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Research Articles

Condition-based maintenance optimisation for multi-component systems using mean residual life

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Pages 4831-4855 | Received 08 Jan 2023, Accepted 30 Oct 2023, Published online: 15 Nov 2023

References

  • Agarwal, S. K., and S. L. Kalla. 1996. “A Generalized Gamma Distribution and Its Applications in Relativity.” Communications in Statistics – Theory and Methods 25 (1): 201–210. https://doi.org/10.1080/03610929608831688.
  • Aharon, B.-T., G. Boaz, and S. Shimrit. 2009. “Robust Multi-Echelon Multi-Period Inventory Control.” European Journal of Operational Research 199 (3): 922–935. https://doi.org/10.1016/j.ejor.2009.01.058.
  • An, Z., and D. Sun. 2017. “Reliability Modeling for Systems Subject to Multiple Dependent Competing Failure Processes with Shock Loads Above a Certain Level.” Reliability Engineering & System Safety 157: 129–138. https://doi.org/10.1016/j.ress.2016.08.025.
  • Badia, F. G., and E. T. Salehi. 2012. “Preservation of Reliability Classes Associated with the Mean Residual Life by a Renewal Process Stopped at a Random Time.” Applied Stochastic Models in Business and Industry 28 (4): 381–394. https://doi.org/10.1002/asmb.921.
  • Baharum, A., F. M. Alwan, and S. T. Hasson. 2013. “A Case Study of Reliability and Performance of the Electric Power Distribution Station Based on Time Between Failures.” Hindawi Publishing Corporation Mathematical Problems in Engineering 2013: Article ID 583683, 6 pages.
  • Balakrishnan, N., José María Sarabia, and Nikolai Kolev. 2010. “A Simple Relation Between the Leimkuhler Curve and the Mean Residual Life.” Journal of Informetrics 4 (4): 602–607. https://doi.org/10.1016/j.joi.2010.06.009.
  • Barlow, R. E., and F. Proshan. 1975. Statistical Theory of Reliability and Life Testing Holt. New York: Rinehart & Winston.
  • Bradley, D. M., and R. C. Gupta. 2003. “Limiting Behaviour of the Mean Residual Life.” Annals of the Institute of Statistical Mathematics 55 (1): 217–226.
  • Buer, S.-V., J. O. Strandhagen, and F. T. S. Chan. 2018. “The Link Between Industry 4.0 and Lean Manufacturing: Mapping Current Research and Establishing a Research Agenda.” International Journal of Production Research 56 (8): 2924–2940. https://doi.org/10.1080/00207543.2018.1442945.
  • Calabria, R., and G. Pulcini. 1987. “On the Asymptotic Behaviour of Mean Residual Life Function.” Reliability Engineering 19 (3): 165–170. https://doi.org/10.1016/0143-8174(87)90001-1.
  • Cassady, C. R., W. P. Murdock, and E. A. Pohl. 2001a. “Selective Maintenance for Support Equipment Involving Multiple Maintenance Actions.” European Journal of Operational Research 129: 252–258. https://doi.org/10.1016/S0377-2217(00)00222-8.
  • Cassady, C. R., E. A. Pohl, and W. P. Murdock. 2001b. “Selective Maintenance Modeling for Industrial Systems.” Journal of Quality in Maintenance Engineering 7 (2): 104–117. https://doi.org/10.1108/13552510110397412.
  • Castro, I. T., N. C. Caballe, and C. J. Perez. 2015. “A Condition-Based Maintenance for a System Subject to Multiple Degradation Processes and External Shocks.” International Journal of Systems Science 46 (9): 1692–1704. https://doi.org/10.1080/00207721.2013.828796.
  • Chaubey, Y. P., and P. K. Sen. 1999. “On Smooth Estimation of Mean Residual Life.” Journal of Statistical Planning and Inference 75 (2): 223–236. https://doi.org/10.1016/S0378-3758(98)00144-X.
  • Chen, Nan, et al. 2015. “Condition-based Maintenance Using the Inverse Gaussian Degradation Model.” European Journal of Operation Research.
  • Chen, Yuan, et al. 2022. “Condition-based Opportunistic Maintenance Policies with Two-Phase Inspections for Continuous-State Systems.” Reliability Engineering & System Safety.
  • Cox, D. R. 1962. Renewal Theory. London: Chapman and Hall.
