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数据驱动的可靠性评估与寿命预测研究进展:基于协变量的方法

喻勇 司小胜 胡昌华 崔忠马 李洪鹏

喻勇, 司小胜, 胡昌华, 崔忠马, 李洪鹏. 数据驱动的可靠性评估与寿命预测研究进展:基于协变量的方法. 自动化学报, 2018, 44(2): 216-227. doi: 10.16383/j.aas.2018.c170005
引用本文: 喻勇, 司小胜, 胡昌华, 崔忠马, 李洪鹏. 数据驱动的可靠性评估与寿命预测研究进展:基于协变量的方法. 自动化学报, 2018, 44(2): 216-227. doi: 10.16383/j.aas.2018.c170005
YU Yong, SI Xiao-Sheng, HU Chang-Hua, CUI Zhong-Ma, LI Hong-Peng. Data Driven Reliability Assessment and Life-time Prognostics: A Review on Covariate Models. ACTA AUTOMATICA SINICA, 2018, 44(2): 216-227. doi: 10.16383/j.aas.2018.c170005
Citation: YU Yong, SI Xiao-Sheng, HU Chang-Hua, CUI Zhong-Ma, LI Hong-Peng. Data Driven Reliability Assessment and Life-time Prognostics: A Review on Covariate Models. ACTA AUTOMATICA SINICA, 2018, 44(2): 216-227. doi: 10.16383/j.aas.2018.c170005

数据驱动的可靠性评估与寿命预测研究进展:基于协变量的方法

doi: 10.16383/j.aas.2018.c170005
基金项目: 

国家自然科学基金 61374126

国家自然科学基金 61174030

国家自然科学基金 61473094

国家自然科学基金 61573365

中国科协青年人才托举工程 2016QNRC001

国家自然科学基金 61374120

国家杰出青年基金 61025014

国家自然科学基金 61773386

详细信息
    作者简介:

    喻勇 火箭军工程大学与航天科工二院25所联合培养博士研究生.主要研究方向为预测与健康管理, 可靠性估计, 预测维护和寿命估计.E-mail:yuyongep@163.com

    司小胜 火箭军工程大学讲师.主要研究方向为预测与健康管理, 剩余寿命估计, 可靠性. E-mail: sxs09@mails.tsinghua.edu.cn

    崔忠马 中国航天科工集团第二研究院第二十五研究所研究员.主要研究方向为遥感设备总体设计, 雷达成像处理. E-mail: czmsy@sina.com

    李洪鹏 中国航天科工集团第二研究院第二十五研究所高级工程师.主要研究方向为遥感系统测试装备设计. E-mail: mail_lhp@sina.com

    通讯作者:

    胡昌华  火箭军工程大学控制工程系教授.主要研究方向为故障诊断, 可靠性工程.本文通信作者.E-mail:hch6603@263.net

Data Driven Reliability Assessment and Life-time Prognostics: A Review on Covariate Models

Funds: 

National Natural Science Foundation of China 61374126

National Natural Science Foundation of China 61174030

National Natural Science Foundation of China 61473094

National Natural Science Foundation of China 61573365

and Young Elite Scientists Sponsorship Program of China Association for Science and Technology 2016QNRC001

National Natural Science Foundation of China 61374120

National Science Fund for Distinguished Youth Scholars of China 61025014

National Natural Science Foundation of China 61773386

More Information
    Author Bio:

    Ph. D. candidate in the Department of Automation Technology, Xian Institute of High-Technology and the Institute No.25, the Second Academy of China Aerospace Science and Industry Corporation. His research interest covers prognostics and health management, reliability estimation, predictive maintenance, and lifetime estimation

    Lecture in the Department of Automation Technology, Xian Institute of High-Technology, Xian Institute of High-Technology. His research interest covers prognostics and health management, remaining useful life estimation, reliability and predictive maintenance

    Researcher in Institute No.25, The Second Academy of China Aerospace Science and Industry Corporation. His research interest covers the overall design of remote sensing equipment and radar imaging processing

    Senior engineer in Institute No.25, The Second Academy of China Aerospace Science and Industry Corporation. His research interest covers the design of the remote sensing system testing equipment

