参考文献

Abdel Hameed M, 1975. A Gamma Wear Process[J]. IEEE Transactions on Reliability, 24(2): 152–153.

Al-Hussaini E K, Abd-El-Hakim N S, 1989. Failure Rate of the Inverse Gaussian-Weibull Mixture Model[J]. Annals of the Institute of Statistical Mathematics, 41(3): 617–622.

Bae S J, Kim S-J, Kim M S, et al., 2008. Degradation Analysis of Nano-Contamination in Plasma Display Panels[J]. IEEE Transactions on Reliability, 57(2): 222–229.

Bae S J, Kvam P H, 2006. A Change-Point Analysis for Modeling Incomplete Burn-in for Light Displays[J]. IIE Transactions, 38(6): 489–498. DOI:10.1080/074081791009068.

Bae S J, Yuan T, Kim S, 2016. Bayesian Degradation Modeling for Reliability Prediction of Organic Light-Emitting Diodes[J]. Journal of Computational Science, 17: 117–125. DOI:10.1016/j.jocs.2016.08.006.

Bae S J, Yuan T, Ning S, et al., 2015. A Bayesian Approach to Modeling Two-Phase Degradation Using Change-Point Regression[J]. Reliability Engineering & System Safety, 134: 66–74.

Barndorff-Nielsen O E, Koudou A E, 1998. Trees with Random Conductivities and the (Reciprocal) Inverse Gaussian Distribution[J]. Advances in Applied Probability, 30(2): 409–424.

Bemis B M, Bain L J, Higgins J J, 1972. Estimation and Hypothesis Testing for the Parameters of a Bivariate Exponential Distribution[J]. Journal of the American Statistical Association, 67(340): 927–929.

Berger J O, 2013. Statistical Decision Theory and Bayesian Analysis[M]. Springer Science & Business Media.

Bernardo J M, Smith A F, 2009. Bayesian Theory[M]. John Wiley & Sons.

Blei D M, Kucukelbir A, McAuliffe J D, 2017. Variational Inference: A Review for Statisticians[J]. Journal of the American Statistical Association, 112(518): 859–877.

Bolstad W M, Curran J M, 2016. Introduction to Bayesian Statistics[M]. John Wiley & Sons.

Borchers H W, 2019. Pracma: Practical Numerical Math Functions[J]. R Package Version, 2(9): 519.

Bousquet N, Fouladirad M, Grall A, et al., 2015. Bayesian Gamma Processes for Optimizing Condition-Based Maintenance Under Uncertainty[J]. Applied Stochastic Models in Business and Industry, 31(3): 360–379.

Casella G, Berger R L, 2021. Statistical Inference[M]. Cengage Learning.

Celeux G, Hurn M, Robert C P, 2000. Computational and Inferential Difficulties with Mixture Posterior Distributions[J]. Journal of the American Statistical Association, 95(451): 957–970.

Chao M A, Kulkarni C, Goebel K, et al., 2022. Fusing Physics-Based and Deep Learning Models for Prognostics[J]. Reliability Engineering & System Safety, 217: 107961.

Chen N, Tsui K L, 2013. Condition Monitoring and Remaining Useful Life Prediction Using Degradation Signals: Revisited[J]. IIE Transactions, 45(9): 939–952. DOI:10.1080/0740817X.2012.706376.

Chen Z, Xia T, Li Y, et al., 2021. Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes[J]. IEEE Transactions on Reliability, 71(1): 47–62.

Chen Z, Xia T, Li Y, et al., 2022. Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes[J]. IEEE Transactions on Reliability, 71(1): 47–62.

Chen P, Ye Z-S, 2017. Estimation of Field Reliability Based on Aggregate Lifetime Data[J]. Technometrics, 59(1): 115–125.

Chen P, Ye Z-S, 2018b. A Systematic Look at the Gamma Process Capability Indices[J]. European Journal of Operational Research, 265(2): 589–597.

Chen P, Ye Z-S, 2018a. Uncertainty Quantification for Monotone Stochastic Degradation Models[J]. Journal of Quality Technology, 50(2): 207–219.

Csorgo S, Welsh A. H., 1989. Testing for Exponential and Marshall-Olkin Distributions[J]. Journal of Statistical Planning and Inference, 23: 287–300.

Damsleth E, 1975. Conjugate Classes for Gamma Distributions[J]. Scandinavian Journal of Statistics, 2(2): 80–84.

Davis P J, Rabinowitz P, 2007. Methods of Numerical Integration[M]. Courier Corporation.

Denison D G, Holmes C C, Mallick B K, et al., 2002. Bayesian Methods for Nonlinear Classification and Regression[M]. John Wiley & Sons.

Doksum K A, Hbyland A, 1992. Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution[J]. Technometrics, 34(1): 74–82.

Duan F, Wang G, 2017. Reliability Modeling of Two-Phase Inverse Gaussian Degradation Process[C]//2017 Second International Conference on Reliability Systems Engineering (ICRSE). IEEE: 1–6.

Duan F, Wang G, 2018. Exponential-Dispersion Degradation Process Models with Random Effects and Covariates[J]. IEEE Transactions on Reliability, 67(3): 1128–1142.

Dunn P K, Smyth G K, 2005. Series Evaluation of Tweedie Exponential Dispersion Model Densities[J]. Statistics and Computing, 15(4): 267–280.