  • Da Costa, P. R., A. Akçay, Y. Zhang, and U. Kaymak. 2020. “Remaining Useful Lifetime Prediction via Deep Domain Adaptation.” Reliability Engineering & System Safety 195: 106682. https://doi.org/10.1016/j.ress.2019.106682.
  • de Jesus Santos, A. C., C. A. V. Cavalcante, and S. Wub. 2023. “Maintenance Policies and Models: A Bibliometric and Literature Review of Strategies for Reuse and Remanufacturing.” Reliability Engineering & System Safety 231: 108983. https://doi.org/10.1016/j.ress.2022.108983.
  • Do, Phuc, and Christophe Bérenguer. 2022. “Residual Life-Based Importance Measures for Predictive Maintenance Decision-Making.” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 236 (1): 98–113. https://doi.org/10.1177/1748006X211028112.
  • Ellefsen, A. L., E. Bjørlykhaug, V. Æsoy, S. Ushakov, and H. Zhang. 2019. “Remaining Useful Life Predictions for Turbofan Engine Degradation Using Semi-Supervised Deep Architecture.” Reliability Engineering & System Safety 183: 240–251. https://doi.org/10.1016/j.ress.2018.11.027.
  • Enrique, Daisy Valle, Giuliano Almeida Marodin, Fernando Bigares Charrua Santos, and Alejandro G. Frank. 2022. “Implementing Industry 4.0 for Flexibility, Quality, and Productivity Improvement: Technology Arrangements for Different Purposes.” International Journal of Production Research. https://doi.org/10.1080/00207543.2022.2142689.
  • Eryilmaz, S. 2017. “Computing Optimal Replacement Time and Mean Residual Life in Reliability Shock Models.” Computers & Industrial Engineering 103: 40–45. https://doi.org/10.1016/j.cie.2016.11.017.
  • Finkelstein, M., and J. H. Cha. 2013. Stochastic Modelling for Reliability (Shocks, Burn-in and Heterogeneous Populations). London: Springer.
  • Finkelstein, M., M. Shafiee, and A. N. Kotchap. 2016. “Classical Optimal Replacement Strategies Revisited.” IEEE Transactions on Reliability 65: 540–546. https://doi.org/10.1109/TR.2016.2515591.
  • Gan, Jie, Wenyu Zhang, Siyu Wang, and Xiaohong Zhang. 2022. “Joint Decision of Condition-Based Opportunistic Maintenance and Scheduling for Multi-Component Production Systems.” International Journal of Production Research 60 (17): 5155–5175. https://doi.org/10.1080/00207543.2021.1951447.
  • Guess, F. M., and F. Proschan. 1988. “Mean Residual Life: Theory and Application.” In Handbook of Statistics, Vol. 7 (Quality Control and Reliability), edited by n Krishnaiah/Roa, 215–224. Amsterdam: North–Holland.
  • Gunn, E. A., and C. Diallo. 2015. “Optimal Opportunistic Indirect Grouping of Preventive Replacements in Multicomponent Systems.” Computers & Industrial Engineering 90: 281–291. https://doi.org/10.1016/j.cie.2015.09.013.
  • Gupta, R. C., and D. M. Bradley. 2003. “Representing the Mean Residual Life in Terms of the Failure Rate.” Mathematical and Computer Modelling 37 (12-13): 1271–1280. https://doi.org/10.1016/S0895-7177(03)90038-0.
  • Gupta, R. C., and S. Lvin. 2005. “Monotonicity of Failure Rate and Mean Residual Life Function of a Gamma-Type Model.” Applied Mathematics and Computation 165 (3): 623–633. https://doi.org/10.1016/j.amc.2004.04.121.
  • Hall, W. J., and J. A. Wallner. 2017. Estimation of Mean Residual Life, imsart-generic ver. 2012/08/31 file: MRL-revived4c.tex date: July 12, 2017.
  • Hill, R. M. 1988. “Stock Control and the Undershoot of the Re-Order Level.” Journal of the Operational Research Society 39 (2): 173–181. https://doi.org/10.1057/jors.1988.29.
  • Hu, C., B. D. Youn, P. Wang, and J. T. Yoon. 2012. “Ensemble of Data-Driven Prognostic Algorithms for Robust Prediction of Remaining Useful Life.” Reliability Engineering & System Safety 103: 120–135. https://doi.org/10.1016/j.ress.2012.03.008.
  • Hwan, C. J., M. Finkelstein, and G. Levitin. 2018. “Bivariate Preventive Maintenance of Systems with Lifetimes Dependent on a Random Shock Process.” European Journal of Operational Research 266 (1): 122–134. https://doi.org/10.1016/j.ejor.2017.09.021.