    Corresponding author: HU Chang-Hua Professor in the Department of Automation Technology, Xi\begin{document}$'$\end{document}an Institute of High-Technology. His research interest covers fault diagnosis and reliability engineering. Corresponding author of this paper
  • 摘要: 作为保障工业过程可靠性和经济性的重要技术,可靠性评估与寿命预测在过去几十年得到了越来越广泛的关注和长足的发展.在实际应用中,由于难以获取复杂、高可靠性设备失效机理的物理模型,数据驱动的可靠性评估与寿命预测方法成为近年来的主流.同时,自动监测技术和传感器技术的快速发展,使得在工程实践中不仅能够获取系统的退化数据,还能得到大量的系统运行环境监测数据,从而使得数据驱动寿命预测中基于协变量的方法得到了广泛应用.本文根据系统运行环境中协变量数据的不同变化规律,将基于协变量方法的可靠性评估模型分为:固定协变量模型、时变协变量模型和随机协变量模型,并分别讨论了各模型的发展现状.最后,讨论了协变量处理中存在的一些挑战及未来的研究方向.
    1)  本文责任编委 文成林
  • 图  1  基于协变量方法的分类

    Fig.  1  Classification of Covariate Models

  • [1] Gorjian N, Ma L, Mittinty M, Yarlagadda P, Sun Y. A review on reliability models with covariates. In: Proceedings of the 4th World Congress on Engineering Asset Management. Athens, Greece: Springer, 2009. 142-157 doi: 10.1007/978-0-85729-320-6_43
    [2] 郑建飞, 胡昌华, 司小胜, 张正新, 张鑫.考虑不确定测量和个体差异的非线性随机退化系统剩余寿命估计.自动化学报, 2017, 43 (2):259-270 http://www.aas.net.cn/CN/abstract/abstract19004.shtml

    Zheng Jian-Fei, Hu Chang-Hua, Si Xiao-Sheng, Zhang Zheng-Xin, Zhang Xin. Remaining useful life estimation for nonlinear stochastic degrading systems with uncertain measurement and unit-to-unit variability. Acta Automatica Sinica, 2017, 43 (2):259-270 http://www.aas.net.cn/CN/abstract/abstract19004.shtml
    [3] 司小胜, 胡昌华, 周东华.带测量误差的非线性退化过程建模与剩余寿命估计.自动化学报, 2013, 39(5):530-541 http://www.aas.net.cn/CN/abstract/abstract17879.shtml

    Si Xiao-Sheng, Hu Chang-Hua, Zhou Dong-Hua. Nonlinear degradation process modeling and remaining useful life estimation subject to measurement error. Acta Automatica Sinica, 2013, 39 (5):530-541 http://www.aas.net.cn/CN/abstract/abstract17879.shtml
    [4] Liao L X, Kottig F. Review of hybrid prognostics approaches for remaining useful life prediction of engineered systems, and an application to battery life prediction. IEEE Transactions on Reliability, 2014, 63 (1):191-207 doi: 10.1109/TR.2014.2299152
    [5] Jardine A K S, Lin D M, Banjevic D. A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 2006, 20 (7):1483-1510 doi: 10.1016/j.ymssp.2005.09.012
    [6] Hu C H, Zhou Z J, Zhang J X, Si X S. A survey on life prediction of equipment. Chinese Journal of Aeronautics, 2015, 28 (1):25-33 doi: 10.1016/j.cja.2014.12.020
    [7] 周东华, 魏慕恒, 司小胜.工业过程异常检测、寿命预测与维修决策的研究进展.自动化学报, 2013, 39 (6):711-722 http://www.aas.net.cn/CN/abstract/abstract18097.shtml

