio

STB

smaller the better

u r

rth virtual weights for the rth output

u r*

optimal value of u r

v i

ith virtual weights for the ith input

v i*

optimal value of v i

X

multidimensional input vector in CEBDS

x io

input vector of DMUo in CCR model

xo

multidimensional input vector of DMUo

Y

multidimensional output vector

y ro

rth output vector of DMUo in CCR model

yo

multidimensional output vector of DMUo

ȳ 2

average of NTB response replicates in Taguchi method

z k

binary 0–1 numbers for group k

quality loss coefficient for NTB response

comparisons of efficiency between different systems

data envelopment analysis

decision making unit

DMU to be individually evaluated on any trial be designated

efficiency of DMUo

efficiency of DMUo measured with respect to the DMUs of group k

number of factors to be studied in Taguchi's orthogonal array

index for DMU's input, that is, i = 1, … , m

index for a DMU, that is, j = 1, … , n

number of groups, that is, k = 1, … , K

loss function for NTB response y

larger the better

number of experiment in OA

nominal the best

orthogonal array

index for DMU's output, that is, r = 1, … , s

calculated replicates variance for NTB response

signal–noise ratio

smaller the better

rth virtual weights for the rth output

optimal value of u r

ith virtual weights for the ith input

optimal value of v i

multidimensional input vector in CEBDS

input vector of DMUo in CCR model

multidimensional input vector of DMUo

multidimensional output vector

rth output vector of DMUo in CCR model

multidimensional output vector of DMUo

average of NTB response replicates in Taguchi method

binary 0–1 numbers for group k