  • Ji, G., W. Wu, B. Zhang, and H. Sun. 2013. “A Renewal-Process-Based Component Outage Model Considering the Effects of Aging and Maintenance.” International Journal of Electrical Power & Energy Systems 44 (1): 52–59. https://doi.org/10.1016/j.ijepes.2012.07.035.
  • Jiao, R., K. Peng, J. Donga, and C. Zhang. 2020. “Fault Monitoring and Remaining Useful Life Prediction Framework for Multiple Fault Modes in Prognostics.” Reliability Engineering & System Safety 203: 107028. https://doi.org/10.1016/j.ress.2020.107028.
  • Jong, W.-R., H.-T. Chen, Y.-H. Lin, Y.-W. Yu-Wei Chen, and T.-C. Li. 2020. “The Multi-Layered Job-Shop Automatic Scheduling System of Mould Manufacturing for Industry 3.5.” Computers & Industrial Engineering 149 (2020): 106797. https://doi.org/10.1016/j.cie.2020.106797.
  • Kalgren, P. W., C. S. Byington, M. J. Roemer, and M. J. Watson. 2006. “Defining PHM, a Lexical Evolution of Maintenance and Logistics.” IEEE Autotestcon, 353–358.
  • Kang, K., and V. Subramaniam. 2018. “Joint Control of Dynamic Maintenance and Production in a Failure-Prone Manufacturing System Subjected to Deterioration.” Computers & Industrial Engineering 119: 309–320. https://doi.org/10.1016/j.cie.2018.03.001.
  • Karlin, S. 1958. “The Application of Renewal Theory to the Study of Inventory Policies.” In Studies in the Mathematical Theory of Inventory and Production, edited by K. Arrow, S. Karlin, and H. Scarf, 270–297. Chapter 15. Stanford, CA: Stanford. University Press.
  • Kayid, M., S. Izadkhah, and H. Alhalees. 2016. “Combination of Mean Residual Life Order with Reliability Applications.” Statistical Methodology 29: 51–69. https://doi.org/10.1016/j.stamet.2015.10.001.
  • Khatab, A., and E. H. Aghezzaf. 2016. “Selective Maintenance Optimization for Series-Parallel Systems with Continuously Monitored Stochastic Degrading Components Subject to Imperfect Maintenance.” IFAC-PapersOnLine 49 (28): 256–261. https://doi.org/10.1016/j.ifacol.2016.11.044.
  • Koochaki, Javid, Jos A.C. Bokhorst, Hans Wortmann, and Warse Klingenberg. 2012. “Condition Based Maintenance in the Context of Opportunistic Maintenance.” International Journal of Production Research 50 (23): 6918–6929. https://doi.org/10.1080/00207543.2011.636924.
  • Kundu, Pradeep, et al. 2019. “Weibull Accelerated Failure Time Regression Model for Remaining Useful Life Prediction of Bearing Working Under Multiple Operating Conditions.” Mechanical Systems and Signal Processing.
  • Kundu, C., and A. K. Nanda. 2010. “On Generalized Mean Residual Life of Record Values.” Statistics & Probability Letters 80 (9-10): 797–806. https://doi.org/10.1016/j.spl.2010.01.013.
  • Laggoune, R., A. Chateauneuf, and D. Aissani. 2010. “Impact of Few Failure Data on the Opportunistic Replacement Policy for Multi-Component Systems.” Reliability Engineering & System Safety 95 (2): 108–119. https://doi.org/10.1016/j.ress.2009.08.007.
  • Lai, C. D., and M. Xie. 2006. Stochastic Ageing and Dependence for Reliability. New York: Springer-Verlag.
  • Lam, Teresa. 1991. Proportional Mean Residual Life, Technical Report No. 91-2, Department of Industrial and operation Engineering, The University of Michigan, Ann Arbor, MI 48109-2117.
  • Liao, Baoyu, Shaojun Lu, Tao Jiang, and Xing Zhu. 2022. “A Variable Neighborhood Search and Mixed-Integer Programming Models for a Distributed Maintenance Service Network Scheduling Problem.” International Journal of Production Research. https://doi.org/10.1080/00207543.2022.2138612.
  • Lundgren, Camilla, Cecilia Berlin, Anders Skoogh, and Anders Källström. 2022. “How Industrial Maintenance Managers Perceive Socio-Technical Changes in Leadership in the Industry 4.0 Context.” International Journal of Production Research, https://doi.org/10.1080/00207543.2022.2101031.
