Quantile Regression Based Accelerated Life Test Analysis for Problem with Competing Risks of Failure

doi:10.3901/JME.2018.17.190

Abstract

Abstract: Based on accelerated life tests (ALT) data, inferences on quantiles of the lifetime distribution at the use condition are obtained via an assumption of a specific working model. But in engineering practice, model misspecification can result in significant estimation bias. In order to solve this problem, a statistical analysis approach based on quantile regression is proposed to estimate quantiles of the lifetime distribution with competing causes of failure. Quantile regression is distribution-free and more flexible in modeling life-stress relations. Full consideration is given to the incompleteness of test data, which is due to Type-Ⅱ progressive censoring as well as competing risks. The martingales based on cause specific hazards are used to construct unbiased estimating equations for the quantile regression model, and the solution of equations is equivalent to search for minimizations of convex functions. By using perturbation resampling approach, the interval estimations are presented. Finally, the Monte Carlo method is used to evaluate the performance of the proposed method.

Key words: accelerated life tests, competing causes of failure, martingale, quantile regression, resampling, type-ii progressive censoring

CLC Number:

O211

ZHOU Yicheng, LÜ Zhenzhou, CHENG Kai, SHI Yan. Quantile Regression Based Accelerated Life Test Analysis for Problem with Competing Risks of Failure[J]. Journal of Mechanical Engineering, 2018, 54(17): 190-199.

References

[1] HAN D,KUNDU D. Inference for a step-stress model with competing risks for failure from the generalized exponential distribution under type-I censoring[J]. IEEE Transactions on Reliability,2015,64(1):31-43.
[2] ROY S,MUKHOPADHYAY C. Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure[J]. Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk & Reliability,2015,229(2):1.
[3] XU A,TANG Y. Statistical analysis of competing failure modes in accelerated life testing based on assumed copulas[J]. Chinese Journal of Applied Probability & Statistics,2012(28):51-62.
[4] ZHANG X P,SHANG J Z,CHEN X,et al. Statistical inference of accelerated life testing with dependent competing failures based on copula theory[J]. IEEE Transactions on Reliability,2014,63(3):764-780.
[5] SHI Y M,JIN L,WEI C,et al. Constant-stress accelerated life test with competing risks under progressive type-Ⅱ hybrid censoring[J]. Advanced Materials Research,2013,712-715:2080-2083.
[6] 师义民,师小琳. 竞争失效产品部分加速寿命试验的统计分析[J]. 西北工业大学学报,2017,35(1):109-115. SHI Yimin,SHI Xiaolin. Statistical analysis of partially accelerated life test for disputed products[J]. Journal of Northwestern Polytechnical University,2017,35(1):109-115.
[7] ESCOBAR L A,MEEKER W Q. A review of accelerated test models[J]. Statistical Science,2006,21(4):552-577.
[8] MEEKER W Q. Accelerated testing:Statistical models,test plans,and data analyses,by wayne nelson[J]. Journal of the American Statistical Association,1990,86(414):548.
[9] SCHMOYER R L. Nonparametric analyses for two-level single-stress accelerated life tests[J]. Technometrics,1991,33(2):175-186.
[10] TYOSKIN O I,KRIVOLAPOV S Y. Nonparametric model for step-stress accelerated life testing[J]. Reliability IEEE Transactions on,1996,45(2):346-350.
[11] MEETER C A,MEEKER W Q. Optimum accelerated life tests with a nonconstant scale parameter[J]. Technometrics,1994,36(1):71-83.
[12] NELSON W. Accelerated testing:Statistical models,test plans,and data analysis[M]. New York:A John Wiley & Sons,2008.
[13] LÜ S,NIU Z,QU L,et al. Reliability modeling of accelerated life tests with both random effects and nonconstant shape parameters[J]. Quality Engineering,2015,27(3):329-340.
[14] KALBFLEISCH J D,PRENTICE R L. The statistical analysis of failure time data[M]. New York:Wiley-Interscience, 2011.
[15] LIECHTY J C,ROBERTS G O. A simple resampling method by perturbing the minimand[J]. Biometrika,2001,88(2):381-390.
[16] CHEN N,TANG Y,YE Z S. Robust quantile analysis for accelerated life test data[J]. IEEE Transactions on Reliability,2016,65(2):901-913.
[17] PORTNOY S. Censored regression quantiles[J]. Journal of the American Statistical Association,2003,98(464):1001-1012.
[18] FITZENBERGER B. A guide to censored quantile regressions[J]. Handbook of Statistics,1997,15(97):405-437.
[19] BUCHINSKY M,HAHN J. An alternative estimator for the censored quantile regression model[J]. Econometrica,1998,66(3):653-671.
[20] PENG L,HUANG Y. Survival analysis with quantile regression models[J]. Journal of the American Statistical Association,2008,103(482):637-649.
[21] LAGARIAS J C,REEDS J A,WRIGHT M H,et al. Convergence properties of the nelder-mead simplex method in low dimensions[J]. Siam Journal on Optimization A Publication of the Society for Industrial & Applied Mathematics,1998,9(1):112-147.
[22] KOENKER R,HALLOCK K F. Quantile regression[J]. Journal of Economic Perspectives,2015,15(4):143-156.
[23] WAYNE N. Statistical methods for reliability data[J]. Technometrics,2014,40(3):255.
[24] MEEKER W,HAHN G J. How to plan an accelerated life test:Some practical guidelines[M]. Milwaukee,WI,USA:American Society for Quality Control,1985.