    Zhou Dong-Hua, Wei Mu-Heng, Si Xiao-Sheng. A survey on anomaly detection, life prediction and maintenance decision for industrial processes. Acta Automatica Sinica, 2013, 39 (6):711-722 http://www.aas.net.cn/CN/abstract/abstract18097.shtml
    [8] Cox D R. Regression models and life-tables. Journal of the Royal Statistical Society, 1972, 34 (2):187-220 http://www.jstor.org/stable/2985181
    [9] Kumar D, Westberg U. Some reliability models for analyzing the effect of operating conditions. International Journal of Reliability, Quality and Safety Engineering, 1996, 4 (2):133-148 doi: 10.1142/S0218539397000102?queryID=%24%7BresultBean.queryID%7D
    [10] Anderson J A, Senthilselvan A. A two-step regression model for hazard functions. Applied Statistics, 1982, 31 (1):44-51 doi: 10.2307/2347073
    [11] Pijnenburg M. Additive hazards models in repairable systems reliability. Reliability Engineering and System Safety, 1991, 31 (3):369-390 doi: 10.1016/0951-8320(91)90078-L
    [12] Andersen P K, Vaeth M. Simple parametric and nonparametric models for excess and relative mortality. Biometrics, 1989, 45 (2):523-535 doi: 10.2307/2531494
    [13] Shyur H J, Elsayed E A, Luxhoj J T. A general model for accelerated life testing with time-dependent covariates. Naval Research Logistics, 1999, 46 (3):303-321 doi: 10.1002/(ISSN)1520-6750
    [14] Ciampi A, Etezadi-Amoli J. A general model for testing the proportional hazards and the accelerated failure time hypotheses in the analysis of censored survival data with covariates. Communications in Statistics-Theory and Methods, 1985, 14 (3):651-667 doi: 10.1080/03610928508828940
    [15] McCullagh P. Regression models for ordinal data. Journal of the Royal Statistical Society:Series B (Methodological), 1980, 42 (2):109-142 http://www.jstor.org/stable/2984952
    [16] Bennett S. Log-logistic regression models for survival data. Applied Statistics, 1983, 32 (2):165-171 doi: 10.2307/2347295
    [17] Liao H T, Zhao W B, Guo H R. Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model. In: Proceedings of the 2006 Annual Reliability and Maintainability Symposium. Newport Beach, CA, USA: IEEE 2006. 127-132 http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1677362
    [18] Sun Y, Ma L, Mathew J, Wang W Y, Zhang S. Mechanical systems hazard estimation using condition monitoring. Mechanical Systems and Signal Processing, 2006, 20 (5):1189-1201 doi: 10.1016/j.ymssp.2004.10.009
    [19] Jardine A K S, Anderson P M, Mann D S. Application of the Weibull proportional hazards model to aircraft and marine engine failure data. Quality and Reliability Engineering International, 1987, 3 (2):77-82 doi: 10.1002/(ISSN)1099-1638
    [20] Aalen O O. Further results on the non-parametric linear regression model in survival analysis. Statistics in Medicine, 1993, 12(17):1569-1588 doi: 10.1002/(ISSN)1097-0258
    [21] Gorjian N, Ma L, Mittinty M, Yarlagadda P, Sun Y. The explicit hazard model-Part 1: theoretical development. In: Proceedings of the Prognostics & System Health Management Conference. Macau, China: IEEE, 2010. 167-179 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5414565
    [22] Sheldon M R. Generalized Poisson shock models. The Annals of Probability, 1981, 9 (5):896-898 doi: 10.1214/aop/1176994318
    [23] Jarrow R A, Lando D, Turnbull S M. A Markov model for the term structure of credit risk spreads. Review of Financial Studies, 1997, 10 (2):481-523 doi: 10.1093/rfs/10.2.481
    [24] Zhao X J, Fouladirad M, Bérenguer C, Bordes L. Condition-based inspection replacement policies for non-monotone deteriorating systems with environmental covariates. Reliability Engineering and System Safety, 2010, 95 (8):921-934 doi: 10.1016/j.ress.2010.04.005