Efron B, 2012. Bayesian Inference and the Parametric Bootstrap[J]. The Annals of Applied Statistics, 6(4): 1971–1997. DOI:10.1214/12-AOAS571.

Efron B, Tibshirani R, 1993. An Introduction to the Bootstrap[M]. Chapman & Hall: 49–54.

Erişoğlu Ü, Erişoğlu M, Erol H, 2011. A Mixture Model of Two Different Distributions Approach to the Analysis of Heterogeneous Survival Data[J]. International Journal of Computational and Mathematical Sciences, 5(6): 544–548.

Fan T-H, Chen C-H, 2017. A Bayesian Predictive Analysis of Step-Stress Accelerated Tests in Gamma Degradation-Based Processes[J]. Quality and Reliability Engineering International.

Fan T-H, Dong Y-S, Peng C-Y, 2024. A Complete Bayesian Degradation Analysis Based on Inverse Gaussian Processes[J]. IEEE Transactions on Reliability, 73(1): 536–548. DOI:10.1109/TR.2023.3304673.

Fang G, Pan R, Wang Y, 2022. Inverse Gaussian Processes with Correlated Random Effects for Multivariate Degradation Modeling[J]. European Journal of Operational Research, 300(3): 1177–1193.

Fan T, Hsu T, 2015. Statistical Inference of a Two-Component Series System with Correlated Log-Normal Lifetime Distribution Under Multiple Type-i Censoring[J]. IEEE Transactions on Reliability, 64(1): 376–385.

Fouladirad M, Grall A, 2011. Condition-Based Maintenance for a System Subject to a Non-Homogeneous Wear Process with a Wear Rate Transition[J]. Reliability Engineering & System Safety, 96(6): 611–618. DOI:10.1016/j.ress.2010.12.008.

Fouladirad M, Grall A, Dieulle L, 2008. On the Use of on-Line Detection for Maintenance of Gradually Deteriorating Systems[J]. Reliability Engineering & System Safety, 93(12): 1814–1820. DOI:10.1016/j.ress.2008.03.020.

Geisser S, Hodges J, Press S, et al., 1990. The Validity of Posterior Expansions Based on Laplace’s Method[J]. Bayesian and Likelihood Methods in Statistics and Econometrics, 7: 473.

Gelman A, 2006. Prior Distributions for Variance Parameters in Hierarchical Models[J]. Bayesian Analysis, 1(3): 515–533.

Gelman A, Carlin J B, Stern H S, et al., 2014. Bayesian Data Analysis[M]. Taylor & Francis.

Gilks W R, Best N G, Tan K K C, 2022. Adaptive Rejection Metropolis Sampling Within Gibbs Sampling[J]. Applied Statistics, 44: 455–472. DOI:10.2307/2986138.

Gilks W R, Wild P, 1992. Adaptive Rejection Sampling for Gibbs Sampling[J]. Journal of the Royal Statistical Society: Series C, 41(2): 337–348.

Giorgio M, Mele A, Pulcini G, 2019. A Perturbed Gamma Degradation Process with Degradation Dependent Non-Gaussian Measurement Errors[J]. Applied Stochastic Models in Business and Industry, 35(2): 198–210.

Grall A, Fouladirad M, 2008. Maintenance Decision Rule with Embedded Online Bayesian Change Detection for Gradually Non-Stationary Deteriorating Systems[J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 222(3): 359–369. DOI:10.1243/1748006XJRR141.

Guida M, Postiglione F, Pulcini G, 2019. A Bayesian Approach for Non-Homogeneous Gamma Degradation Processes[J]. Communications in Statistics-Theory and Methods, 48(7): 1748–1765.

Guo J, Wang C, Cabrera J, et al., 2018. Improved Inverse Gaussian Process and Bootstrap: Degradation and Reliability Metrics[J]. Reliability Engineering & System Safety, 178: 269–277.

Hall P, Wang J Z, 2005. Bayesian Likelihood Methods for Estimating the End Point of a Distribution[J]. Journal of the Royal Statistical Society: Series B, 67(5): 717–729.

Hao H, Su C, Li C, 2015. LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function[J]. International Journal of Photoenergy, 2015.

Hao S, Yang J, Berenguer C, 2019. Degradation Analysis Based on an Extended Inverse Gaussian Process Model with Skew-Normal Random Effects and Measurement Errors[J]. Reliability Engineering & System Safety, 189: 261–270. DOI:10.1016/j.ress.2019.04.031.

Hartzell A L, Da Silva M G, Shea H R, 2011. Lifetime Prediction[M]//MEMS Reliability. Springer, New York: 9–42.

Hazra I, Pandey M D, Manzana N, 2020. Approximate Bayesian Computation Method for Estimating Parameters of the Gamma Process Using Noisy Data[J]. Reliability Engineering & System Safety, 198: 106780.

Hong Y, Duan Y, Meeker W Q, et al., 2015. Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data[J]. Technometrics, 57(2): 180–193.

Hong L, Ye Z-S, 2017. When Is Acceleration Unnecessary in a Degradation Test?[J]. Statistica Sinica, 27(3): 1461–1483.

Hong L, Zhai Q, Wang X, et al., 2019. System Reliability Evaluation Under Dynamic Operating Conditions[J]. IEEE Transactions on Reliability, 68(3): 800–809.

