The Reliability of Weighted k-out-of-n Systems with Randomized Components of Several Batches

[1] Barlow, R. E., Proschan, F., “Statistical Theory of Reliability and Life Testing: Probability models”, Silver Spring, MD, (1981).

[2] Berdichevsky, V., Gitterman, M., “Stochastic resonance and ratchets new manifestations”, Physics A, 249 (1998) 88-95.

[3] Bhattacharya, B., Nandram, B., “Bayesian inference for multinomial populations under stochastic ordering”, Journal of Statistica1 Cornputation and Simulution, 54 (1996) 145-163.

[4] Bier, M., “Brownian ratchets in physics and biology”, Contemporary Physics, 38 (1997) 371-379.

[5] Chen, Y., Yang, Q., “Reliability of two-stage weighted k-out-of-n systems with components in common”, IEEE Transactions on Reliability, 54 (2005) 431-440.

[6] Cui, L., Xie, M., “On a generalized k-out-of-n system and its reliability”, International Journal of Systems Science, 36 (2005) 267-274.

[7] Di Crescenzo, A., “A Parrondo paradox in reliability theory”, The Mathematical Scientis, 32 (2007) 17-22.

[8] Di Crescenzo, A., Pellerey, F., “Stochastic comparisons of series and parallel systems with randomized independent components”, Operations Research Letters, 39 (2011) 380-384.

[9] Eryilmaz, S., “Dynamic behavior of k-out-of-n:G systems”, Operations Research Letters, 39 (2011) 155-159.

[10] Eryilmaz, S., “Mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes.”, Reliability Engineering and System Safety, 119 (2013) 290-293.

[11] Eryilmaz, S., “Multivariate copula based dynamic reliability modeling with application to weighted-k-out-of-n systems of dependent components”, Structural Safety, 51(2014) 23-28.

[12] Eryilmaz, S., Coolen, F.P.A., Coolen-Maturi, T., ”Marginal and joint reliability importance based on survival signature”, Reliability Engineering and system safety, 172 (2018) 118-128.

[13] Eryilmaz, S., Sarikaya, K., “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 O: Journal Risk and Reliabality, 201 (2013) 1-7.

[14] Genest, C., Neslehova, J., Ghorbal, N.B., “Estimators based on Kendall’s tau in multivariate copula models”, Australian New Zealand Journal of Statistics, 53(2011) 157-177.

[15] Hazra, N. K., Nanda, A. K., “Some results on series and parallel systems of randomized components”, Operations Research Letters, 42 (2014) 132-136.

[16] Kochar, S., Xu, M., “On residual lifetimes of k-out-of-n systems with nonidentical components”, Probability in the Engineering and Informational Sciences, 24 (2010) 109-127.

[17] Kuo, W., Zuo, M.J., “Optimal Reliability Modeling: Principles and Applications”, John Wiley and Sons, NewYork, (2003).

[18] Li, H., Li, X., “Stochastic Orders in Reliability and Risk”, Springer, New York, (2013).

[19] Navarro, J., Del Aguila, Y., “Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components”, Metrika, 80 (2017) 627-648.

[20] Navarro, J., Pellerey, F., Di Crescenzo, A., “Orderings of coherent systems with randomized dependent components”, European Journal of Operational Research, 240 (2015) 127-139.

[21] Navarro, J., Spizzichino, F., “Comparisons of series and parallel systems with components sharing the same copula”, Applied Stochastic Models in Business and Industry, 26 (2010) 775-791.

[22] Nelsen, R.B., “An Introduction to Copulas”, Springer, NewYork, (2006).

[23] Salehi, M., Shishebor, Z., Asadi, M., “On the reliability modeling of weighted k-outof-n systems with randomly chosen components”, Metrika, 82 (2018) 1-17.

[24] Samaniego, F.J., Navarro, J., “On comparing coherent systems with heterogeneous components”, Advances in Apllied Probability, 48(1) (2016) 88-111.

[25] Samaniego, F.J., Shaked, M., “Systems with weighted components”, Statistics and Probability Letters, 78 (2008) 815-823.

[26] Shaked, M., Shanthikumar, J.G., “Stochastic Orders”, Springer, Springer series in statistics, New York, (2007).

[27] Wang, Y., Pham, H., “Modeling the dependent competing risks with multiple degradation processes and random shock using time-varying copulas”, IEEE Transactions on Reliability, 61 (2012) 13-22.

[28] Wu, J.S., Chen, R.J., “An algorithm for computing the reliability of a weighted-kout-of-n system”, IEEE Transactions on Reliability, 43 (1994a) 327-328.

[29] Wu, J.S., Chen, R.J., “Efficient algorithms for k-out-of-n and consecutive weighted k-out-of-n : F system”, IEEE Transactions on Reliability, 43 (1994b) 650-655.