    [25] Banjevic D, Jardine A K S. Calculation of reliability function and remaining useful life for a Markov failure time process. IMA Journal of Management Mathematics, 2006, 17 (2):115-130 doi: 10.1093/imaman/dpi029
    [26] Myers L E. Survival functions induced by stochastic covariate processes. Journal of Applied Probability, 1981, 18 (2):523-529 doi: 10.2307/3213300
    [27] Berman S M, Frydman H. Parametric estimation of hazard functions with stochastic covariate processes. Sankhyā:The Indian Journal of Statistics, 1999, 61 (2):174-188 http://www.ams.org/mathscinet-getitem?mr=1714869
    [28] Yu J C, Liu Y Y, Cai J W, Sandler D P, Zhou H B. Outcome-dependent sampling design and inference for Cox's proportional hazards Model. Journal of Statistical Planning and Inference, 2016, 178 (5):24-36 http://www2.cscc.unc.edu/impact7/node/771
    [29] Lin H Z, He Y, Huang J. A global partial likelihood estimation in the additive Cox proportional hazards model. Journal of Statistical Planning and Inference, 2016, 169 (9):71-87 https://www.researchgate.net/publication/282528853_A_global_partial_likelihood_estimation_in_the_additive_Cox_proportional_hazards_model
    [30] Cao Y X, Yu J C, Liu Y Y. Optimal generalized case-cohort analysis with Cox's proportional hazards model. Acta Mathematicae Applicatae Sinica, 2015, 31 (3):841-854 doi: 10.1007/s10255-015-0555-4
    [31] Luo J, Su Z. A note on variance estimation in the Cox proportional hazards model. Journal of Applied Statistics, 2013, 40 (5):1132-1139 doi: 10.1080/02664763.2013.780161
    [32] Cox D R. Partial likelihood. Biometrika, 1975, 62 (2):269-276 doi: 10.1093/biomet/62.2.269
    [33] Kalbfleisch J D, Prentice R L. Marginal likelihoods based on Cox's regression and life model. Biometrika, 1973, 60 (2):267-278 doi: 10.1093/biomet/60.2.267
    [34] Makis V, Jardine A K S. Optimal replacement policy for a general model with imperfect repair. Journal of the Operational Research Society, 1992, 43 (2):111-120 doi: 10.1057/jors.1992.17
    [35] Banjevic D, Jardine A K S, Makis V, Ennis M. A Control-Limit Policy And Software For Condition-Based Maintenance Optimization. INFOR:Information Systems and Operational Research, 2001, 39(1):32-50 doi: 10.1080/03155986.2001.11732424
    [36] Jardine A K S, Banjevic D, Makis V. Optimal replacement policy and the structure of software for condition-based maintenance. Journal of Quality in Maintenance Engineering, 1997, 3 (2):109-119 doi: 10.1108/13552519710167728
    [37] Jardine A K S, Joseph T, Banjevic D. Optimizing condition-based maintenance decisions for equipment subject to vibration monitoring. Journal of Quality in Maintenance Engineering, 1999, 5 (3):192-202 doi: 10.1108/13552519910282647
    [38] Vlok P J, Wnek M, Zygmunt M. Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mechanical Systems and Signal Processing, 2004, 18 (4):833-847 doi: 10.1016/j.ymssp.2003.09.003
    [39] Kay R. Proportional hazard regression models and the analysis of censored survival data. Applied Statistics, 1977, 26 (3):227-237 doi: 10.2307/2346962
    [40] Kumar D. Proportional hazards modelling of repairable systems. Quality and Reliability Engineering International, 1995, 11 (5):361-369 doi: 10.1002/(ISSN)1099-1638
    [41] Hanson T, Jara A, Zhao L P. A Bayesian semiparametric temporally-stratified proportional hazards model with spatial frailties. Bayesian Analysis, 2012, 7 (1):147-188 doi: 10.1214/12-BA705
    [42] Fibrinogen Studies Collaboration. Measures to assess the prognostic ability of the stratified Cox proportional hazards model. Statistics in Medicine, 2009, 28 (3):389-411 doi: 10.1002/sim.v28:3
    [43] Mau J. On a graphical method for the detection of time-dependent effects of covariates in survival data. Applied Statistics, 1986, 35 (3):245-255 doi: 10.2307/2348023
