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Lifetime performance evaluation and analysis model of passive component capacitor products

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.

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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

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Correspondence to Chun-Min Yu.

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Chen, KS., Yu, CM. Lifetime performance evaluation and analysis model of passive component capacitor products. Ann Oper Res (2021). https://doi.org/10.1007/s10479-021-04242-6

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Keywords

  • Capacitor
  • Relative lifetime performance index
  • Reliability function
  • Confidence interval
  • Fuzzy testing