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Modeling lifetime of sequential \(r\)-out-of-\(n\) systems with independent and heterogeneous components. (English) Zbl 1462.62612

Summary: This article deals with an extension of sequential order statistics which is useful for describing system lifetimes with independent but heterogeneous components. Explicit expressions for marginal distributions as well means of system lifetimes are derived. Some special cases and illustrative examples are also investigated.

MSC:

62N05 Reliability and life testing
62G30 Order statistics; empirical distribution functions
Full Text: DOI

References:

[1] Balakrishnan, N., Beutner, E., Kamps, U. (2008). Order restricted inference for sequential {\it{\it k}}-out-of-{\it{\it n}} systems. {\it Journal of Multivariate Analysis} 99:1489-1502. · Zbl 1140.62018
[2] Balakrishnan, N., Cramer, E. (2014). {\it The Art of Progressive Censoring: Applications to Reliability and Quality}. New York: Springer. · Zbl 1365.62001
[3] Barlow, R. E., Proschan, F. (1975). {\it Statistical Theory of Reliability and Life Testing}. New York: Holt. · Zbl 0379.62080
[4] Beutner, E. (2010). Nonparametric model checking for {\it{\it k}}-out-of-{\it{\it n}} systems. {\it Journal of Statistical Planning and Inference} 140:626-639. · Zbl 1177.62061
[5] Billinton, R., Allan, R. N. (1992). {\it Reliability Evaluation of Engineering Systems: Concepts and Techniques}. 2nd ed. New York: Springer. · Zbl 0837.62074
[6] Burkschat, M., Navarro, J., (2011). Ageing properties of sequential order statistics. {\it Probability in the Engineering and Informational Sciences} 25:1-19. · Zbl 1238.90047
[7] Burkschat, M., Torrado, N. (2014). On the reversed hazard rate of sequential order statistics. {\it Statistics & Probability Letters} 85:106-113. · Zbl 1284.62292
[8] Cramer, E., Kamps, U. (1996). Sequential order statistics and {\it{\it k}}-out-of-{\it{\it n}} systems with sequentially adjusted failure rates. {\it Annals of the Institute of Statistical Mathematics} 48(3):535-549. · Zbl 0925.62424
[9] Cramer, E., Kamps, U. (2001). Sequential {\it{\it k}}-out-of-{\it{\it n}} systems. In Balakrishnan. N, Rao, C. R., ed., {\it Handbook of Statistics 20: Advances in Reliability}. Vol. 20. Netherlands: Elsevier, Ch. 12, pp. 301-372.
[10] Cramer, E., Kamps, U. (2003). Marginal distributions of sequential and generalized order statistics. {\it Metrika} 58:293-310. · Zbl 1042.62048
[11] David, H. A., Nagaraja, H. N. (2003). {\it Order Statistics}. 3rd ed. New Jersey: Wiley. · Zbl 1053.62060
[12] Esmailian, M., Doostparast, M. (2014). Estimation based on sequential order statistics with random removals. {\it Probability and Mathematical Statistics} 6:81-95. · Zbl 1418.62113
[13] Kamps, U. (1995). A concept of generalized order statistics. {\it Journal of Statistical Planning and Inference} 48:1-23. · Zbl 0838.62038
[14] Moustafa, M. S. (1996). Transient analysis of reliability with and without repair for {\it{\it k}}-out-of-{\it{\it n}}:G systems with two failure modes. {\it Reliability Engineering and System Safety} 53:31-35.
[15] Reddy. C. R., (1993). Optimisation of {\it{\it k}}-out-of-{\it{\it n}} systems subject to common cause failures with repair provision. {\it Microelectronics Reliability} 33:175-183.
[16] Shafay, A. R., Balakrishnan, N., Sultan, K. S. (2014). Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples. {\it Journal of Statistical Computation and Simulation} 84:526-544. · Zbl 1453.62482
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