  • Madadi, M., P. Khalilpoor, and A. Jamalizadeh. 2015. “Regression Mean Residual Life of a System with Three Dependent Components with Normal Lifetimes.” Statistics & Probability Letters 100: 182–191. https://doi.org/10.1016/j.spl.2015.02.003.
  • Muth, E. J. 1980. “Memory as a Property of Probability Distributions.” IEEE Transactions on Reliability R-29: 160–164. https://doi.org/10.1109/TR.1980.5220764.
  • Najafi, Seyed vahid, et al. 2021. “An Optimal Opportunistic Maintenance Policy for a Two-Unit Series System with General Repair Using Proportional Hazards Models.” Reliability Engineering & System Safety.
  • Nanda, A. K. 2010. “Characterization of Distributions Through Failure Rate and Mean Residual Life Functions.” Statistics and Probability Letters 80 (9-10): 752–755. https://doi.org/10.1016/j.spl.2010.01.006.
  • Pargar, F., O. Kauppila, and J. Kujala. 2017. “Integrated Scheduling of Preventive Maintenance and Renewal Projects for Multi-Unit Systems with Grouping and Balancing.” Computers & Industrial Engineering 110: 43–58. https://doi.org/10.1016/j.cie.2017.05.024.
  • Pokorný, P., P. Hutař, and L. Náhlík. 2016. “Residual Fatigue Lifetime Estimation of Railway Axles for Various Loading Spectra.” Theoretical and Applied Fracture Mechanics 82: 25–32. https://doi.org/10.1016/j.tafmec.2015.06.007.
  • Rajagopalan, R., and C. R. Cassady. 2006. “An Improved Selective Maintenance Solution Approach.” Journal of Quality in Maintenance Engineering 12 (2): 172–185. https://doi.org/10.1108/13552510610667183.
  • Raqab, M. Z., and M. Asadi. 2008. “On the Mean Residual Life of Records.” Journal of Statistical Planning and Inference 138 (12): 3660–3666. https://doi.org/10.1016/j.jspi.2007.11.014.
  • Rebaiaia, M. L., and D. Ait-Kadi. 2016. “Notes on the Mean Residual Life Function of Coherent Systems: Application for a Reliability System’s Structure.” In The Proc. of MOSIM 2016 conference, ETS, Montréal, Canada.
  • Rebaiaia, M. L., and D. Ait-Kadi. 2019. “An Optimum Comparative Analysis for Minimal Repair and Replacement on Failures.” In IESM’2019, IEEE Xplore, 1–6.
  • Rebaiaia, Mohamed Larbi, and Daoud Ait-Kadi. 2021. “Maintenance Policies with Minimal Repair and Replacement on Failures: Analysis and Comparison.” International Journal of Production Research 59 (23): 6995–7017. https://doi.org/10.1080/00207543.2020.1832275.
  • Rebaiaia, Mohamed-Larbi, and Daoud Ait-Kadi. 2022. “A Remaining Useful Life Model for Optimizing Maintenance Cost and Spare-Parts Replacement of Production Systems in the Context of Sustainability.” IFAC-PapersOnLine 55 (10): 1562–1568. https://doi.org/10.1016/j.ifacol.2022.09.613.
  • Rebaiaia, M. L., D. Ait-Kadi, M. A. Jamali, and C. Mascle. 2015. “Modified Periodic Replacement with Used Items at Stochastic Failure: Focusing Sustainability and Profit Advantages.” In Safety and Reliability of Complex Engineered Systems. CRC Press Taylor & Francis Group. ISBN: 978-1-138-02879-.
  • Rebaiaia, M. L., D. Ait-Kadi, and A. Jamshidi. 2017. “Periodic Replacement Strategies: Optimality Conditions and Numerical Performance Comparisons.” International Journal of Production Research 55 (23): 7135–7152. https://doi.org/10.1080/00207543.2017.1349953.
  • Rice, W. F., C. R. Cassady, and J. Nachlas. 1998. “Optimal Maintenance Plans under Limited Maintenance Time.” In Proceedings of Industrial Engineering Conference, Banff, BC, Canada.
  • Ross, S. M. 1996. Stochastic Process. 2nd ed. New York: John Wiley & Sons. Inc.
  • Ross, S. M. 2010. Introduction to Probability Models. 10th ed. Ed. Elsevier.
