Reliability Structures Consisting of Weighted Components: Synopsis and New Advances
DOI:
https://doi.org/10.13052/jrss0974-8024.1612Keywords:
Reliability function, coherent systems, weighted structures, consecutive-type systemsAbstract
Throughout the lines of the present article the family of reliability systems consisting of weighted components is examined. A synoptic exposition of the existing reliability structures with n weighted components is carried out. Among others, some newfangled and crucial points for every structure that belongs to this class are reported. In addition, a new weighted consecutive-type structure is introduced, while its characteristics are also studied in some detail.
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Barlow, R. E. and K. D. Heidtmann. 1984. Computing k-out-of-n system reliability. IEEE Transactions on Reliability, 33: 322–323.
Birnbaum, Z. W. 1969. On the importance of different components in a multicomponent system. In Multivariate analysis II (ed. P. R. Krishnaiah), Academic Press, New York, pp. 581–592.
Chang, J.-C., R.-J. Chen, and Hwang, F. K. 1998. A fast reliability algorithm for the circular consecutive-weighted-k-out-of-n: F systems. IEEE Transactions on Reliability, 47: 472–474.
Chaube, S. and S. B. Singh. 2016. Fuzzy reliability of two-stage weighted-k-out-of-n systems with common components. International Journal of Mathematical, Engineering and Management Sciences. 1: 41–51.
Chen, Y. and Q. Yang. 2005. Reliability of two-stage weighted-k-out-of-n systems with components in common. IEEE Transactions on Reliability. 54: 431–440.
Cook, J. L. 2018. Reliability analysis of weighted k-out-of-n systems with variable demand. Quality Engineering. 30: 687–693.
Cui,L., W. Kuo, and M. Xie.. 2006. On the dual reliability systems of (n,f,k) and
n,f,k>
. Statistics and Probability Letters. 76: 1081–1088.
Derman, C., G. J. Lieberman, and S. M. Ross. 1982. On the consecutive-k-out-of-n: F system. IEEE Transactions on Reliability. 31: 57–63.
Eryilmaz, S. 2013. Mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes. Reliability Engineering and System Safety. 119: 290–293.
Eryilmaz, S. 2014. Multivariate copula based dynamic reliability modeling with application to weighted k-out-of-n: G systems of dependent components. Structural Safety. 51: 23–28.
Eryilmaz, S. 2015a. Capacity loss and residual capacity in weighted k-out-of-n: G systems, Reliability Engineering and System Safety. 136, 140–144.
Eryilmaz, S. 2015b. Mean Time to Failure of weighted k-out-of-n: G systems. Communication in Statistics: Simulation and Computation. 44: 2705–2713.
Eryilmaz, S. and K.Sarikaya. 2014. Modeling and analysis of weighted k-out-of-n:G system consisting of two different types of components. Proceedings of the Institution of Mechanical Engineers: Part 0: Journal of Risk and Reliability. 228: 265–271.
Eryilmaz, S. and M. J. Zuo. 2010. Constrained (k,d)-out-of-n systems. International Journal of Systems Science. 41: 679–685.
Eryilmaz, S. and G. Y. Tutuncu. 2009. Reliability evaluation of linear consecutive-weighted-k-out-of-n: F system. Asia-Pacific Journal of Operational Research. 26: 805–816.
Franco, C., G. Y. Tutuncu, and S. Eryilmaz. 2017. Reliability of weighted k-out-of-n: G systems consisting of two types of components and a cold standby component. Communication in Statistics: Simulation and Computation. 46: 4067–4081.
Griffith, W. S. 1986. On consecutive–k–out–of–n: failure systems and their generalizations. In Reliability and Quality Control Basu, A.P. (ed.). Elsevier, Amsterdam, pp. 157–165.
Hamdan, K., M. Tavangar, and M. Asadi, 2021. Optimal preventive maintenance for repairable weighted k-out-of-n systems. Reliability Engineering and System Safety. 205: 107267.
Higashiyama, Y. 2001. A factored reliability formula for weighted-k-out-of-n system. Asia-Pacific Journal of Operational Research. 18: 61–66.
Kumar, A., S. B. Singh, and M. Ram. 2019. Reliability appraisal for consecutive-k-out-of-n: F system of non-identical components with intuitionistic fuzzy set. International Journal of Operational Research. 36: 362–374.