Hougaard P, 1995. Frailty Models for Survival Data[J]. Lifetime Data Analysis, 1(3): 255–273.

Hu J, Chen P, 2020. Predictive Maintenance of Systems Subject to Hard Failure Based on Proportional Hazards Model[J]. Reliability Engineering & System Safety, 196: 106707.

Huynh K T, 2021. An Adaptive Predictive Maintenance Model for Repairable Deteriorating Systems Using Inverse Gaussian Degradation Process[J]. Reliability Engineering & System Safety, 213: 107695.

Jaakkola T S, Jordan M I, 2000. Bayesian Parameter Estimation via Variational Methods[J]. Statistics and Computing, 10(1): 25–37.

Jamshidian M, Jennrich R I, 1997. Acceleration of the EM Algorithm by Using Quasi-Newton Methods[J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59(3): 569–587. DOI:10.1111/1467-9868.00083.

Jørgensen B, 1986. Some Properties of Exponential Dispersion Models[J]. Scandinavian Journal of Statistics, 13(3): 187–197.

Jørgensen B, 1987. Exponential Dispersion Models[J]. Journal of the Royal Statistical Society, 49(2): 127–162.

Jørgensen B, 1992. Exponential Dispersion Models and Extensions: A Review[J]. International Statistical Review, 60(1): 5–20.

Jørgensen B, 1998. The Theory of Exponential Dispersion Models[M]. Chapman & Hall.

Komárek A, Lesaffre E, 2008. Generalized Linear Mixed Model with a Penalized Gaussian Mixture as a Random Effects Distribution[J]. Computational Statistics & Data Analysis, 52(7): 3441–3458.

Kong D J, Balakrishnan N, Cui L R, 2017. Two-Phase Degradation Process Model with Abrupt Jump at Change Point Governed by Wiener Process[J]. IEEE Transactions on Reliability, 66(4): 1345–1360. DOI:10.1109/Tr.2017.2711621.

Kontar R, Son J, Zhou S, et al., 2017. Remaining Useful Life Prediction Based on the Mixed Effects Model with Mixture Prior Distribution[J]. IISE Transactions, 49(7): 682–697.

Kotz S, Lai C D, Xie M, 2003. On the Effect of Redundancy for Systems with Dependent Components[J]. IIE Transactions, 35(12): 1103–1110.

Krishnamoorthy K, 2016. Handbook of Statistical Distributions with Applications[M]. CRC Press.

Kundu D, Gupta A K, 2013. Bayes Estimation for the Marshall–Olkin Bivariate Weibull Distribution[J]. Computational Statistics & Data Analysis, 57(1): 271–281.

Kvalseth T O, 1985. Cautionary Note about R²[J]. The American Statistician, 39(4): 279–285.

Lai C D, Xie M, 2006. Stochastic Ageing and Dependence for Reliability[M]. Springer.

Lawless J, Crowder M, 2004. Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure[J]. Lifetime Data Analysis, 10: 213–227. DOI:10.1023/B:LIDA.0000036389.14073.dd.

Lee I-C, Tseng S-T, Hong Y, 2020. Global Planning of Accelerated Degradation Tests Based on Exponential Dispersion Degradation Models[J]. Naval Research Logistics, 67(6): 469–483.

Lesaffre E, Molenberghs G, 1991. Multivariate Probit Analysis: A Neglected Procedure in Medical Statistics[J]. Statistics in Medicine, 10(9): 1391–1403.

Lewis-Beck C, Tian Q, Meeker W Q, 2022. Prediction of Future Failures for Heterogeneous Reliability Field Data[J]. Technometrics, 64(1): 125–138.

Li M, Meng H, Zhang Q, 2017. A Nonparametric Bayesian Modeling Approach for Heterogeneous Lifetime Data with Covariates[J]. Reliability Engineering & System Safety, 167: 95–104.

Lindstrom M J, Bates D M, 1988. Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data[J]. Journal of the American Statistical Association, 83: 1014–1022.

Ling M H, Ng H, Tsui K L, 2019. Bayesian and Likelihood Inferences on Remaining Useful Life in Two-Phase Degradation Models Under Gamma Process[J]. Reliability Engineering & System Safety, 184: 77–85.

Lin C P, Ling M H, Cabrera J, et al., 2021. Prognostics for Lithium-Ion Batteries Using a Two-Phase Gamma Degradation Process Model[J]. Reliability Engineering & System Safety, 214: 107797. DOI:10.1016/j.ress.2021.107797.

Liu X, 2012. Planning of Accelerated Life Tests with Dependent Failure Modes Based on a Gamma Frailty Model[J]. Technometrics, 54(4): 398–409.

Liu Q, Pierce D A, 1994. A Note on Gauss—Hermite Quadrature[J]. Biometrika, 81(3): 624–629.

Liu X, Yeo K, Kalagnanam J, 2018. A Statistical Modeling Approach for Spatio-Temporal Degradation Data[J]. Journal of Quality Technology, 50(2): 166–182.

Li J, Wang Z, Zhang Y, et al., 2017. Degradation Data Analysis Based on a Generalized Wiener Process Subject to Measurement Error[J]. Mechanical Systems and Signal Processing, 94: 57–72.