  • Sen, A., and G. K. Bhattacharya. 1995. “Inference Procedures for the Linear Failure Rate Model.” Journal of Statistical Planning and Inference 46 (1): 59–76. https://doi.org/10.1016/0378-3758(94)00099-H.
  • Sepehrifar, M. B., K. Khorshidian, and A. R. Jamshidian. 2015. “On Renewal Increasing Mean Residual Life Distributions: An age Replacement Model with Hypothesis Testing Application.” Statistics & Probability Letters 96: 117–122. https://doi.org/10.1016/j.spl.2014.09.009.
  • Shafiee, Mahmood, and Maxim Finkelstein. 2015. “An Optimal Age-Based Group Maintenance Policy for Multi-Unit Degrading Systems.” Reliability Engineering and System Safety 134: 230–238. https://doi.org/10.1016/j.ress.2014.09.016.
  • Sheikh-Zadeh, A., H. Farhangi, and M. D. Rossetti. 2020. “Inventory Grouping and Sensitivity Analysis in Multi-Echelon Spare Part Provisioning Systems.” Computers & Industrial Engineering 143: 106230. https://doi.org/10.1016/j.cie.2019.106230.
  • Shi, Yue, et al. 2020. “Condition-based Maintenance Optimization for Multi-Component Systems Subject to a System Reliability Requirement.” Reliability Engineering & System Safety 202: 1–14.
  • Singleton, R. K., E. Strangas, and S. Aviyente. 2015. “Extended Kalman Filtering for Remaining-Useful-Life Estimation of Bearings.” IEEE Transactions on Industrial Electronics 62 (3): 1781–1790. https://doi.org/10.1109/TIE.2014.2336616.
  • Stein, W. E., and R. Dattero. 1999. “Bondesson’s Functions in Reliability Theory.” Applied Stochastic Models in Business and Industry 15 (2): 103–109.
  • Sudheesh, K. K. 2016. An exact Test for Renewal Increasing Mean Residual Life, arxiv.org/pdf/ 1503.08452.pdf.
  • Tang, L. C., Y. Lu, and E. P. Chew. 1999. “Mean Residual Life of Lifetime Distributions.” IEEE Transactions on Reliability 48 (1): 73–78.
  • Tang, Diyin, Viliam Makis, Leila Jafari, and Jinsong Yu. 2015. “Optimal Maintenance Policy and Residual Life Estimation for a Slowly Degrading System Subject to Condition Monitoring.” Reliability Engineering & System Safety 134: 198–207. https://doi.org/10.1016/j.ress.2014.10.015.
  • Timashev, S. A., and A. V. Bushinskaya. 2015. “Markov Approach to Early Diagnostics, Reliability Assessment, Residual Life and Optimal Maintenance of Pipeline Systems.” Structural Safety 56: 68–79. https://doi.org/10.1016/j.strusafe.2015.05.006.
  • Unnikrishnan, N., and P. G. Sankaran. 2010. “Properties of a Mean Residual Life Function Arising from Renewal Theory.” Naval Research Logistics (NRL) 57 (4): 373–379. https://doi.org/10.1002/nav.20413.
  • Vu, H.-C., P. Do, and A. Barros. 2016. “A Stationary Grouping Maintenance Strategy Using Mean Residual Life and the Birnbaum Importance Measure for Complex Structures.” IEEE Transactions on Reliability 65 (1): 217–234. https://doi.org/10.1109/TR.2015.2455498.
  • Vu, C., P. Do, A. Barros, and C. Bérenguer. 2012. “Maintenance Activities Planning and Grouping for Complex Structure Systems.” In Proc. Annu. Conf. Eur. Safety and Reliability Association, PSAM11 & ESREL 2012, 181–190.
  • Vu, C., P. Do, A. Barros, and C. Bérenguer. 2014. “Maintenance Grouping Strategy for Multi-Component Systems with Dynamic Contexts.” Reliability Engineering & System Safety 132: 233–249. https://doi.org/10.1016/j.ress.2014.08.002.
  • Vu, C., P. Do, A. Barros, and C. Bérenguer. 2015. “Maintenance Planning and Dynamic Grouping for Multi-Component Systems with Positive and Negative Economic Dependencies.” IMA Journal of Management Math 26 (2): 145–170.
  • Wang, H., and H. Pham. 2006. Reliability and Optimal Maintenance. London: Springer.
