Skip to main content

Advertisement

SpringerLink
Log in

Lifetime performance evaluation and analysis model of passive component capacitor products

  • S.I.: Reliability Modeling with Applications Based on Big Data
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

With the rise of the semiconductor industry, passive components have become a foundation of the electronics industry and propelled the development of peripheral equipment and industries. This paper focused on improving the lifetime performance of products to increase product value and achieve the green production goals of energy conservation and waste reduction. We first established a relative lifetime performance index for passive component capacitors. Next, we derived the cumulative distribution function and reliability function based on the probability density function of relative lifetime to investigate the properties of the relative lifetime performance index. The results indicated that the reliability increased with the index value and that the probability of the product lifetime exceeding the minimum requirement also increased with the index value. Due to the fact that the index contains unknown parameters, using point estimates to estimate product lifetime performance may lead to misjudgment caused by sampling errors. For this reason, we propose a uniformly minimum-variance unbiased estimator for the index and derived its probability density function. In addition, we establish a fuzzy testing model based on the confidence interval to determine whether the lifetime performance of a product reaches the required performance level. Finally, we present a numerical example of passive components to demonstrate application of the proposed model. This example further demonstrates how the proposed model improves product lifetime performance, which in turn increases product value and also achieves the green objectives of energy conservation and waste reduction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Abbreviations

T:

The lifetime of electronic component

\({f_T}(t)\) :

Probability density function of \(T\)

\({C_L}\) :

The lifetime performance index

L:

The minimum required unit of time for the lifetime

\(\lambda \) :

Average component lifetime

X:

Relative lifetime

UMVUE:

Uniformly minimum variance unbiased estimator

\({\theta_L}\) :

The relative life time performance index

\({f_X}(x)\) :

The probability density function of X

\({r_X}(x)\) :

Failure rate

\({R_X}(x)\) :

The reliability function of \(X\)

\({F_X}(x)\) :

The cumulative distribution function of \(X\)

\({p_r}\) :

Product reliability

\(\theta_L^*\) :

The unbiased estimator of \({\theta_L}\)

\({\phi_{X_j}}(t)\) :

The characteristic function of \({X_j}\)

\({f_{X_j}}({x_j})\) :

One-parameter exponential type probability density function of \({X_j}\)

\({f_Y}(y)\) :

Probability density function of \(\theta_L^*\)

\(L{\theta_L}\) :

Lower confidence limit of \({\theta_L}\)

\({\theta_L}\) :

Upper confidence limit of \({\theta_L}\)

\(l{\theta_L}\) :

The length of the confidence intervals for \({\theta_L}\)

\(E\left( {l{\theta_L}} \right)\) :

The expected value of \(l{\theta_L}\)

n:

Sample size

\({H_0}\) :

Null hypothesis

\({H_1}\) :

Alternative hypothesis

k:

Required level

\({C_0}\) :

Critical value

\(\beta \) :

Significance level

\(\tilde \theta_L^*\) \(\left[ \alpha \right]\) :

The \(\alpha {\text{-cuts}}\) of triangular shaped fuzzy number \(\tilde \theta_L^*\)

\(\tilde \theta^{\prime *}_L\) :

The new triangular shaped fuzzy number of \(\theta_L^*\)

\(\eta (x)\) :

The membership function of \(\tilde \theta^{\prime *}_L\)

\({\tilde C_0}\) \(\left[ \alpha \right]\) :

The \(\alpha {\text{-cuts}}\) of triangular shaped fuzzy critical value number \({\tilde C_0}\)

\({\tilde C_0}\) :

The triangular shaped fuzzy number of \({C_0}\)

\(\eta ^{\prime}(x)\) :

The membership function of fuzzy number \(\tilde {C_0}\)

\({A_T}\) :

The area under the graph of \(\eta (x)\)

\({A_{Tj}}\) :

jth block of \({A_T}\)

\({d_j}\) :

The length d of the jth horizontal line

\({A_R}\) :

The area under the graph of \(\eta (x)\) but to the left of the vertical line \(x = {C_0}\)

\({A_{Rj}}\) :

jth block of \({A_R}\)

\({r_j}\) :

The length r of the jth horizontal line

References

  • Anderson, D. R., Sweeney, D. J., & Williams, T. A. (1990). Statistics for business and economics. West Publishing Company.

    Google Scholar 

  • Buckley, J. J. (2005). Fuzzy statistics: Hypothesis testing. Soft Computing, 9(7), 512–518.

    Article  Google Scholar 

  • Chan, L. K., Cheng, S. W., & Spiring, F. A. (1988). A new measure of process capability Cpm. Journal of Quality Technology, 20(3), 162–175.

    Article  Google Scholar 

  • Chang, P. L., & Tsai, C. T. (2002). Finding the niche position—Competition strategy of Taiwan’s IC design industry. Technovation, 22(2), 101–111.

    Article  Google Scholar 

  • Chen, K. S. (2019a). Two-tailed Buckley fuzzy testing for operating performance index. Journal of Computational and Applied Mathematics, 361, 55–63.

    Article  Google Scholar 

  • Chen, K. S. (2019b). Fuzzy testing of operating performance index based on confidence intervals. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03242-x

    Article  Google Scholar 

  • Chen, K. S. (2020). Fuzzy testing decision-making model for intelligent manufacturing process with Taguchi capability index. Journal of Intelligent & Fuzzy Systems, 38(2), 2129–2139.

    Article  Google Scholar 

  • Chen, K. S., & Chang, T. C. (2020). Construction and fuzzy hypothesis testing of Taguchi Six Sigma quality index. International Journal of Production Research, 58(10), 3110–3125.