Li J, Wang Z, Zhang Y, et al., 2018. A Nonlinear Wiener Process Degradation Model with Autoregressive Errors[J]. Reliability Engineering & System Safety, 173: 48–57.

Louis T A, 1982. Finding the Observed Information Matrix When Using the EM Algorithm[J]. Journal of the Royal Statistical Society, Series B, 44: 226–233.

Lu B, Chen Z, Zhao X, 2022. Data-Driven Dynamic Adaptive Replacement Policy for Units Subject to Heterogeneous Degradation[J]. Computers & Industrial Engineering, 171: 108478. DOI:10.1016/j.cie.2022.108478.

Lu C J, Meeker W O, 1993. Using Degradation Measures to Estimate a Time-to-Failure Distribution[J]. Technometrics, 35(2): 161–174.

Lu L, Wang B, Hong Y, et al., 2020. General Path Models for Degradation Data with Multiple Characteristics and Covariates[J]. Technometrics, 63(3): 354–369.

Ma Y, Chen Y, Zhou X, et al., 2019. Remaining Useful Life Prediction of Lithium-Ion Battery Based on Gauss–Hermite Particle Filter[J]. IEEE Transactions on Control Systems Technology, 27(4): 1788–1795.

Marin J-M, Mengersen K, Robert C P, 2005. Bayesian Modelling and Inference on Mixtures of Distributions[J]. Handbook of Statistics, 25: 459–507.

Marsaglia G, Tsang W W, Wang J, 2003. Evaluating Kolmogorov’s Distribution[J]. Journal of Statistical Software, 8: 1–4.

Marshall A W, Olkin I, 1967. A Multivariate Exponential Distribution[J]. Journal of the American Statistical Association, 62(317): 30–44.

Ma Z, Wang S, Liao H, et al., 2019. Engineering-Driven Performance Degradation Analysis of Hydraulic Piston Pump Based on the Inverse Gaussian Process[J]. Quality and Reliability Engineering International, 35(7): 2278–2296.

McLachlan G J, Krishnan T, 2007. The EM Algorithm and Extensions[M]. John Wiley & Sons.

Meeker W Q, Escobar L A, Pascual F G, 1998. Statistical Methods for Reliability Data[M]. John Wiley & Sons.

Meintanis S G, 2007. Test of Fit for Marshall–Olkin Distributions with Applications[J]. Journal of Statistical Planning and Inference, 137: 3954–3963.

Miller K W, Morell L J, Noonan R E, et al., 1992. Estimating the Probability of Failure When Testing Reveals No Failures[J]. IEEE Transactions on Software Engineering, 18(1): 33.

Nelson W, 1980. Accelerated Life Testing-Step-Stress Models and Data Analyses[J]. IEEE Transactions on Reliability, 29(2): 103–108.

Nguyen K T, Medjaher K, Gogu C, 2022. Probabilistic Deep Learning Methodology for Uncertainty Quantification of Remaining Useful Lifetime of Multi-Component Systems[J]. Reliability Engineering & System Safety, 222: 108383.

Ntzoufras I, 2011. Bayesian Modeling Using WinBUGS[M]. John Wiley & Sons.

Pan D, Liu J-B, Cao J, 2016. Remaining Useful Life Estimation Using an Inverse Gaussian Degradation Model[J]. Neurocomputing, 185: 64–72.

Pan D, Liu J-B, Huang F, et al., 2017. A Wiener Process Model with Truncated Normal Distribution for Reliability Analysis[J]. Applied Mathematical Modelling, 50: 333–346.

Park C, Padgett W, 2005. Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes[J]. Lifetime Data Analysis, 11(4): 511–527.

Park C, Padgett W J, 2006. Stochastic Degradation Models with Several Accelerating Variables[J]. IEEE Transactions on Reliability, 55(2): 379–390. DOI:10.1109/TR.2006.874937.

Park C, Padgett W J, 2014. Cumulative Damage Models Based on Gamma Processes[J]. Wiley StatsRef: Statistics Reference Online.

Paroissin C, 2015. Inference for the Wiener Process with Random Initiation Time[J]. IEEE Transactions on Reliability, 65(1): 147–157.

Paroissin C, 2017. Online Estimation Methods for the Gamma Degradation Process[J]. IEEE Transactions on Reliability, 66(4): 1361–1367.

Peng C-Y, 2015. Inverse Gaussian Processes with Random Effects and Explanatory Variables for Degradation Data[J]. Technometrics, 57(1): 100–111.

Peng C-Y, Cheng Y-S, 2020. Student-t Processes for Degradation Analysis[J]. Technometrics, 62(2): 223–235.

Peng W, Chen Y, Xu A, et al., 2024. Collaborative Online RUL Prediction of Multiple Assets with Analytically Recursive Bayesian Inference[J]. IEEE Transactions on Reliability, 73(1): 506–520.

Peng C-Y, Hsu S-C, 2012. A Note on a Wiener Process with Measurement Error[J]. Applied Mathematics Letters, 25(4): 729–732.

Peng W, Li Y-F, Yang Y-J, et al., 2014. Inverse Gaussian Process Models for Degradation Analysis: A Bayesian Perspective[J]. Reliability Engineering & System Safety, 130: 175–189.

