Change-point analysis of the failure mechanisms based on accelerated life tests

Abstract In the accelerated life tests, the common failure mechanism is considered as a necessary condition for the extrapolated procedure. The traditional extrapolation model may become unreliable if the failure mechanisms under the accelerated stress levels are different from that under the normal operating condition. In this paper, we propose a change-point model for the coefficients of variation to fit the abrupt change behavior of the failure mechanisms with a nonparametric empirical likelihood approach. The related statistical inferences of the proposed model are studied to test whether there exists a change and estimate the corresponding location of the change. Monte Carlo simulations are conducted to investigate the performance of the proposed change-point test model. For the small sample data, a bootstrapping method is presented as an alternative detecting procedure. The detailed calculation process is illustrated by the lifetime data of the metal oxide semiconductor transistors in the power distribution system of Chinese Tiangong aircrafts.

[1]  Changliang Zou,et al.  Empirical likelihood ratio test for the change-point problem , 2007 .

[2]  Orit Shechtman,et al.  The Coefficient of Variation as an Index of Measurement Reliability , 2013 .

[3]  E. Aly,et al.  Nonparametric Tests for Comparing Several Coefficients of Variation , 2014 .

[4]  Dong Wang,et al.  EMPIRICAL LIKELIHOOD FOR ESTIMATING EQUATIONS WITH MISSING VALUES , 2009, 0903.0726.

[5]  Wanyi Huang,et al.  Constrained optimal designs for step-stress accelerated life testing experiments , 2018, 2018 IEEE 3rd International Conference on Cloud Computing and Big Data Analysis (ICCCBDA).

[6]  Mustafa Altun,et al.  A change-point based reliability prediction model using field return data , 2016, Reliab. Eng. Syst. Saf..

[7]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[8]  A. Amiri,et al.  Estimation of Change Point in Two-Stage Processes Subject to Step Change and Linear Trend , 2016 .

[9]  Arjun K. Gupta,et al.  Parametric Statistical Change Point Analysis , 2000 .

[10]  Shipra Banik,et al.  Estimating the Population Coefficient of Variation by Confidence Intervals , 2011, Commun. Stat. Simul. Comput..

[11]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[12]  Mashroor Ahmad Khan,et al.  Analysis and Optimum Plan for 3-Step Step-Stress Accelerated Life Tests with Lomax Model Under Progressive Type-I Censoring , 2018 .

[13]  Frank P. A. Coolen,et al.  An imprecise statistical method for accelerated life testing using the power-Weibull model , 2017, Reliab. Eng. Syst. Saf..

[14]  Philippe Castagliola,et al.  Run-sum control charts for monitoring the coefficient of variation , 2017, Eur. J. Oper. Res..

[15]  Suk Joo Bae,et al.  Bayesian Approach for Two-Phase Degradation Data Based on Change-Point Wiener Process With Measurement Errors , 2018, IEEE Transactions on Reliability.

[16]  W. Nelson Statistical Methods for Reliability Data , 1998 .

[17]  Zhi-Sheng Ye,et al.  Generalized Fiducial Inference for Accelerated Life Tests With Weibull Distribution and Progressively Type-II Censoring , 2016, IEEE Transactions on Reliability.

[18]  Firoozeh Haghighi,et al.  Optimal design of accelerated life tests for an extension of the exponential distribution , 2014, Reliab. Eng. Syst. Saf..

[19]  Xun Chen,et al.  Statistical Inference of Accelerated Life Testing With Dependent Competing Failures Based on Copula Theory , 2014, IEEE Transactions on Reliability.

[20]  Yincai Tang,et al.  Bayesian analysis of constant-stress accelerated life test for the Weibull distribution using noninformative priors , 2015 .

[21]  Liang Wang,et al.  Estimation of constant-stress accelerated life test for Weibull distribution with nonconstant shape parameter , 2018, J. Comput. Appl. Math..

[22]  J. Lawless,et al.  Empirical Likelihood and General Estimating Equations , 1994 .

[23]  Chenlei Leng,et al.  Penalized empirical likelihood and growing dimensional general estimating equations , 2012 .

[24]  David W. Coit,et al.  System Reliability Optimization Considering Uncertainty: Minimization of the Coefficient of Variation for Series-Parallel Systems , 2011, IEEE Transactions on Reliability.

[25]  Petr Volf,et al.  On selection of optimal stochastic model for accelerated life testing , 2014, Reliab. Eng. Syst. Saf..

[26]  Hui Xiao,et al.  Reliability of Linear Consecutive-k-Out-of-n Systems With Two Change Points , 2018, IEEE Transactions on Reliability.

[27]  Cheng Yong Tang,et al.  A new scope of penalized empirical likelihood with high-dimensional estimating equations , 2017, The Annals of Statistics.

[28]  Christel Ruwet,et al.  Multivariate coefficients of variation: Comparison and influence functions , 2015, J. Multivar. Anal..

[29]  Wei Ning,et al.  Empirical likelihood ratio test for a mean change point model with a linear trend followed by an abrupt change , 2012 .