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Predicting failure times of coherent systems. (English) Zbl 07892789

Summary: The article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are identically distributed (homogeneous components). The heterogeneous components’ case can be addressed similarly but more complexly. The present study is for non-repairable systems, but the information obtained could be used to decide if a maintenance action should be carried out at time \( t \). Different cases are considered regarding the information available at time \( t \). We use quantile regression techniques to predict the system failure times and to provide prediction intervals. The theoretical results are applied to specific system structures in some illustrative examples.
© 2024 The Authors. Naval Research Logistics published by Wiley Periodicals LLC.

MSC:

62-XX Statistics

References:

[1] Ahmadi, R., Castro, I. T., & Bautista, L. (2023). Reliability modeling and maintenance planning for a parallel system with respect to the state‐dependent mean residual time. Journal of the Operational Research Society. Advance online publication. https://doi.org/10.1080/01605682.2023.2194316 · doi:10.1080/01605682.2023.2194316
[2] Arriaza, A., Navarro, J., Sordo, M. A., & Suárez‐Llorens, A. (2023). A variance‐based importance index for systems with dependent components. Fuzzy Sets and Systems, 467, 108482. · Zbl 07898140
[3] Asadi, M., Hashemi, M., & Balakrishnan, N. (2023). An overview of some classical models and discussion of the signature‐based models of preventive maintenance. Applied Stochastic Models in Business and Industry, 39, 4-53. · Zbl 07889599
[4] Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing. Holt, Rinehart and Winston. · Zbl 0379.62080
[5] Bdair, O. M., & Raqab, M. Z. (2022). Prediction of future censored lifetimes from mixture exponential distribution. Metrika, 85, 833-857. · Zbl 07575566
[6] David, H. A., & Nagaraja, H. N. (2003). Order statistics (3rd ed.). Wiley. · Zbl 1053.62060
[7] Durante, F., & Sempi, C. (2016). Principles of copula theory. CRC/Chapman & Hall. · Zbl 1380.62008
[8] Eryilmaz, S. (2017). Computing optimal replacement time and mean residual life in reliability shock models. Computers & Industrial Engineering, 103, 40-45.
[9] Koenker, R. (2005). Quantile regression. Cambridge University Press. · Zbl 1111.62037
[10] Macci, C., & Navarro, J. (2023). Method‐of‐moment estimators of a scale parameter based on samples from a coherent system. Probability in the Engineering and Informational Sciences. 1-18. Advance online publication. https://doi.org/10.1017/S0269964823000037 · doi:10.1017/S0269964823000037
[11] Müller, A., & Stoyan, D. (2002). Comparison methods for stochastic models and risk. Wiley. · Zbl 0999.60002
[12] Navarro, J. (2018). Distribution‐free comparisons of residual lifetimes of coherent systems based on copula properties. Statistical Papers, 59, 781-800. · Zbl 1396.60029
[13] Navarro, J. (2022a). Introduction to system reliability theory. Springer.
[14] Navarro, J. (2022b). Prediction of record values by using quantile regression curves and distortion functions. Metrika, 85, 675-706. · Zbl 1490.62118
[15] Navarro, J., Arriaza, A., & Suárez, A. (2019). Minimal repair of failed components in coherent systems. European Journal of Operational Research, 279, 951-964. · Zbl 1430.90217
[16] Navarro, J., & Buono, F. (2023). Predicting future failure times by using quantile regression. Metrika, 86, 543-576. · Zbl 07702610
[17] Navarro, J., & Calì, C. (2019). Inactivity times of coherent systems with dependent components under periodical inspection. Applied Stochastic Models in Business and Industry, 35, 871-892. · Zbl 07883130
[18] Navarro, J., Calì, C., Longobardi, M., & Durante, F. (2022). Distortion representations of multivariate distributions. Statistical Methods & Applications, 31, 925-954. · Zbl 1495.62035
[19] Navarro, J., delÁguila, Y., Sordo, M. A., & Suárez‐Llorens, A. (2016). Preservation of stochastic orders under the formation of generalized distorted distributions. Applications to coherent systems. Methodology and Computing in Applied Probability, 18, 529-545. · Zbl 1371.60046
[20] Navarro, J., & Durante, F. (2017). Copula‐based representations for the reliability of the residual lifetimes of coherent systems with dependent components. Journal of Multivariate Analysis, 158, 87-102. · Zbl 1397.62391
[21] Navarro, J., Pellerey, F., & Longobardi, M. (2017). Comparison results for inactivity times of k‐out‐of‐n and general coherent systems with dependent components. Test, 26, 822-846. · Zbl 1458.62163
[22] Nelsen, R. B. (2006). An introduction to copulas. Springer. · Zbl 1152.62030
[23] Patwardhan, A., Verma, A. K., & Kumar, U. (2016). A survey on predictive maintenance through big data. In U.Kumar (ed.), A.Ahmadi (ed.), A.Verma (ed.), & P.Varde (ed.) (Eds.), Current trends in reliability, availability, maintainability and safetyLecture Notes in Mechanical Engineering. Springer.
[24] Samaniego, F. J. (2007). System signatures and their applications in engineering reliabilityInternational Series in Operations Research & Management Science (Vol. 110). Springer. · Zbl 1154.62075
[25] Takeuchi, I., Le, Q. V., Sears, T. D., & Smola, A. J. (2006). Nonparametric quantile estimation. Journal of Machine Learning Research, 7, 1231-1264. · Zbl 1222.68316
[26] Torrado, N., Arriaza, A., & Navarro, J. (2021). A study on multi‐level redundancy allocation in coherent systems formed by modules. Reliability Engineering & System Safety, 213, 107694.
[27] Yang, S., Frangopol, D. M., & Neves, L. C. (2004). Service life prediction of structural systems using lifetime functions with emphasis on bridges. Reliability Engineering & System Safety, 86, 39-51.
[28] Yang, Y., Ng, H. K. T., & Balakrishnan, N. (2016). A stochastic expectation‐maximization algorithm for the analysis of system lifetime data with known signature. Computational Statistics, 31, 609-641. · Zbl 1342.65073
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