Peng W W, Li Y F, Yang Y J, et al., 2016. Bivariate Analysis of Incomplete Degradation Observations Based on Inverse Gaussian Processes and Copulas[J]. IEEE Transactions on Reliability, 65(2): 624–639.

Peng W, Li Y-F, Yang Y-J, et al., 2017. Bayesian Degradation Analysis with Inverse Gaussian Process Models Under Time-Varying Degradation Rates[J]. IEEE Transactions on Reliability, 66(1): 84–96. DOI:10.1109/TR.2016.2635149.

Peng W, Shen L, Shen Y, et al., 2018. Reliability Analysis of Repairable Systems with Recurrent Misuse-Induced Failures and Normal-Operation Failures[J]. Reliability Engineering & System Safety, 171: 87–98.

Peng C-Y, Tseng S-T, 2009. Mis-Specification Analysis of Linear Degradation Models[J]. IEEE Transactions on Reliability, 58(3): 444–455.

Peng Y, Wang Y, Zi Y, et al., 2017. Dynamic Reliability Assessment and Prediction for Repairable Systems with Interval-Censored Data[J]. Reliability Engineering & System Safety, 159: 301–309.

Peng Weiwen, Ye Z-S, Chen N, 2018. Joint Online RUL Prediction for Multivariate Deteriorating Systems[J]. IEEE Transactions on Industrial Informatics, 15(5): 2870–2878. DOI:10.1109/TII.2018.2869429.

Peng W, Zhu S-P, Shen L, 2019. The Transformed Inverse Gaussian Process as an Age-and State-Dependent Degradation Model[J]. Applied Mathematical Modelling, 75: 837–852.

Polson N G, Scott J G, 2012. On the Half-Cauchy Prior for a Global Scale Parameter[J]. Bayesian Analysis, 7(4): 887–901.

Pulcini G, 2016. A Perturbed Gamma Process with Statistically Dependent Measurement Errors[J]. Reliability Engineering & System Safety, 152: 296–306.

Ren L, Jia Z, Laili Y, et al., 2024. Deep Learning for Time-Series Prediction in IIoT: Progress, Challenges, and Prospects[J]. IEEE Transactions on Neural Networks and Learning Systems, 35(11): 15072–15091.

Robinson M E, Crowder M J, 2000. Bayesian Methods for a Growth-Curve Degradation Model with Repeated Measures[J]. Lifetime Data Analysis, 6: 357–374.

Schrödinger E, 1915. Notiz über Den Kapillardruck in Gasblasen[J]. Annalen Der Physik, 351(3): 413–418.

Seo K, Pan R, 2017. Data Analysis of Step-Stress Accelerated Life Tests with Heterogeneous Group Effects[J]. IISE Transactions, 49(9): 885–898.

Severson K A, Attia P M, Jin N, et al., 2019. Data-Driven Prediction of Battery Cycle Life Before Capacity Degradation[J]. Nature Energy, 4(5): 383–391.

Shaked M A, 1977. Concept of Positive Dependence for Exchangeable Random Variables[J]. Annals of Statistics, 5(3): 505–515.

Shen L, Wang Y, Zhai Q, et al., 2018. Degradation Modeling Using Stochastic Processes with Random Initial Degradation[J]. IEEE Transactions on Reliability, 68(4): 1320–1329. DOI:10.1109/TR.2018.2885133.

Sheu S-H, Tsai H-N, Sheu U-Y, et al., 2019. Optimal Replacement Policies for a System Based on a One-Cycle Criterion[J]. Reliability Engineering & System Safety, 191: 106527. DOI:10.1016/j.ress.2019.106527.

Shuster J, 1968. On the Inverse Gaussian Distribution Function[J]. Journal of the American Statistical Association, 63(324): 1514–1516.

Si X-S, Hu C, Wang W, et al., 2011. An Adaptive and Nonlinear Drift-Based Wiener Process for Remaining Useful Life Estimation[C]. 2011 Prognostics; System Health Managment Confernece: 1–5.

Singpurwalla N, 1997. Gamma Processes and Their Generalizations: An Overview[J]. Engineering Probabilistic Design and Maintenance for Flood Protection, : 67–75.

Si X-S, Wang W, Hu C-H, et al., 2012. Remaining Useful Life Estimation Based on a Nonlinear Diffusion Degradation Process[J]. IEEE Transactions on Reliability, 61(1): 50–67.

Si W, Yang Q, Wu X, et al., 2018. Reliability Analysis Considering Dynamic Material Local Deformation[J]. Journal of Quality Technology, 50(2): 183–197.

Si X-S, Zhou D, 2013. A Generalized Result for Degradation Model-Based Reliability Estimation[J]. IEEE Transactions on Automation Science and Engineering, 11(2): 632–637.

Song S, Coit D W, Feng Q, et al., 2014. Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes[J]. IEEE Transactions on Reliability, 63(1): 331–345.

Sun B, Li Y, Wang Z, et al., 2021. An Improved Inverse Gaussian Process with Random Effects and Measurement Errors for RUL Prediction of Hydraulic Piston Pump[J]. Measurement, 173: 108604.

Tang S, Guo X, Yu C, et al., 2014. Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects[J]. Mathematical Problems in Engineering, 2014(1): 560726.

Tang S, Yu C, Wang X, et al., 2014. Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Wiener Process with Measurement Error[J]. Energies, 7(2): 520–547.

