Kalpesh P. Amrutkar
Department of Statistics, School of Mathematical Sciences, North Maharashtra University, Jalgaon, India.
Kirtee K. Kamalja
Department of Statistics, School of Mathematical Sciences, North Maharashtra University, Jalgaon, India.
One of the purposes of system reliability analysis is to identify the weaknesses or the critical components in a system and to quantify the impact of component’s failures. Various importance measures are being introduced by many researchers since 1969. These component importance measures provide a numerical rank to determine which components are more important to system reliability improvement or more critical to system failure. In this paper, we overview various components importance measures and briefly discuss them with examples. We also discuss some other extended importance measures and review the developments in study of various importance measures with respect to some of the popular reliability systems.
Keywords- Reliability systems, Importance measures.
Amrutkar, K. P., & Kamalja, K. K. (2017). An Overview of Various Importance Measures of Reliability System. International Journal of Mathematical, Engineering and Management Sciences, 2(3), 150-171. https://dx.doi.org/10.33889/IJMEMS.2017.2.3-014.
Conflict of Interest
(i) This work is supported by UGC, New Delhi, India, through the Major Research Project (F. No. 40-246/2011 (SR)).
(ii) The first author is thankful to the CSIR, New Delhi, for awarding Senior Research Fellowship (F. No. 09/728 (0033)/2014-EMR-I).
(iii) The authors would like to thank Guest Editor (s) for their constructive comments that improved the manuscript.
Amrutkar, K. P., & Kamalja, K. K. (2014). Reliability and importance measures of weighted-k-out-of-n:F system. International Journal of Reliability, Quality and Safety Engineering, 21(03), 1450015.
Armstrong, M. J. (1995). Joint reliability-importance of components. IEEE Transaction on Reliability, 44(3), 408-412.
Aven, T. (1986). On the computation of certain measures of importance of system components. Microelectronics Reliability, 26(2), 279-281.
Aven, T., & Jensen, U. (1999). Stochastic models in reliability. Springer, New York.
Barlow, R. E., & Proschan, F. (1975). Importance of system components and fault tree event. Stochastic Processes and their Applications, 3(2), 153-173.
Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing. Holt, Rinheart and Winston, New York.
Bergman, B., Arjas, E., Rausand, M., Natvig, B., Doksum, K. A., & Schweder, T. (1985). On reliability theory and its applications [with Discussion and Reply]. Scandinavian Journal of Statistics, 1-41.
Birnbaum, Z. W. (1969). On the importance of different components in a multi-component system. Multivariate Analysis–II, P.R. Krishnaiah (Editor), Academic, New York, 581-592.
Boland, P. J., & El-Neweihi, E. (1995). Measures of component importance in reliability theory. Computers & Operations Research, 22(4), 455-463.
Boland, P. J., & Proschan, F. (1983). The reliability of k"-" out-of"-" n systems. The Annals of Probability, 11(3), 760-764.
Boland, P. J., Proschan, F., & Tong, Y. L. (1989). Optimal arrangement of components via pairwise rearrangements. Naval Research Logistics, 36, 807-815.
Butler, D. A. (1979). A complete importance ranking for components of binary coherent systems, with extensions to multi‐state systems. Naval Research Logistics Quarterly, 26(4), 565-578.
Cai, Z., Si, S., Sun, S., & Li, C. (2016). Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm. Reliability Engineering & System Safety, 152, 248-258.
Chadjiconstantinidis, S., & Koutras, M. V. (1999). Measures of component importance for Markov chain imbeddable reliability structures. Naval Research Logistics (NRL), 46(6), 613-639.
Chang, G. J., Cui, L., & Hwang, F. K. (1999). New comparisons in Birnbaum importance for the consecutive-k-out-of-n system. Probability in the Engineering and Informational Sciences, 13(02), 187-192.
Chang, H. W., & Jan, S. (2006). Joint reliability importance of k-out-of-n systems and series-parallel systems. Proceeding Techniques and Applications & Conference on Real-Time Computing Systems and Applications, PDPTA, Las Vegas, Nevada, USA.
Chang, H. W., Chen, R. J., & Hwang, F. K. (2002). The structural Birnbaum importance of consecutive-k systems. Journal of Combinatorial Optimization, 6(2), 183-197.
Cheok, M. C., Parry, G. W., & Sherry, R. R. (1998a). Response to ‘Supplemental viewpoints on the use of importance measures in risk-informed regulatory applications’. Reliability Engineering & System Safety, 60(3), 261.
Cheok, M. C., Parry, G. W., & Sherry, R. R. (1998b). Use of importance measures in risk-informed regulatory applications. Reliability Engineering & System Safety, 60(3), 213-226.
Eryilmaz, S., & Bozbulut, A. R. (2014). Computing marginal and joint Birnbaum, and Barlow–Proschan importances in weighted-k-out-of-n: G systems. Computers & Industrial Engineering, 72, 255-260.
Freixas, J., & Pons, M. (2008). The influence of the node criticality relation on some measures of component importance. Operation Research Letters, 36(5), 557-560.
Fussell, J. B., & Vesely, W. E. (1972). A new methodology for obtaining cut sets for fault trees. Transactions of the American Nuclear Society, 15, 262-263.
Gao, X., Cui, L., & Li, J. (2007). Analysis for joint importance of components in a coherent system. European Journal of Operational Research, 182(1), 282-299.
Hong, J. S., & Lie, C. H. (1993). Joint reliability-importance of two edges in an undirected network. IEEE Transactions on Reliability, 42(1), 17-23.
Hong, J. S., Koo, H. Y., & Lie, C. H. (2002). Joint reliability importance of k-out-of-n systems. European Journal of Operational Research, 142(3), 539-547.
