分位数回归在竞争失效加速寿命试验统计分析中的应用

doi:10.3901/JME.2018.17.190

机械工程学报 ›› 2018, Vol. 54 ›› Issue (17): 190-199.doi: 10.3901/JME.2018.17.190

• 特邀专栏：智能制造装备 • 上一篇下一篇

扫码分享

分位数回归在竞争失效加速寿命试验统计分析中的应用

周易成, 吕震宙, 成凯, 石岩

西北工业大学航空学院西安 710072

收稿日期:2017-12-09 修回日期:2018-03-11 出版日期:2018-09-05 发布日期:2018-09-05
通讯作者: 吕震宙(通信作者),女,1966年出生,教授,博士研究生导师。主要研究方向为飞行器总体设计、飞行器结构设计、飞行器可靠性工程、安全工程。E-mail:zhenzhoulu@nwpu.edu.cn
作者简介:周易成,男,1993年出生,博士研究生。主要研究方向为飞行器可靠性工程。E-mail:494519858@mail.nwpu.edu.cn
基金资助:
国家自然科学基金资助项目（51775439）。

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

ZHOU Yicheng, LÜ Zhenzhou, CHENG Kai, SHI Yan

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072

Received:2017-12-09 Revised:2018-03-11 Online:2018-09-05 Published:2018-09-05

摘要/Abstract

摘要： 利用加速寿命试验的失效数据对产品的分位数寿命进行统计推断时，需要对统计模型做具体的假设。但是在工程实际中，错误的模型设定会严重影响估计精度。针对这个问题，提出了一种基于分位数回归的竞争失效产品分位数寿命的统计分析方法。分位数回归模型不受寿命分布假设的约束，且描述产品寿命与加速应力的关系时更加灵活。考虑到由于逐步Ⅱ型截尾和竞争失效模式而产生的试验数据非完整性，采用基于cause-specific hazard（CSH）的鞅方法为待估的分位数回归模型构造无偏估计方程，并将方程的求解等价为凸函数的极小值的求解。同时采用扰动重抽样方法得到参数的区间估计值。最后应用实例验证了方法的有效性。

关键词: 分位数回归, 竞争失效模式, 寿命加速试验, 鞅, 重抽样, 逐步II型截尾

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

中图分类号:

O211

周易成, 吕震宙, 成凯, 石岩. 分位数回归在竞争失效加速寿命试验统计分析中的应用[J]. 机械工程学报, 2018, 54(17): 190-199.

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.

参考文献

[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.

分位数回归在竞争失效加速寿命试验统计分析中的应用

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价