Eryilmaz, Serkan and Kan, Cihangir and Akici, Fatih (2009): Consecutive k-within-m-out-of-n:F system with exchangeable components. Published in: Naval Research Logistics
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As a generalization of k-out-of-n:F and consecutive k-out-of-n:F systems, the consecutive k-within-m-out-of-n:F system consists of n linearly ordered components such that the system fails iff there are m consecutive components which include among them at least k failed components. In this article, the reliability properties of consecutive k-within-m-out-of-n:F systems with exchangeable components are studied. The bounds and approximations for the survival function are provided. A Monte Carlo estimator of system signature is obtained and used to approximate survival function. The results are illustrated and numerics are provided for an exchangeable multivariate Pareto distribution.
|Item Type:||MPRA Paper|
|Original Title:||Consecutive k-within-m-out-of-n:F system with exchangeable components|
|Keywords:||exchangeable lifetimes; meantime to failure; Monte Carlo simulation; moving order statistics; multivariate Pareto distribution; Samaniego’s signature|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General
|Date Deposited:||19. Nov 2010 13:31|
|Last Modified:||30. Dec 2015 18:16|
B. Bassan and F. Spizzichino, Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes, J Multivariate Anal 93 (2005), 313–339.
T.M. Costigan, Combination setwise-Bonferroni-type bounds, Naval Res Logistics 43 (1996), 59–77.
H.A. David and H.N. Nagaraja, Order Statistics,Wiley Series in Probability and Statistics, Wiley, New Jersey, 2003.
S. Eryılmaz, On the lifetime distribution of consecutive k-out-of-n:F system, IEEE Trans Reliabil 56 (2007), 35–39.  S. Eryılmaz, Lifetime of combined k-out-of-n, and consecutive kc-out-of-n systems, IEEE Trans Reliabil 57 (2008), 331–335.
S. Eryılmaz, Reliability properties of consecutive k-out-ofn systems of arbitrarily dependent components, Reliabil Eng System Safety 94 (2009), 350–356.
E.O. George and D. Bowman, A full likelihood procedure for analysing exchangeable binary data, Biometrics 51 (1995), 512–523.
W.S. Griffith, On consecutive k-out-of-n failure systems and their generalizations, Reliabil Quality Control (1986), 157–165.
A. Habib, R.O. Al-Seedy, and T. Radwan, Reliability evaluation of multi-state consecutive k-out-of-r-from-n:G system, Appl Math Model 31 (2007), 2412–2423.
A. Habib and T. Szantai, New bounds on the reliability of the consecutive k-out-of-r-from-n:F system, Reliabil Eng System Safety 68 (2000), 97–104.
D. Hunter, An upper bound for the probability of a union, J Appl Probabil 13 (1976), 597–603.
S. Iyer, Distribution of the lifetime of consecutive k-within-mout- of-n:F systems, IEEE Trans Reliabil 41 (1992), 448–450.
S. Kochar, H. Mukerjee, and F. Samaniego, The “signature” of a coherent system and its application to comparison among systems, Naval Res Logist 46 (1999), 507–523.
W. Kuo and M.J. Zuo, Optimal reliability modeling, principles and applications, Wiley, New York, 2003.
J. Navarro, Likelihood ratio ordering of order statistics, mixtures, and systems, J Stat Plann Inference 138 (2008), 1242–1257.
J. Navarro and S. Eryılmaz, Mean residual lifetimes of consecutive k-out-of-n systems, J Appl Probabil 44 (2007), 82–98.
J. Navarro, J.M. Ruiz, and C.J. Sandoval, A note on comparisons among coherent systems with dependent components using signatures, Stat Probabil Lett 72 (2005), 179–185.
J. Navarro and T. Rychlik, Reliability and expectation bounds for coherent systems with exchangeable components, J Multivariate Anal 98 (2007), 102–113.
J. Navarro, F.J. Samaniego, N. Balakrishnan, and D. Bhattacharya, On the application and extension of system signatures in engineering reliability, Naval Res Log 55 (2008), 313–327.
S.G. Papastavridis, Lifetime distribution of circular consecutive k-out-of-n:F systems with exchangeable lifetimes, IEEE Trans Reliabil 38 (1989), 460–461.
S.G. Papastavridis and M.V. Koutras, Bounds for reliability of consecutive k-within-m-out-of-n:F systems, IEEE Trans Reliabil 42 (1993), 156–160.
F. Samaniego, On closure of the IFR class under formation of coherent systems, IEEE Trans Reliabil R-34 (1985), 69–72.
M. Sfakianakis, S. Kounias, and A. Hillaris, Reliability of a consecutive k-out-of-r-from-n:F system, IEEE Trans Reliabil 41 (1992), 442–447.
J.G. Shanthikumar, Lifetime distribution of consecutive kout- of-n:F systems with exchangeable lifetimes, IEEE Trans Reliabil R-34 (1985), 480–483.
K.J. Worsley, An improved Bonferroni inequality and applications, Biometrika 69 (1982), 297–302.
G. Xiao, Z. Li, and T. Li, Dependability estimation for non- Markov consecutive k-out-of-n:F repairable systems by fast simulation, Reliabil Eng System Safety 92 (2007), 293– 299.
W.Y. Yun, G.R. Kim, and H. Yamamoto, Economic design of a circular consecutive k-out-of-n:F system with (k − 1) step Markov dependence, Reliabil Eng System Safety 92 (2007), 464–478.