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PERFORMANCE OF PROGNOSIS INDICATORS FOR SUPERIMPOSED RENEWAL PROCESSES

Published online by Cambridge University Press:  01 June 2020

Xingheng Liu Open the ORCID record for Xingheng Liu [Opens in a new window] ,
Yann Dijoux Open the ORCID record for Yann Dijoux [Opens in a new window] ,
Jørn Vatn  and
Håkon Toftaker
Xingheng Liu
Affiliation:
The Laboratory of Systems Modelling and Dependability, Université de Technologie de Troyes, Troyes, France; Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway
Yann Dijoux
Affiliation:
The Laboratory of Systems Modelling and Dependability, Université de Technologie de Troyes, Troyes, France. E-mail: [email protected]
Jørn Vatn
Affiliation:
Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway
Håkon Toftaker
Affiliation:
Monitoring and Analysis, Bane NOR SF, Hamar, Norway
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Abstract

The paper deals with prognosis estimation for industrial systems in a series configuration, modeled by superimposed renewal processes (SRP), when the cause of failures is not available. In the presence of missing information, an SRP is commonly approximated by a Poisson process or a virtual age model. The performance of the approximations was assessed in the ideal configuration where all parameters of the models are known. The current article adopts a practitioner's perspective by assuming that the parameters of the models are unknown and must be estimated. In addition to inference procedures, the assessment of the prognosis indicators, such as the remaining useful life, is discussed. Finally, we investigate a fleet of infrastructure components of the Norwegian railway network operated by Bane NOR.