    [44] Aalen O O. A linear regression model for the analysis of life times. Statistics in Medicine, 1989, 8 (8):907-925 doi: 10.1002/(ISSN)1097-0258
    [45] Newby M. Why no additive hazards models? IEEE Transactions on Reliability, 1994, 43 (3):484-488 doi: 10.1109/24.326450
    [46] Newby M. A critical look at some point-process models for repairable systems. IMA Journal of Management Mathematics, 1992, 4 (4):375-394 doi: 10.1093/imaman/4.4.375
    [47] Álvarez E E, Ferrario J. Robust estimation in the additive hazards model. Communications in Statistics:Theory & Methods, 2016, 45 (4):906-921 doi: 10.1080/03610926.2013.853790
    [48] Wightman D, Bendell T. Comparison of proportional hazards modeling, additive hazards modeling and proportional intensity modeling when applied to repairable system reliability. International Journal of Reliability, Quality and Safety Engineering, 1995, 2 (1):23-34 doi: 10.1142/S0218539395000046
    [49] Badía F G, Berrade M D, Campos C A. Aging properties of the additive and proportional hazard mixing models. Reliability Engineering & System Safety, 2002, 78 (2):165-172 https://www.sciencedirect.com/science/article/pii/S0951832002001564
    [50] Cox D R, Oakes D. Analysis of Survival Data. New York:Chapman and Hall, 1984. 32-37
    [51] Lin Z, Fei H. A nonparametric approach to progressive stress accelerated life testing. IEEE Transactions on Reliability, 1991, 40 (2):173-176 doi: 10.1109/24.87123
    [52] Mettas A. Modeling and analysis for multiple stress-type accelerated life data. In: Proceedings of the 2000 Annual Reliability and Maintainability Symposium. Los Angeles, CA, USA: IEEE 2000. 138-143 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=816297
    [53] Gosho M, Maruo K, Sato Y. Effect of covariate omission in Weibull accelerated failure time model:a caution. Biometrical Journal, 2014, 56 (6):991-1000 doi: 10.1002/bimj.201300006
    [54] Newby M. Accelerated failure time models for reliability data analysis. Reliability Engineering & System Safety, 1988, 20 (3):187-197 https://www.researchgate.net/publication/222366290_Accelerated_failure_time_models_for_reliability_data_analysis_Reliability_Engineering_System_Safety_203_187-197
    [55] Galanova N S, Lemeshko B Y, Chimitova E V. Using nonparametric goodness-of-fit tests to validate accelerated failure time models. Optoelectronics, Instrumentation and Data Processing, 2012, 48 (6):580-592 doi: 10.3103/S8756699012060064
    [56] Wang H, Dai H, Fu B. Accelerated failure time models for censored survival data under referral bias. Biostatistics, 2013, 14 (2):313-326 doi: 10.1093/biostatistics/kxs041
    [57] Yang M G, Chen L H, Dong G H. Semiparametric Bayesian accelerated failure time model with interval-censored data. Journal of Statistical Computation and Simulation, 2015, 85 (10):2049-2058 doi: 10.1080/00949655.2014.915400
    [58] Wang S Y, Hu T, Xiang L M, Cui H J. Generalized M-estimation for the accelerated failure time model. Statistics, 2016, 50 (1):114-138 doi: 10.1080/02331888.2015.1032970
    [59] Etezadi-Amoli J, Ciampi A. Extended hazard regression for censored survival data with covariates:a spline approximation for the baseline hazard function. Biometrics, 1987, 43 (1):181-192 doi: 10.2307/2531958
    [60] Louzada-Neto F. Extended hazard regression model for reliability and survival analysis. Lifetime Data Analysis, 1997, 3 (4):367-381 doi: 10.1023/A:1009606229786
    [61] Tseng Y K, Su Y R, Mao M, Wang J L. An extended hazard model with longitudinal covariates. Biometrika, 2015, 102 (1):135-150 doi: 10.1093/biomet/asu058
    [62] Tseng Y K, Hsu K N, Yang Y F. A semiparametric extended hazard regression model with time-dependent covariates. Journal of Nonparametric Statistics, 2014, 26 (1):115-128 doi: 10.1080/10485252.2013.836521