Taylor D, Rigdon S E, Pan R, et al., 2024. Bayesian D-Optimal Design for Life Testing with Censoring[J]. Quality and Reliability Engineering International, 40(1): 71–90. DOI:10.1002/qre.322.

Tsai C, Tseng S, Balakrishnan N, 2011. Mis-Specification Analyses of Gamma and Wiener Degradation Processes[J]. Journal of Statistical Planning and Inference, 141(12): 3725–3735.

Tsai C-C, Tseng S-T, Balakrishnan N, 2012. Optimal Design for Degradation Tests Based on Gamma Processes with Random Effects[J]. IEEE Transactions on Reliability, 61(2): 604–613.

Tseng S-T, Lee I-C, 2016. Optimum Allocation Rule for Accelerated Degradation Tests with a Class of Exponential-Dispersion Degradation Models[J]. Technometrics, 58(2): 244–254.

Tseng S-T, Peng C-Y, 2007. Stochastic Diffusion Modeling of Degradation Data[J]. Journal of Data Science, 5(3): 315–333.

Turlapaty A C, 2020. Variational Bayesian Estimation of Statistical Properties of Composite Gamma Log-Normal Distribution[J]. IEEE Transactions on Signal Processing, 68: 6481–6492.

Tweedie M C, 1984. An Index Which Distinguishes Between Some Important Exponential Families[J]. 579: 579–604.

Van der Vaart A W, 1998. Asymptotic Statistics[M]. Cambridge University Press.

Van Noortwijk J M, 2009. A Survey of the Application of Gamma Processes in Maintenance[J]. Reliability Engineering & System Safety, 94(1): 2–21.

Wang X, 2008. A Pseudo-Likelihood Estimation Method for Nonhomogeneous Gamma Process Model with Random Effects[J]. Statistica Sinica, 18(3): 1153–1163.

Wang X, 2010. Wiener Processes with Random Effects for Degradation Data[J]. Journal of Multivariate Analysis, 101(2): 340–351.

Wang X, Balakrishnan N, Guo B, 2014. Residual Life Estimation Based on a Generalized Wiener Degradation Process[J]. Reliability Engineering & System Safety, 124: 13–23.

Wang X, Guo B, Cheng Z, 2014. Residual Life Estimation Based on Bivariate Wiener Degradation Process with Time-Scale Transformations[J]. Journal of Statistical Computation and Simulation, 84(3): 545–563.

Wang H, Ma X, Zhao Y, 2019. An Improved Wiener Process Model with Adaptive Drift and Diffusion for Online Remaining Useful Life Prediction[J]. Mechanical Systems and Signal Processing, 127: 370–387.

Wang X, Schumitzky A, D’Argenio D Z, 2007. Nonlinear Random Effects Mixture Models: Maximum Likelihood Estimation via the EM Algorithm[J]. Computational Statistics & Data Analysis, 51: 6614–6623.

Wang P, Tang Y, Bae S J, He Y, 2018. Bayesian Analysis of Two-Phase Degradation Data Based on Change-Point Wiener Process[J]. Reliability Engineering & System Safety, 170: 244–256.

Wang P, Tang Y, Bae S J, Xu A, 2018. Bayesian Approach for Two-Phase Degradation Data Based on Change-Point Wiener Process with Measurement Errors[J]. IEEE Transactions on Reliability, 67(2): 688–700. DOI:10.1109/tr.2017.2785978.

Wang P, Tang Y, Joo Bae S, et al., 2018. Bayesian Analysis of Two-Phase Degradation Data Based on Change-Point Wiener Process[J]. Reliability Engineering & System Safety, 170: 244–256. DOI:10.1016/j.ress.2017.09.027.

Wang B, Titterington D M, 2005. Inadequacy of Interval Estimates Corresponding to Variational Bayesian Approximations[C]//International Workshop on Artificial Intelligence and Statistics. PMLR: 373–380.

Wang X, Wang B X, Jiang P H, et al., 2020. Accurate Reliability Inference Based on Wiener Process with Random Effects for Degradation Data[J]. Reliability Engineering & System Safety, 193: 106631.

Wang X, Xu D, 2010. An Inverse Gaussian Process Model for Degradation Data[J]. Technometrics, 52(2): 188–197.

Wang B, Yu K, Jones M C, 2010. Inference Under Progressively Type II Right-Censored Sampling for Certain Lifetime Distributions[J]. Technometrics, 52(4): 453–460.

Wang Z, Zhai Q, Chen P, 2021. Degradation Modeling Considering Unit-to-Unit Heterogeneity-a General Model and Comparative Study[J]. Reliability Engineering & System Safety, 216: 107897.

Weerahandi S, 1993. Generalized Confidence Intervals[J]. Journal of the American Statistical Association, 88: 899–905.

Wen Y, Rahman M F, Xu H, et al., 2022. Recent Advances and Trends of Predictive Maintenance from Data-Driven Machine Prognostics Perspective[J]. Measurement, 187: 110276.

Whitmore G, 1995. Estimating Degradation by a Wiener Diffusion Process Subject to Measurement Error[J]. Lifetime Data Analysis, 1(3): 307–319.

