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Confidence-interval-based fuzzy supplier selection model with lifetime performance index

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Abstract

An electronic product usually contains numerous electronic components. To improve market competitiveness and operational flexibility, the electronics industry has begun to outsource electronic components. To help firms ensure that the lifetimes of procured electronic components meet market needs, this study proposes a fuzzy supplier selection model based on the confidence interval of the lifetime performance index proposed by (Chen and Yu, Annals of Operations Research 311:51–64, 2022). Under the assumption that the lifetime of an electronic component follows an exponential distribution, we derive the confidence intervals of the lifetime performance index for each supplier and use the confidence intervals of various suppliers to construct a fuzzy membership function. We propose a model based on this function to identify the optimal supplier. The fuzzy test incorporates historical data and expert experience to maintain evaluation accuracy in cases of small sample sizes. A numerical example is provided to demonstrate the efficacy of this method.

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Abbreviations

\(T_{h}\) :

Lifetime

h :

Supplier

\(\lambda_{h}\) :

The mean time between failures (MTBF)

\(\theta_{Lh}\) :

Lifetime performance index

L :

Warranty period

\(X_{h}\) :

Relative lifetime

\(f_{{X_{h} }} (x)\) :

Probability density function

\(r_{{X_{h} }} (x)\) :

Failure rate

\(p_{rh}\) :

Product reliability

\(R_{{X_{h} }} (x)\) :

Reliability function of relative lifetime \(X_{h}\)

\(\theta_{Lh}^{*}\) :

Unbiased estimator of index \(\theta_{Lh}\)

\(M_{{X_{h} }} (\tau )\) :

Moment-generating function of \(X_{h,j}\)

\(M_{{\sum\nolimits_{j = 1}^{n} {X_{h,j} } }} (\tau )\) :

Moment-generating function of \(\sum\nolimits_{j = 1}^{n} {X_{h,j} }\)

\(W_{h}\) :

\(n\theta_{Lh}^{*} /\theta_{Lh}\)

\(f_{{W_{h} }} (w)\) :

Probability density function of \(W_{h}\)

\(GAMINV\left( {\alpha^{\prime},n,1} \right)\) :

The lower \(\alpha^{\prime}\) quantile of \(G(n,1)\), where \(\alpha^{\prime} = \alpha /2\) or \(\alpha^{\prime} = 1 - \alpha /2\)

\(1 - \alpha\) :

Confidence level

\(L\theta_{Lh}\) :

Lower confidence interval limit

\(U\theta_{Lh}\) :

Upper confidence interval limit

n:

Sample size

\(\theta_{Lh0}^{ * }\) :

Observed value of \(\theta_{Lh}^{ * }\)

\(\sum\nolimits_{j = 1}^{n} {x_{h,j} }\) :

Observed values of \(\sum\nolimits_{j = 1}^{n} {X_{h,j} }\)

\(L\theta_{Lh0}\) :

Observed values of \(L\theta_{Lh}\)

\(U\theta_{Lh0}\) :

Observed values of \(U\theta_{Lh}\)

\(l\theta_{Lh0}\) :

The length of \(1 - \alpha\) confidence level \(\left[ {L\theta_{Lh0} \left( n \right),U\theta_{Lh0} \left( n \right)} \right]\)

\(\left[ {L\theta_{Li0} \left( n \right),U\theta_{Li0} \left( n \right)} \right]\) :

The confidence interval for the lifetime performance index of supplier i

\(\left[ {L\theta_{Lj0} \left( n \right),U\theta_{Lj0} \left( n \right)} \right]\) :

The confidence interval for the lifetime performance index of supplier j

\(\tilde{\theta }_{Lh0}^{*} \left[ \alpha \right]\) :

The \(\alpha {\text{ - cuts}}\) of triangular fuzzy number \(\tilde{\theta }_{Lh0}^{*}\) with \(\left[ {L\theta_{Lh0} ,U\theta_{Lh0} } \right]\)

\(\tilde{\theta }_{Lh0}^{*}\) :

The triangular fuzzy number of \(\theta_{Lh0}^{*}\)

\(\eta_{h} (x)\) :

The membership function of \(\tilde{\theta }_{Lh0}^{*}\)

\(PROBGAM\left( { \cdot ,n,1} \right)\) :

The cumulative function of gamma distribution

\(A_{Tj}\) :

The area between membership function \(\eta_{j} (x)\) and the x axis

\(A_{ij}\) :

The area under the graph of \(\eta_{j} (x)\) to the left of the vertical line \(x = c_{ij}\)

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Acknowledgements

The earlier version of this paper was presented at the 27th ISSAT International Conference on Reliability and Quality in Design (RQD), August 4-6, 2022, held in Virtual Conference. The author would like to thank the Editor, Hoang Pham, and anonymous referees for their helpful comments and careful reading, which significantly improved this paper. This work was supported by the National Science and Technology Council, Taiwan, Republic of China, Under Grant No. MOST 110-2622-E-167-011 and MOST 110-2222-E-167-005.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chin-Yi University of Technology, No.57, Sec. 2, Zhongshan Rd., Taiping Dist, Taichung, 411030, Taiwan, ROC

    Kuen-Suan Chen & Chun-Min Yu

  2. Department of Business Administration, Chaoyang University of Technology, Taichung, 413310, Taiwan, ROC

    Kuen-Suan Chen

  3. Department of Business Administration, Asia University, Taichung, 413305, Taiwan, ROC

    Kuen-Suan Chen

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  1. Kuen-Suan Chen
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Correspondence to Chun-Min Yu.

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Chen, KS., Yu, CM. Confidence-interval-based fuzzy supplier selection model with lifetime performance index. Ann Oper Res (2023). https://doi.org/10.1007/s10479-023-05566-1

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