    Article  Google Scholar 

  • Chen, K. S., & Yang, C. M. (2018). Developing a performance index with a Poisson process and an exponential distribution for operations management and continuous improvement. Journal of Computational and Applied Mathematics, 343, 737–747.

    Article  Google Scholar 

  • Chen, K. S., & Yu, C. M. (2020). Fuzzy test model for performance evaluation matrix of service operating systems. Computers & Industrial Engineering, 140, 106240.

    Article  Google Scholar 

  • Chen, K. S., Chen, H. T., & Chang, T. C. (2017). The construction and application of Six Sigma quality indices. International Journal of Production Research, 55(8), 2365–2384.

    Article  Google Scholar 

  • Chen, K. S., Wang, C. C., Wang, C. H., & Huang, C. F. (2010). Application of RPN analysis to parameter optimization of passive components. Microelectronics Reliability, 50(12), 2012–2019.

    Article  Google Scholar 

  • Chen, K. S., Wang, C. H., & Tan, K. H. (2019a). Developing a fuzzy green supplier selection model using Six Sigma quality indices. International Journal of Production Economics, 212, 1–7.

    Article  Google Scholar 

  • Chen, K. S., Wang, C. H., Tan, K. H., & Chiu, S. F. (2019b). Developing one-sided specification Six-Sigma fuzzy quality index and testing model to measure the process performance of fuzzy information. International Journal of Production Economics, 208, 560–565.

    Article  Google Scholar 

  • Dharmasena, L. S., & Zeephongsekul, P. (2016). A new process capability index for multiple quality characteristics based on principal components. International Journal of Production Research, 54(15), 4617–4633.

    Article  Google Scholar 

  • Elsayed, E. A. (2012). Overview of reliability testing. IEEE Transactions on Reliability, 61(2), 282–291.

    Article  Google Scholar 

  • Gu, K., Jia, X., Liu, H., & You, H. (2015). Yield-based capability index for evaluating the performance of multivariate manufacturing process. Quality and Reliability Engineering International, 31(3), 419–430.

    Article  Google Scholar 

  • Huang, C. F. (2019). Evaluation of system reliability for a stochastic delivery-flow distribution network with inventory. Annals of Operations Research, 277(1), 33–45.

    Article  Google Scholar 

  • Huang, C. F., Chen, K. S., Sheu, S. H., & Sheu, T. S. (2010). Enhancement of axle bearing quality in sewing machines using six sigma. Proceedings of the Institution of Mechanical Engineers Part B - Journal of Engineering Manufacture, 224(10), 1581–1590.

    Article  Google Scholar 

  • Huang, C. F., Huang, D. H., & Lin, Y. K. (2020). System reliability analysis for a cloud-based network under edge server capacity and budget constraints. Annals of Operations Research. https://doi.org/10.1007/s10479-020-03851-x

    Article  Google Scholar 

  • Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41–52.

    Article  Google Scholar 

  • Kargar, M., Mashinchi, M., & Parchami, A. (2014). A bayesian approach to capability testing based on Cpk with multiple samples. Quality and Reliability Engineering International, 30(5), 615–621.

    Article  Google Scholar 

  • Kai, S., & Jin, W. (2019). Semiconductor chip’s quality analysis based on its high dimensional test data. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03240-z

    Article  Google Scholar 

  • Keller, G., Warrack, B., & Bartel, H. (1994). Statistics for management and economics. Duxbury Press.

    Google Scholar 

  • Lin, K. P., Yu, C. M., & Chen, K. S. (2019a). Production data analysis system using novel process capability indices- based circular economy. Industrial Management & Data Systems, 119(8), 1655–1668.

    Article  Google Scholar 

  • Lin, Y. K., Zuo, M. J., & Pham, H. (2019b). Preface: Reliability and quality management in stochastic systems. Annals of Operations Research. https://doi.org/10.1007/s10479-019-03197-z

    Article  Google Scholar 

  • Tong, L. I., Chen, K. S., & Chen, H. T. (2002). Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution. International Journal of Quality & Reliability Management, 19(7), 812–824.

    Article  Google Scholar 

  • Tseng, M. L., Chiang, J. H., & Lan, L. W. (2009). Selection of optimal supplier in supply chain management strategy with analytic network process and choquet integral. Computer & Industrial Engineering, 57(1), 330–340.

    Article  Google Scholar 

  • Tung, A. C. (2001). Taiwan’s semiconductor industry: What the state did and did not. Review of Development Economics., 5(2), 266–288.

    Article  Google Scholar 

  • Wu, S. F., & Chiu, C. J. (2014). Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution based on the multiply type II censored sample. Journal of Statistical Computation and Simulation, 84(10), 2106–2122.

    Article  Google Scholar 

  • Yu, C. M., Luo, W. J., Hsu, T. H., & Lai, K. K. (2020). Two-tailed fuzzy hypothesis testing for unilateral specification process Quality Index. Mathematics, 8, 2129.

    Article  Google Scholar 

Download references

Author information

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, 41170, Taiwan, ROC

    Kuen-Suan Chen & Chun-Min Yu

  2. Department of Business Administration, Chaoyang University of Technology, Taichung, 41349, Taiwan, ROC

    Kuen-Suan Chen

  3. Institute of Innovation and Circular Economy, Asia University, Taichung, 41354, Taiwan, ROC

    Kuen-Suan Chen

Authors
  1. Kuen-Suan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-Min Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun-Min Yu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, KS., Yu, CM. Lifetime performance evaluation and analysis model of passive component capacitor products. Ann Oper Res 311, 51–64 (2022). https://doi.org/10.1007/s10479-021-04242-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-021-04242-6

Keywords

Search

Navigation