Whitmore G A, Schenkelberg F, 1997. Modelling Accelerated Degradation Data Using Wiener Diffusion with a Time Scale Transformation[J]. Lifetime Data Analysis, 3(1): 27–45.

Wu C, 1983. On the Convergence Properties of the EM Algorithm[J]. The Annals of Statistics, 11(1): 95–103.

Wu S, Castro I T, 2020. Maintenance Policy for a System with a Weighted Linear Combination of Degradation Processes[J]. European Journal of Operational Research, 280(1): 124–133.

Wu W F, Ni C C, 2003. A Study of Stochastic Fatigue Crack Growth Modeling Through Experimental Data[J]. Probabilistic Engineering Mechanics, 18(2): 107–118.

Wu W, Wang B X, Chen J, et al., 2023. Interval Estimation of the Two-Parameter Exponential Constant Stress Accelerated Life Test Model Under Type-II Censoring[J]. Quality Technology & Quantitative Management, 20(6): 751–762. DOI:10.1080/16843703.2022.2147688.

Xia J, Feng Y, Teng D, et al., 2022. Distance Self-Attention Network Method for Remaining Useful Life Estimation of Aeroengine with Parallel Computing[J]. Reliability Engineering & System Safety, 225: 108636.

Xiao T, Park C, Lin C, et al., 2023. Hybrid Reliability Analysis with Incomplete Interval Data Based on Adaptive Kriging[J]. Reliability Engineering & System Safety, 237: 109362. DOI:10.1016/j.ress.2023.10936.

Xu L, Jordan M I, 1996. On Convergence Properties of the EM Algorithm for Gaussian Mixtures[J]. Neural Computation, 8: 129–151.

Xu A, Sanjib B, Tang Y, 2014. A Full Bayesian Approach for Masked Data in Step-Stress Accelerated Life Testing[J]. IEEE Transactions on Reliability, 63(3): 798–806.

Xu A, Shen L, 2018. Improved on-Line Estimation for Gamma Process[J]. Statistics & Probability Letters, 143: 67–73.

Xu A, Shen L, Wang B, et al., 2018. On Modeling Bivariate Wiener Degradation Process[J]. IEEE Transactions on Reliability, 67(3): 897–906.

Xu A, Tang Y, 2012. Objective Bayesian Analysis for Linear Degradation Models[J]. Communications in Statistics-Theory and Methods, 41(21): 4034–4046.

Xu A, Zhou S, 2017. Bayesian Analysis of Series System with Dependent Causes of Failure[J]. Statistical Theory and Related Fields, 1: 128–140.

Xu A, Zhou S, Tang Y, 2021. A Unified Model for System Reliability Evaluation Under Dynamic Operating Conditions[J]. IEEE Transactions on Reliability, 70(1): 65–72.

Yalaoui A, Chu C, Chatelet E, 2005. Reliability Allocation Problem in a Series-Parallel System[J]. Reliability Engineering & System Safety, 90(1): 55–61.

Yang G, 2008. Life Cycle Reliability Engineering[M]. John Wiley & Sons, Inc.

Yang L, Ma X, Zhao Y, 2017. A Condition-Based Maintenance Model for a Three-State System Subject to Degradation and Environmental Shocks[J]. Computers & Industrial Engineering, 105: 210–222. DOI:10.1016/j.cie.2017.01.012.

Yan B, Ma X, Yang L, et al., 2020. A Novel Degradation-Rate-Volatility Related Effect Wiener Process Model with Its Extension to Accelerated Ageing Data Analysis[J]. Reliability Engineering & System Safety, 204: 107138.

Ye Z-S, Chen N, 2014. The Inverse Gaussian Process as a Degradation Model[J]. Technometrics, 56(3): 302–311.

Ye Z-S, Chen N, Shen Y, 2015. A New Class of Wiener Process Models for Degradation Analysis[J]. Reliability Engineering & System Safety, 139: 58–67.

Ye Z-S, Chen L-P, Tang L C, et al., 2014. Accelerated Degradation Test Planning Using the Inverse Gaussian Process[J]. IEEE Transactions on Reliability, 63(3): 750–763.

Ye Z-S, Hong Y, Xie Y, 2013. How Do Heterogeneities in Operating Environments Affect Field Failure Predictions and Test Planning?[J]. The Annals of Applied Statistics, 7(4): 2249–2271.

Ye Z-S, Shen Y, Xie M, 2012. Degradation-Based Burn-in with Preventive Maintenance[J]. European Journal of Operational Research, 221(2): 360–367.

Ye Z-S, Wang Y, Tsui K-L, et al., 2013. Degradation Data Analysis Using Wiener Processes with Measurement Errors[J]. IEEE Transactions on Reliability, 62(4): 772–780.

Ye Z-S, Xie M, 2015. Stochastic Modelling and Analysis of Degradation for Highly Reliable Products[J]. Applied Stochastic Models in Business and Industry, 31(1): 16–32.

Ye Z-S, Xie M, Tang L-C, et al., 2012. Degradation-Based Burn-in Planning Under Competing Risks[J]. Technometrics, 54(2): 159–168.

Yuan T, Bae S J, Zhu X, 2016. A Bayesian Approach to Degradation-Based Burn-in Optimization for Display Products Exhibiting Two-Phase Degradation Patterns[J]. Reliability Engineering & System Safety, 155: 55–63.