    [63] Shyur H J, Keng H, Ia-Ka I, Huang C L. Using extended hazard regression model to assess the probability of aviation event. Applied Mathematics and Computation, 2012, 218 (21):10647-10655 doi: 10.1016/j.amc.2012.04.029
    [64] Bennett S. Analysis of survival data by the proportional odds model. Statistics in Medicine, 1983, 2 (2):273-277 doi: 10.1002/(ISSN)1097-0258
    [65] Zahid F M, Ramzan S, Heumann C. Regularized proportional odds models. Journal of Statistical Computation and Simulation, 2015, 85 (2):251-168 doi: 10.1080/00949655.2013.814133
    [66] Sinha S, Ma Y Y. Analysis of proportional odds models with censoring and errors-in-covariates. Journal of the American Statistical Association, 2016, 111 (515):1301-1312 doi: 10.1080/01621459.2015.1093943
    [67] Zahid F M, Tutz G. Proportional odds models with high-dimensional data structure. International Statistical Review, 2013, 81 (3):388-406 doi: 10.1111/insr.v81.3
    [68] Landers T L, Soroudi H E. Robustness of a semi-parametric proportional intensity model. IEEE Transactions on Reliability, 1991, 40 (2):161-164 doi: 10.1109/24.87120
    [69] Lugtigheid D, Jardine Andrew K S, Jiang X Y. Optimizing the performance of a repairable system under a maintenance and repair contract. Quality and Reliability Engineering International, 2007, 23 (8):943-960 doi: 10.1002/(ISSN)1099-1638
    [70] Kumar D, Westberg U. Proportional hazards modeling of time-dependent covariates using linear regression:a case study. IEEE Transactions on Reliability, 1996, 45 (3):386-392 doi: 10.1109/24.536990
    [71] Jiang S T, Landers T L, Rhoads T R. Proportional intensity models robustness with overhaul intervals. Quality and Reliability Engineering International, 2006, 22 (3):251-263 doi: 10.1002/(ISSN)1099-1638
    [72] Prentice R L, Williams B J, Peterson A V. On the regression analysis of multivariate failure time data. Biometrika, 1981, 68 (2):373-379 doi: 10.1093/biomet/68.2.373
    [73] Yuan F Q, Kumar U. Proportional Intensity Model considering imperfect repair for repairable systems. International Journal of Performability Engineering, 2013, 9(2):163-174 http://paris.utdallas.edu/IJPE/Vol09/Issue02/pp.163-174%20Paper%204%20IJPE%20407.12%20Fuqing.pdf
    [74] Percy D F, Kobbacy K A H, Ascher H E. Using proportional-intensities models to schedule preventive-maintenance intervals. IMA Journal of Management Mathematics, 1998, 9 (3):289-302 doi: 10.1093/imaman/9.3.289
    [75] Alkali B. Evaluation of generalised proportional intensities models with application to the maintenance of gas turbines. Quality and Reliability Engineering International, 2012, 28 (6):577-584 https://www.deepdyve.com/lp/wiley/evaluation-of-generalised-proportional-intensities-models-with-fZ2VbgUKzF
    [76] Syamsundar A, Achutha Naikan V N. Imperfect repair proportional intensity models for maintained systems. IEEE Transactions on Reliability, 2011, 60 (4):782-787 doi: 10.1109/TR.2011.2161110
    [77] Wu J B. Modified restricted Liu estimator in logistic regression model. Computational Statistics, 2016, 31 (4):1557-1567 doi: 10.1007/s00180-015-0609-3
    [78] Li C S. A test for the linearity of the nonparametric part of a semiparametric logistic regression model. Journal of Applied Statistics, 2016, 43 (3):461-475 doi: 10.1080/02664763.2015.1070803
    [79] Sun Y, Ma L. Notes on "mechanical systems hazard estimation using condition monitoring"-Response to the letter to the editor by Daming Lin and Murray Wiseman. Mechanical Systems and Signal Processing, 2007, 21 (7):2950-2955 doi: 10.1016/j.ymssp.2007.06.004
    [80] Cai G G, Chen X F, Li B, Chen B J, He Z J. Operation reliability assessment for cutting tools by applying a proportional covariate model to condition monitoring information. Sensors, 2012, 12 (10):12964-12987 http://www.mdpi.com/1424-8220/12/10/12988
