Search for Author, Title, Keyword
Time-dependent system reliability under stress-strength setup
More details
Hide details
Department of Statistics, Faculty of Science Fırat University, TR-23119 Elazığ, Turkey
Publication date: 2018-09-30
Eksploatacja i Niezawodność – Maintenance and Reliability 2018;20(3):420-424
Consider a system which has n independent components whose time dependent strengths YtY t Y t 1 ( ), , , 2 ( ) … n ( ) are independent identically distributed random processes. Let random processes XtX t X t 1 ( ), , , 2 ( ) … m ( ) denote the common multiple stresses experienced by the components at time t . The reliabilities of the components in the system can chance as a result of their deterioration or in consequence of variable stresses over time. Degradation in components reliabilities in the system can lead to the degradation of the entire system reliability. In this paper, we propose a new method for determining the time dependent component reliability of the system under stress-strength setup. The proposed method provides a simple way for evaluating the reliability of the system at a certain time period. Computational results are also presented for the reliability of coherent system and consecutive k -out-of- n system.
Andrzejczak K. Some properties of multistate BW-systems. Serdica Bulgaricae Mathematicae Publicationes 1987; 13: 341-346.
Andrzejczak K. Deterministic properties of the multistate systems. Proceedings of the Fifth Anniversary International Conference RELCOMEX'89, Poland, Książ Castle, September. 1989; 25-32.
Andrzejczak K. Structure analysis of multistate coherent systems. Optimization 1992; 25: 301-316,
Awad A M, Gharraf M K. Estimating of P(Y.
Basu A P, Ebrahimi N. On the reliability of stochastic systems. Statist. Probab. Lett. 1983; 1: 265-267,
Basu S, Lingham R T. Bayesian estimation of system reliability in Brownian stress-strength models. Ann. Inst. Statist. Math. 2003; 55: 7-19,
Brunelle R D, Kapur K C. Review and classification of reliability measures for multistate and continuum models. IIE Transactions 1999; 31: 1171-1180,
Chandra S, Owen D B. On estimating the reliability of a component subject to several different stresses (strengths). Naval Res. Log. Quart. 1975; 22: 31-40,
Dahlhaus R. On Kullback-Leibler information divergence of locally stationary processes. Stoch. Process. Appl. 1996; 62: 139-168,
Do M N. Fast approximation of Kullback-Leibler distance for dependence trees and hidden Markov models. IEEE Signal Processing Lett. 2003; 10: 115-118,
Ebrahimi N. Multistate reliability models. Naval Research Logistics Quarterly 1984; 31: 671-680,
Ebrahimi N. Two suggestions of how to define a stochastic stress-strength system. Statist. Probab. Lett. 1985; 3: 295-297,
Ebrahimi N. Ramallingam T. Estimation of system reliability in Brownian stress-strength models based on sample paths. Ann. Inst. Statist.Math. 1993; 45: 9-19,
El-Neweihi E, Proschan F, Sethuraman J. Multi-state coherent system. Journal of Applied Probability 1978; 15: 675-688,
Eryılmaz S. Mean Residual and Mean Past Lifetime of Multi-State Systems With Identical Components. IEEE Trans. Reliab. 2010; 59: 644-649,
Eryılmaz S, İşçioğlu F. Reliability evaluation for a multi-state system under stress-strength setup. Commun. Statist. Theor. Meth. 2011; 40: 547-558,
Gradshteyn I S, Ryzhik I M. Table of Integrals, Series and Products. 6th ed. California: Academic Press, 2000.
Hall P. On Kullback-Leibler loss and density estimation. Ann. Statist. 1987; 15: 1491-1519,
Hudson J C, Kapur K C. Reliability analysis for multistate systems with multistate components. IIE Transactions 1983; 15: 127-135,
Kotz S, Lumelskii Y, Pensky M. The Stress-Strength Model and its Generalizations. Theory and Applications. Singapore: World Scientific, 2003,
Kullback S, Leibler R A. On information and sufficiency. Ann. Math. Statist. 1951; 22: 79-86,
Kuo W, Zuo M J. Optimal Reliability Modeling, Principles and Applications. New York: John Wiley & Sons, 2003. 23, Lee Y K, Park B U. Estimation of Kullback-Leibler divergence by local likelihood. Ann. Inst. Statist. Math. 2006; 58: 327-340.
Lee Y K, Park B U. Estimation of Kullback-Leibler divergence by local likelihood. Ann. Inst. Statist. Math. 2006; 58: 327-340.
Nadarajah S, Kotz S. Reliability for some bivariate exponential distributions. Mathematical Problems in Engineering 2006; 2006: 1-14,
Rached Z, Alajaji F, Lorne Campbell L. The Kullback-Leibler Divergence Rate Between Markov Sources. IEEE Trans. Inform. Theory Eksploatacja i Niezawodnosc – Mainten ance and 372 Reliability Vol.18, No. 3, 2016 Scien ce and Technology 2004; 50: 917-921,
Smith A, Naik P A, Tsai C L. Markov-switching model selection using Kullback-Leibler divergence. Journal of Econometrics 2006; 134: 553-577,
Wang Q, Kulkarni S, Verdú S. Divergence Estimation of Continuous Distribution based on data-dependent Partitions. IEEE Trans. Inform. Theory 2005; 51: 3064-3074,
Whitmore G A. On the reliability of stochastic systems: a comment. Statist. Probab. Lett. 1990; 10: 65-67,
Reliability estimation of s-out-of-k system in a multicomponent stress–strength dependent model based on copula function
Tiefeng Zhu
Journal of Computational and Applied Mathematics
Advances in Lightweight Materials and Structures
V. Sonde, P. Warnekar, P. Ashtankar, V. Ghutke
Reliability and Optimal Replacement Policy for a Consecutive k-out-of-n:F System with Independent and Nonidentical Distributed Components
Fahrettin Özbey
International Journal of Reliability, Quality and Safety Engineering
Journals System - logo
Scroll to top