Hoyland, A., & Rousand, M. (1994). System Reliability Theory. New York: John Wiley & Sons.
Hsu, S. J., & Yuang, M. C. (1999). Efficient computation of marginal reliability importance for reducible networks in network management. Proceedings of the 1999 IEEE International Conference on Communications, 1039-1045.
Hwang, F. K. (2001). A new index of component importance. Operations Research Letters, 28(2), 75-79.
Hwang, F. K., Cui, L., Chang, J. C., & Lin, W. D. (2000). Comments on “reliability and component importance of a consecutive-k-out-of-n system” by Zuo. Microelectronics Reliability, 40(6), 1061-1063.
Iyer, S. (1992). The Barlow–Proschan importance and its generalizations with dependent components. Stochastic Processes and their Applications, 42(2), 353-359.
Jain, K., Dewan, I., & Rani, M. (2014). Multicomponent joint reliability importance of series-in-parallel and parallel-in-series systems. International Journal of Quality & Reliability Management, 31(7), 858-876.
Kamalja, K. K. & Amrutkar, K. P. (2014). Computational methods for reliability and importance measures of weighted-consecutive-systems, IEEE Transaction on Reliability, 63(1), 94-104.
Kamalja, K. K. (2012). Birnbaum importance for consecutive-k systems. International Journal of Reliability, Quality and Safety Engineering, 19(4), 1250016 (25 pages).
Kontoleon, J. M. (1980). Reliability determination of a r-successive-out-of-n: F system. IEEE Transactions on Reliability, 29(5), 437-437.
Koutras, M. V., Papadopoylos, G., & Papastavridis, S. G. (1994). Note: Pairwise rearrangements in reliability structures. Naval Research Logistics, 41, 683-687.
Kuo, W., & Zhu, X. (2012a). Relations and generalizations of importance measures in reliability. IEEE Transactions on Reliability, 61(3), 659-674.
Kuo, W., & Zhu, X. (2012b). Some recent advances on importance measures in reliability. IEEE Transactions on Reliability, 61(2), 344-360.
Kuo, W., & Zhu, X. (2012c). Importance measures in reliability, risk and optimization: principles and applications. John Wiley & Sons, Chichester, UK. 472.
Kuo, W., & Zuo, M.J. (2003). Optimal reliability modelling: Principles and Applications. John Wiley & Sons, New Jersey.
Lambert, H. E. (1975). Measure of importance of events and cut sets in fault trees. Reliability and Fault Tree Analysis (eds. Barlow, R.E., Fussell, J.B. and Singpurwalla, N.D.). Society for Industrial and Applied Mathematics, Philadelphia, 77-100.
Lin, C., Cui, L., Coit, D. W., & Lv, M. (2016). Reliability modeling on consecutive-$ k_r $-out-of-$ n_r $: F linear zigzag structure and circular polygon structure. IEEE Transactions on Reliability, 65(3), 1509-1521.
Lu, L., & Jiang, J. (2007). Joint failure importance for noncoherent fault trees. IEEE Transactions on Reliability, 56(3), 435-443.
Meng, F. C. (1996). Comparing the importance of system components by some structural characteristics, IEEE Transactions on Reliability, 45(1), 59–65.
Natvig, B. (1979). A suggestion of a new measure of importance of system components. Stochastic Processes and their Applications, 9(3), 319-330.
Rahmani, R. A., Izadi, M., & Khaledi, B. E. (2016). Importance of components in k-out-of-n system with components having random weights. Journal of Computational and Applied Mathematics, 296, 1-9.
Rani, M., Jain, K., & Dewan, I. (2011). On conditional marginal and conditional joint reliability importance. International Journal of Reliability, Quality and Safety Engineering, 18(2), 119-138.
Samaniego, F. J., & Shaked, M. (2008). Systems with weighted components. Statistics & Probability Letters, 78(6), 815-823.
Shen, J., & Cui, L. (2015). Reliability and Birnbaum importance for sparsely connected circular consecutive-$ k $ systems. IEEE Transactions on Reliability, 64(4), 1140-1157.
Van der Borst, M., & Schoonakker, H. (2001). An overview of PSA importance measures. Reliability Engineering & System Safety, 72(3), 241-245.
Wang, W., Loman, J., & Vassiliou, P. (2004). Reliability importance of components in a complex system, Reprinted from “2004 Proceedings Annual Reliability and Maintainability Symposium,” Los Angeles, California, USA, January 26-29.
Wu, J. S., & Chen, R. J. (1994a). An algorithm for computing the reliability of weighted-k-out-of-n systems. IEEE Transactions on Reliability, 43(2), 327-328.
Wu, J. S., & Chen, R. J. (1994b). Efficient algorithms for k-out-of-n and consecutive-weighted-k-out-of-n: F system. IEEE Transactions on Reliability, 43(4), 650-655.
Xie, M. (1987). On some importance measures of system components. Stochastic Process and their Applications, 25, 273-280.
Xie, M. (1988). A note on the natvig measure. Scandinavian Journal of Statistics, 15, 211-214.
Zhu, X., & Kuo, W. (2014). Importance measures in reliability and mathematical programming. Annals of Operations Research, 212(1), 241-267.
Zhu, X., Boushaba, M., & Reghioua, M. (2015). Joint reliability importance in a consecutive-k-out-of-n: F system and an m-consecutive-k-out-of-n: F system for Markov-dependent components. IEEE Transactions on Reliability, 64(2), 784-798.
Zuo, M. (1993). Reliability and component importance of a consecutive-k-out-of-n system. Microelectronics Reliability, 33(2), 243-258.