    [81] Pettitt A N, Daud I B. Investigating time dependence in Cox's proportional hazards model. Applied Statistics, 1990, 39 (3):313-329 doi: 10.2307/2347382
    [82] Jardine A K S. Component and system replacement decisions. Image Sequence Processing and Dynamic Scene Analysis. Berlin:Springer-Verlag, 1983. 647-654
    [83] Jardine A K S, Ralston P, Reid N, Stafford J. Proportional hazards analysis of diesel engine failure data. Quality and Reliability Engineering International, 1989, 5 (3):207-216 doi: 10.1002/(ISSN)1099-1638
    [84] Jóźwiak I J. An introduction to the studies of reliability of systems using the Weibull proportional hazards model. Microelectronics Reliability, 1997, 37 (6):915-918 doi: 10.1016/S0026-2714(96)00285-5
    [85] Jardine A K S, Anders M. Use of concomitant variables for reliability estimation. Maintenance Management International, 1985, 5 (4):135-140 https://www.researchgate.net/publication/291839844_USE_OF_CONCOMITANT_VARIABLES_FOR_RELIABILITY_ESTIMATION
    [86] Newby M. Perspective on Weibull proportional-hazards models. IEEE Transactions on Reliability, 1994, 43 (2):217-223 doi: 10.1109/24.294993
    [87] Sha N J, Pan R. Bayesian analysis for step-stress accelerated life testing using Weibull proportional hazard model. Statistical Papers, 2014, 55 (3):715-726 doi: 10.1007/s00362-013-0521-2
    [88] Zhang Q, Hua C, Xua G H. A mixture Weibull proportional hazard model for mechanical system failure prediction utilising lifetime and monitoring data. Mechanical Systems and Signal Processing, 2014, 43 (1-2):103-112 doi: 10.1016/j.ymssp.2013.10.013
    [89] Gorjian N, Mittinty M, Ma L, Yarlagadda P, Sun Y. The explicit hazard model-Part 2: applications. In: Proceedings of the 2010 Prognostics and Health Management Conference. Macau, China: IEEE, 2010. 189-202 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5413493
    [90] Cha J H, Mi J. Study of a stochastic failure model in a random environment. Journal of Applied Probability, 2007, 44 (1):151-163 doi: 10.1239/jap/1175267169
    [91] Cha J H, Lee E Y. An extended stochastic failure model for a system subject to random shocks. Operations Research Letters, 2010, 38 (5):468-473 doi: 10.1016/j.orl.2010.06.004
    [92] Cha J H, Mi J. On a stochastic survival model for a system under randomly variable environment. Methodology and Computing in Applied Probability, 2011, 13 (3):549-561 doi: 10.1007/s11009-010-9171-1
    [93] Junca M, Sanchez Silva M. Optimal maintenance policy for a compound Poisson shock model. IEEE Transactions on Reliability, 2013, 62 (1):66-72 doi: 10.1109/TR.2013.2241193
    [94] Jiang H Y. Parameter estimation of the Poisson shock model using masked data. International Journal of Pure and Applied Mathematics, 2011, 71 (4):559-569 https://www.researchgate.net/publication/264993406_Parameter_estimation_of_the_Poisson_shock_model_using_masked_data
    [95] Pandey A, Mitra M. Poisson shock models leading to new classes of non-monotonic aging life distributions. Microelectronics and Reliability, 2011, 51 (12):2412-2415 doi: 10.1016/j.microrel.2011.04.001
    [96] Ghasemi A, Yacout S, Salah-Ouali M. Evaluating the reliability function and the mean residual life for equipment with unobservable states. IEEE Transactions on Reliability, 2010, 59 (1):45-54 doi: 10.1109/TR.2009.2034947
    [97] Çinlar E. Markov additive processes. I. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1972, 24 (2):85-93 http://en.cnki.com.cn/Article_en/CJFDTOTAL-WHDY404.003.htm
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出版历程
  • 收稿日期:  2017-01-04
  • 录用日期:  2017-06-12
  • 刊出日期:  2018-02-20

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