Yuan X-X, Higo E, Pandey M D, 2021. Estimation of the Value of an Inspection and Maintenance Program: A Bayesian Gamma Process Model[J]. Reliability Engineering & System Safety, 216: 107912.

Yuan T, Ji Y, 2015. A Hierarchical Bayesian Degradation Model for Heterogeneous Data[J]. IEEE Transactions on Reliability, 64(1): 63–70.

Yuan T, Zhu X, 2012. Reliability Study of Ultra-Thin Dielectric Films with Variable Thickness Levels[J]. IIE Transactions, 44(9): 744–753.

Zaidan M A, Mills A R, Harrison R F, et al., 2016. Gas Turbine Engine Prognostics Using Bayesian Hierarchical Models: A Variational Approach[J]. Mechanical Systems and Signal Processing, 70: 120–140.

Zellner A, 1986. On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions[J]. Bayesian Inference and Decision Techniques.

Zhai Q, Chen P, Hong L, et al., 2018. A Random-Effects Wiener Degradation Model Based on Accelerated Failure Time[J]. Reliability Engineering & System Safety, 180: 94–103.

Zhai Q, Xu A, Yang J, et al., 2023. Statistical Modeling and Reliability Analysis for Degradation Processes Indexed by Two Scales[J]. IEEE Transactions on Industrial Informatics, 20(3): 3675–3684.

Zhai Q, Ye Z-S, 2018. Degradation in Common Dynamic Environments[J]. Technometrics, 60(4): 461–471. DOI:10.1080/00401706.2017.1375994.

Zhai Q, Ye Z-S, 2023. A Multivariate Stochastic Degradation Model for Dependent Performance Characteristics[J]. Technometrics, 65(3): 315–327. DOI:10.1080/00401706.2022.2157881.

Zhang H, Chen M, Shang J, et al., 2021. Stochastic Process-Based Degradation Modeling and RUL Prediction: From Brownian Motion to Fractional Brownian Motion[J]. Science China Information Sciences, 64(7): 171201.

Zhang Y, Feng F, Wang S, et al., 2023. Joint Nonlinear-Drift-Driven Wiener Process-Markov Chain Degradation Switching Model for Adaptive Online Predicting Lithium-Ion Battery Remaining Useful Life[J]. Applied Energy, 341: 121043. DOI:10.1016/j.apenergy.2023.121043.

Zhang J, Huang X, Fang Y, et al., 2016. Optimal Inspection-Based Preventive Maintenance Policy for Three-State Mechanical Components Under Competing Failure Modes[J]. Reliability Engineering & System Safety, 152: 95–103. DOI:10.1016/j.ress.2016.02.007.

Zhang Z, Hu C, Si X, et al., 2017. Stochastic Degradation Process Modeling and Remaining Useful Life Estimation with Flexible Random-Effects[J]. Journal of the Franklin Institute, 354(6): 2477–2499.

Zhang Y, Ouyang L, Meng X, et al., 2024. Condition-Based Maintenance Considering Imperfect Inspection for a Multi-State System Subject to Competing and Hidden Failures[J]. Computers & Industrial Engineering, 188: 109856. DOI:10.1016/j.cie.2023.109856.

Zhang Z, Si X, Hu C, et al., 2018. Degradation Data Analysis and Remaining Useful Life Estimation: A Review on Wiener-Process-Based Methods[J]. European Journal of Operational Research, 271(3): 775–796.

Zhou S, Tang Y, Xu A, 2021. A Generalized Wiener Process with Dependent Degradation Rate and Volatility and Time-Varying Mean-to-Variance Ratio[J]. Reliability Engineering & System Safety, 216: 107895.

Zhou S, Xu A, 2019. Exponential Dispersion Process for Degradation Analysis[J]. IEEE Transactions on Reliability, 68(2): 398–409.

Zhou S, Xu A, Lian Y, et al., 2020. Variational Bayesian Analysis for Wiener Degradation Model with Random Effects[J]. Communications in Statistics-Theory and Methods, : 1–21.

Zhou S, Xu A, Tang Y, et al., 2023. Fast Bayesian Inference of Reparameterized Gamma Process with Random Effects[J]. IEEE Transactions on Reliability, 73(1): 399–412. DOI:10.1109/TR.2023.3263940.

Zhuang L, Xu A, Wang Y, et al., 2024. Remaining Useful Life Prediction for Two-Phase Degradation Model Based on Reparameterized Inverse Gaussian Process[J]. European Journal of Operational Research, 319(3): 877–890. DOI:https://doi.org/10.1016/j.ejor.2024.06.032.

Zhu R, Chen Y, Peng W, et al., 2022. Bayesian Deep-Learning for RUL Prediction: An Active Learning Perspective[J]. Reliability Engineering & System Safety, 228: 108758. DOI:10.1016/j.ress.2022.108758.

张志华, 2002. 加速寿命试验及其统计分析[M]. 加速寿命试验及其统计分析.

李海洋, 谢里阳, 李铭, et al., 2018. 一种新的无失效数据可靠性评估方法研究[J]. 兵工学报, 39(8): 1622.

茆诗松, 汤银才, 王玲玲, 2008. 可靠性统计[M]. 可靠性统计.

韩明, 2003. 产品无失效数据的综合处理[J]. 机械工程学报, 39(2): 129–132.