  • Wang, J., F. Zhang, J. Jianchuan Zhang, W. Liua, and K. Zhoub. 2023. “A Flexible RUL Prediction Method Based on Poly-Cell LSTM with Applications to Lithium Battery Data.” Reliability Engineering & System Safety 231: 108976. https://doi.org/10.1016/j.ress.2022.108976.
  • Xiao, Lei, Tangbin Xia, Ershun Pan, and Xinghui Zhang. 2020. “Long-term Predictive Opportunistic Replacement Optimisation for a Small Multi-Component System Using Partial Condition Monitoring Data to Date.” International Journal of Production Research 58 (13): 4015–4032. https://doi.org/10.1080/00207543.2019.1641236.
  • Yang, G. L. 1978. “Estimation of a Biometric Function.” The Annals of Statistics 6 (1): 112–116.
  • Yang, G., and Y. Zhou. 2014. “Semiparametric Varying-Coefficient Study of Mean Residual Life Models.” Journal of Multivariate Analysis 128: 226–238. https://doi.org/10.1016/j.jmva.2014.03.011.
  • Zeng, J., and H. Shi. 2016. “Real-time Prediction of Remaining Useful Life and Preventive Opportunistic Maintenance Strategy for Multi-Component Systems Considering Stochastic Dependence.” Computers & Industrial Engineering 93: 192–204. https://doi.org/10.1016/j.cie.2015.12.016.
  • Zhang, Zhengxin, et al. 2018. “Degradation Data Analysis and Remaining Useful Life Estimation: A Review on Wiener-Process-Based Methods.” European Journal of Operation Research 271 (3): 775–796.
  • Zhang, Nan, et al. 2022. “A Condition-Based Maintenance Policy Considering Failure Dependence and Imperfect Inspection for a Two-Component System.” Reliability Engineering & System Safety 217.
  • Zhang, N., Y. Deng, B. Liu, and J. Zhang. 2023b. “Condition-based Maintenance for a Multi-Component System in a Dynamic Operating Environment.” Reliability Engineering & System Safety 231: 108988. https://doi.org/10.1016/j.ress.2022.108988.
  • Zhang, J., X. Li, T. Tian, Y. Jiang, and S. Yin. 2023c. “A Variational Local Weighted Deep Sub-Domain Adaptation Network for Remaining Useful Life Prediction Facing Cross-Domain Condition.” Reliability Engineering & System Safety 231: 108986. https://doi.org/10.1016/j.ress.2022.108986.
  • Zhang, T., J. Shuai, Y. Shuai, L. Yua, H. Kui, K. Xu, D. Xie, and Y. Mei. 2023a. “Efficient Prediction Method of Triple Failure Pressure for Corroded Pipelines Under Complex Loads Based on a Backpropagation Neural Network.” Reliability Engineering & System Safety 231: 108990. https://doi.org/10.1016/j.ress.2022.108990.
  • Zhang, Xiaohong, and Jianchao Zeng. 2015. “Deterioration State Space Partitioning Method for Opportunistic Maintenance Modelling of Identical Multi-Unit Systems.” International Journal of Production Research 53 (7): 2100–2118. https://doi.org/10.1080/00207543.2014.965354.
  • Zhao, Xuejing, et al. 2010. “Condition-based Inspection/ Replacement Policies for Non-Monotone Deteriorating Systems with Environmental Covariates.” Reliability Engineering & System Safety 95 (8): 921–934.
  • Zhao, X., K. Cai, X. Wang, and Y. Song. 2018. “Optimal Replacement Policies for a Shock Model with a Change Point.” Computers & Industrial Engineering 118: 383–393. https://doi.org/10.1016/j.cie.2018.03.005.
  • Zhao, M., H. Jiang, and X. Liu. 2013. “A Note on Estimation of the Mean Residual Life Function with Left-Truncated and Right-Censored Data.” Statistics & Probability Letters 83 (10): 2332–2336. https://doi.org/10.1016/j.spl.2013.06.020.
  • Zhao, X., Z. Lv, Z. He, and W. Wang. 2019. “Reliability and Opportunistic Maintenance for a Series System with Multi-Stage Accelerated Damage in Shock Environments.” Computers & Industrial Engineering 137: 106029. https://doi.org/10.1016/j.cie.2019.106029.
  • Zhou, R., N. Serban, and N. Gebraeel. 2014. “Degradation-based Residual Life Prediction Under Different Environments.” The Annals of Applied Statistics 8 (3): 1671–1689. https://doi.org/10.1214/14-AOAS749.

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