caa a22 4500 47706275X CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960301xx s 000 0 eng 10.1007/BF00049298 doi (NATIONALLICENCE)springer-10.1007/BF00049298 Lifetime distribution and estimation problems of consecutive- k -out-of- n :F systems [Elektronische Daten] [Sigeo Aki, Katuomi Hirano] Explicit formula is given for the lifetime distribution of a consecutive-k-out-of-n:F system. It is given as a linear combination of distributions of order statistics of the lifetimes of n components. We assume that the lifetimes are independent and identically distributed. The results should make it possible to treat the parametric estimation problems based on the observations of the lifetimes of the system. In fact, we take up, as some examples, the cases where the lifetimes of the components follow the exponential, the Weibull, and the Pareto distributions, and obtain feasible estimators by moment method. In particular, it is shown that the moment estimator is quite good for the exponential case in the sense that the asymptotic efficiency is close to one. The Institute of Statistical Mathematics, 1996 Consecutive- k -out-of- n :F system nationallicence system reliability nationallicence failure time nationallicence discrete distributions of order k nationallicence order statistics nationallicence exponential distribution nationallicence Weibull distribution nationallicence Pareto distribution nationallicence moment estimator nationallicence Aki Sigeo Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Machikaneyama-cho, 560, Toyonaka, Osaka, Japan aut Hirano Katuomi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 185-199 0020-3157 48:1<185 1996 48 10463 https://doi.org/10.1007/BF00049298 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00049298 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aki Sigeo Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Machikaneyama-cho, 560, Toyonaka, Osaka, Japan aut NATIONALLICENCE 700 1- Hirano Katuomi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/1(1996-03-01), 185-199 0020-3157 48:1<185 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer