A comparative review of solution methods and techniques for analyzing reliability in the transient state
Abstract views: 142
/ 
PDF downloads: 134
Keywords:
Comparative study 1, Differential Equations 2, Markov model 3, Transient state 4, Reliabiity 5, Numerical methods 6, large scale systems 7Abstract
The primary goal of this comparative study is to address various solution methods and techniques for transient analysis of a three-component system’s reliability. To analyse the system’s transient reliability, a Markov model is used. To determine the outcome of the differential equations of a three-component system in the transient state, three methods are used: the Laplace Transform method, the Matrix approach, and simple integration. These procedures are executed that has been reviewed using MATLAB 7.8.0 (R2009a). These tools and numerical methods offer a more reliable mathematical framework and methodology for evaluating the transient reliability of the system. The introduction of these techniques is useful for researchers to assess reliability and availability in large scale systems.
References
Singh, J., On multiple parallel channels with a finite source, Jnanabha Sect. A, 5, (1975), 1–7.
Barton, R., and Damon, W., Reliability in a multi-state system, Proceedings of the Sixth Annual South eastern Symposium on Systems theory, Baton Rouge, LA, USA (1974).
Murchland, J., Fundamental concepts and relations for 0 reliability analysis of multi-state systems and fault tree analysis, Theoretical and Applied Aspects of System Reliability and Fault Tree Analysis, (1975), 581–618 SIAM, Philadelphia, PA, USA.
Mahajan, P., Availability analysis of redundant repairable systems, Ph.D. thesis, Kurukshetra University, (1999).
Lisnianski, A., and Levitin, G., Multi-State System Reliability: Assessment, Optimization and Applications, World Scientific Publishing Co Pte Ltd, New York, NY, USA, (2003).
Levitin, G., Common supply failures in linear multi-state sliding window systems, Reliability Engineering and System Safety, 82 (1), (2003), 55–62.
Navarro, J., Ruiz, J. M., and Sandoval, C. J., A note on comparisons among coherent systems with dependent components using signatures, Statistics and Probability Letters, 27, (2005), 179–185.
Dembinska, A., On reliability analysis of k-out-of-n systems consisting of heterogeneous components with discrete lifetimes, IEEE Transactions on Reliability, 67 (3), (2018), 1071–1083.
Navarro, J., del Aguila, Y., Sordo, M. A., Suarez Llorens, A., Stochastic ordering properties for systems with dependent identically distributed components, Applied Stochastic Models in Business and Industry, 29, (2013), 264–278.
Parsa, M., Di Crescenzo, A., and Jabbari, H., Analysis of reliability systems via Gini-type index, European Journal of Operational Research, 264, (2018), 340–353.
Li, X., Zuo, M. J., Yam, R. C. M., Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down, Reliability Engineering and System Safety, 91, (2006), 305–310.
Azaron, A., Katagiri, H., Kato, K., Sakawa, M., Reliability evaluation of multicomponent cold standby redundant systems, Applied Mathematics and Computation, 173, (2006), 137–149.
Amiri, M., and Ghassemi, F., A methodology for analysing the transient availability and survivability of a system with repairable components, Applied Mathematics and Computation, 184, (2007), 300–307.
Amiri, M., and Ghassemi, F., A methodology for analysing the transient reliability of systems with identical components and identical repairmen, International Journal of Science and Technology, Iranica, 14, (2007), 72–77.
Esary, J. D., and Proschan, F., Coherent structures of non-identical components, Technometrics, 5 (2), (1963), 191–209.
Birnbaum, Z. W., Esary, J. D., and Saunders, S. C., Multi-component systems and structures and their reliability, Technometrics, 3 (1), (1961), 55–77.
Eryilmaz, S., Dynamic behavior of k-out-of-n: G systems, Operations Research Letters, 39, (2011), 155–159.
Eryilmaz, S., On the mean residual life of a k-out-of-n: G system with a single cold standby component, European Journal of Operational Research, 222, (2012), 273–277.
Eryilmaz, S., On reliability of a k-out-of-n system equipped with a single warm standby component, IEEE Transactions on Reliability, 62, (2013), 499–503.
Gurler, S., and Bairamov, I., Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions, Applied Mathematical Modeling, 33, (2009), 1116–1125.
Freixas, J., and Puente, M. A., Consecutive expansions of k-out-of-n systems, Operations Research Letters, 37, (2009), 438–442
Petchrompo, S., Li, H., Erguido, A., Riches, C., and Parlikad, A. K., A value-based approach to optimising long-term maintenance plans for a multi-asset k-out-of-N system, Reliability Engineering and System Safety, (2020), 106924.
Ram, M., On system reliability approaches: A brief survey, International Journal of systems assurance engineering and management, 4 (2), (2013), 101–117.
Franko, C., and Tutuncu, G. Y., Signature based reliability analysis of repairable weighted k-out-of-n: G systems, IEEE Transactions on Reliability, 65 (2), (2016), 843–850.
Eryilmaz, S. The number of failed components in a k-out-of-n system consisting of multiple types of components, Reliability Engineering and System Safety, 175, (2018), 246–250.
Zhang, N., Fouladirad, M., and Barros, A., Reliability-based measures and prognostic analysis of a K-outof-N system in a random environment, European Journal of Operational Research, 272 (3), (2019), 1120–1131.
Jia, J., Li, Z., Jia, P., and Yang, Z., Reliability analysis of common cause failure multistate system based on CUGF, Journal Mathematical problems in Eingineering, Article ID 4608124, (2020), 14 pages.
Zhang, Y., Reliability analysis of randomly weighted k-out-of-n systems with heterogeneous components, Reliability Engineering and System Safety, 205, (2021), 101784.
Cerqueti, R., A new concept of reliability system and applications in finance, Statistical reliability modelling and optimization, Annals of operations research, 312, (2022), 45–64.