Kuo, W. and M. J. Zuo 2003. Optimal Reliability Modeling: Principles and Applications, John Wiley & Sons, N.J.
Li, X., Y. You, and R.Fang 2016. On weighted k-out-of-n systems with statistically dependent component lifetimes. Probability in the Engineering and Informational Sciences. 30: 533–546.
Mahmoudi, E. and R. Meshkat, 2020. Reliability analysis of weighted-k-out-of-n: G system consisting of two different types of nonidentical components each with its own positive integer-valued weight. Journal of Statistical Theory and Applications. 19: 408–414.
Meshkat, R. and E. Mahmoudi, 2017. Joint reliability and weighted importance measures of a k-out-of-n system with random weights for components. Journal of Computational and Applied Mathematics. 326: 273–283.
Pham, H. and S. J. Upadhyaya 1988. The efficiency of computing the reliability of k-out-of-n systems. IEEE Transactions on Reliability. 36: 78–79.
Rahmani, R.-A., M. Izadi, and B.-E. Khaledi. 2016. Stochastic comparisons of total capacity of weighted- k-out-of-n systems. Statistics and Probability Letters. 117: 216–220.
Rahmani, R.-A., M. Izadi, and B.-E. Khaledi. 2016. Importance of components in k-out-of-n system with components having random weights. Journal of Computational and Applied Mathematics. 296: 1–9.
Ram, M. 2013. On system reliability approaches: a brief survey. International Journal of System Assurance Engineering and Management. 4: 101–117.
Rushdi, A. M. 1990. Threshold systems and their reliability. Microelectronics Reliability. 30: 299–312.
Rushdi, A. M. and A. M. Alturki. 2018. Novel representations for a coherent threshold reliability system: a tale of eight signal flow graphs. Turkish Journal of Electrical Engineering & Computer Sciences. 26: 257–269.
Samaniego, F. J. and M. Shaked. 2008. Systems with weighted components, Statistics & Probability Letters. 78: 815–823.
Tong, Y. L. 1985. A rearrangement inequality for the longest run, with an application to network reliability. Journal of Applied Probability. 22: 386–393.
Triantafyllou, I. S. and M. V. Koutras. 2011. Signature and IFR preservation of 2-within-consecutive k-out-of-n:F systems. IEEE Transactions on Reliability. 60: 315–322.
Triantafyllou, I. S. 2015. Consecutive-type reliability systems: an overview and some applications. Journal of Quality and Reliability Engineering. 2015. Article ID 212303: 20 pages.
Triantafyllou, I. S. 2020. On the consecutive k1
- and k2
-out-of-n reliability systems. Mathematics. 8: 630.
Triantafyllou, I. S. 2021a. Reliability Study of
n, f, 2>
systems: A Generating Function Approach. International Journal of Mathematical, Engineering and Management Sciences. 6: 44–65.
Triantafyllou, I. S. 2021b. On the lifetime and signature of the constrained (k,d) out-of-n: F reliability systems. International Journal of Mathematical, Engineering and Management Sciences. 6: 66–78.
Wu, J. S. and R. J.Chen, 1994a. An algorithm for computing the reliability of a weighted-k-out-of-n system. IEEE Transactions on Reliability. 43: 327–328.
Wu, J. S. and R. J. Chen 1994b. Efficient algorithms for k-out-of-n & consecutive weighted-k-out-of-n system. IEEE Transactions on Reliability. 43: 650–655.
Zhang, Y. 2018. Optimal allocation of active redundancies in weighted k-out-of-n systems. Statistics and Probability Letters. 135: 110–117.
Zhang, Y., W. Ding, and P. Zhao. 2018. On total capacity of k-out-of-n systems with random weights. Naval Research Logistics. 65: 347–359.
Zhang, Y. 2021. Reliability analysis of randomly weighted-k-out-of-n systems with heterogeneous components. Reliability Engineering and System Safety. 205: 107184.
Zhao, X., L. Cui, and X. Yang. 2006. A consecutive k1
and k2
-out-of-n system and its reliability. In Advanced Reliability Modeling II. Yun, W. Y. & Dohi, T. (eds), pp. 97–103.