Keywords

applied probabilityreliability theorysimulationstochastic modelling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 17 - 40
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Balakrishnan, N. & Lai, C.-D. (2009). Continuous bivariate distributions, 2nd ed. New York: Springer.Google Scholar
Bedford, T. & Lindqvist, B. (2004). The identifiability problem for repairable systems subject to competing risks. Advances in Applied Probability 36: 774–790.CrossRefGoogle Scholar
Bedford, T., Alkali, B., & Burnham, R. (2014). Competing risks in reliability. American Cancer Society. doi:10.1002/9781118445112.stat03670CrossRefGoogle Scholar
Brown, M. & Proschan, F. (1983). Imperfect repair. Journal of Applied Probability 20(4): 851–859.CrossRefGoogle Scholar
Caillault, C. & Guegan, D. (2005). Empirical estimation of tail dependence using copulas. Application to Asian markets. Quantitative Finance 5: 489–501.CrossRefGoogle Scholar
Cha, J. & Finkelstein, M. (2014). Some notes on unobserved parameters (frailties) in reliability modeling. Reliability Engineering & System Safety 123: 99–103.10.1016/j.ress.2013.10.008CrossRefGoogle Scholar
Cox, D.R. & Smith, W.L. (1954). On the superposition of renewal processes. Biometrika 41(1/2): 91–99.10.1093/biomet/41.1-2.91CrossRefGoogle Scholar
de Toledo, M.L.G., Freitas, M.A., Colosimo, E.A., & Gilardoni, G.L. (2015). ARA and ARI imperfect repair models: estimation, goodness-of-fit and reliability prediction. Reliability Engineering & System Safety 140: 107–115.CrossRefGoogle Scholar
Dijoux, Y., Fouladirad, M., & Nguyen, D.T. (2016). Statistical inference for imperfect maintenance models with missing data. Reliability Engineering & System Safety 154: 84–96.CrossRefGoogle Scholar
Doyen, L. (2011). On the Brown-Proschan model when repair effects are unknown. Applied Stochastic Models in Business and Industry 27(6): 600–618.10.1002/asmb.869CrossRefGoogle Scholar
Doyen, L. & Gaudoin, O. (2004). Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliability Engineering & System Safety 84(1): 45–56.Selected papers from ESREL 2002.CrossRefGoogle Scholar
Drenick, R. (1960). The failure law of complex equipment. Journal of the Society for Industrial and Applied Mathematics 8(4): 680–690.CrossRefGoogle Scholar
Efron, B. & Hinkley, D.V. (1978). Assessing the accuracy of the maximum likelihood estimator: observed versus expected fisher information. Biometrika 65(3): 457–482.CrossRefGoogle Scholar
Frahm, G., Junker, M., & Schmidt, R. (2005). Estimating the tail-dependence coefficient: properties and pitfalls. Insurance: Mathematics and Economics 37(1): 80–100. Papers presented at the DeMoSTAFI Conference, Québec, 20–22 May 2004.Google Scholar
Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness-of-fit tests for copulas: a review and a power study. Insurance: Mathematics and Economics 44(2): 199–213.Google Scholar
Joe, H. (2014). Dependence modeling with copulas. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Hoboken, NJ: Taylor and Francis.10.1201/b17116CrossRefGoogle Scholar
Karlin, S. & Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions. Journal of Multivariate Analysis 10(4): 499–516.CrossRefGoogle Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability 26(1): 89–102.CrossRefGoogle Scholar
Lehmann, E.L. (1966). Some concepts of dependence. Annals of Mathematical Statistics 37(5): 1137–1153.CrossRefGoogle Scholar
Lim, T. (1998). Estimating system reliability with fully masked data under Brown-Proschan imperfect repair model. Reliability Engineering & System Safety 59(3): 277–289.CrossRefGoogle Scholar
Liu, X., Dijoux, Y., & Vatn, J. (2019). On approximation of superposition of renewal process. In Proceedings of the 29th European Safety and Reliability Conference, Hanover (DE). Singapore:Published by Research Publishing, pp. 623–628.Google Scholar
Liu, X., Dijoux, Y., & Vatn, J. (2020). Approximation of superimposed renewal processes by virtual age models and copulas. Under submission.Google Scholar
Liu, X., Finkelstein, M., Vatn, J., & Dijoux, Y. (2020). Steady-state imperfect repair models. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2020.03.057CrossRefGoogle Scholar
Nafisah, I., Shrahili, M., Alotaibi, N., & Scarf, P. (2019). Virtual series-system models of imperfect repair. Reliability Engineering & System Safety 188: 604–613.CrossRefGoogle Scholar
Nguyen, D.T., Dijoux, Y., & Fouladirad, M. (2017). Analytical properties of an imperfect repair model and application in preventive maintenance scheduling. European Journal of Operational Research 256(2): 439–453.10.1016/j.ejor.2016.06.026CrossRefGoogle Scholar
Proschan, F. (1963). Theoretical explanation of observed decreasing failure rate. Technometrics 5(3): 375–383.CrossRefGoogle Scholar
Proschan, F. & Barlow, R.E. (1987). Mathematical theory of reliability. Classics in Applied Mathematics Series. Philadelphia, USA: Society for Industrial and Applied Mathematics.Google Scholar
Rigdon, S.E. & Basu, A.P. (1989). The power law process: a model for the reliability of repairable systems. Journal of Quality Technology 21(4): 251–260.CrossRefGoogle Scholar
Shih, J.H. & Louis, T. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51(4): 1384–1399.10.2307/2533269CrossRefGoogle ScholarPubMed
Sklar, A. (1996). Random variables, distribution functions, and copulas: a personal look backward and forward. Lecture Notes – Monograph Series 28: 1–14.Google Scholar
Song, S. & Xie, M. (2018). An integrated method for estimation with superimposed failure data. In 2018 IEEE International Conference on Prognostics and Health Management (ICPHM), Seattle, WA, pp. 1–5.CrossRefGoogle Scholar
Tanwar, M., Rai, R.N., & Bolia, N. (2014). Imperfect repair modeling using Kijima type generalized renewal process. Reliability Engineering & System Safety 124: 24–31.CrossRefGoogle Scholar
Torab, P. & Kamen, E.W. (2001). On approximate renewal models for the superposition of renewal processes. In IEEE International Conference on Communications, vol. 9. Helsinki, Finland: IEEE, pp. 2901–2906.10.1109/ICC.2001.936680CrossRefGoogle Scholar
Whitt, W. (1982). Approximating a point process by a renewal process, I: two basic methods. Operations Research 30(1): 125–147.CrossRefGoogle Scholar
Wu, S. (2019). A failure process model with the exponential smoothing of intensity functions. European Journal of Operational Research 275(2): 502–513.10.1016/j.ejor.2018.11.045CrossRefGoogle Scholar
Zhang, W., Tian, Y., Escobar, L.A., & Meeker, W.Q. (2017). Estimating a parametric component lifetime distribution from a collection of superimposed renewal processes. Technometrics 59(2): 202–214.CrossRefGoogle Scholar