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Zbl 1141.62081
Bairamov, Ismihan; Arnold, Barry C.
On the residual lifelengths of the remaining components in an $n - k+1$ out of $n$ system.
(English)
[J] Stat. Probab. Lett. 78, No. 8, 945-952 (2008). ISSN 0167-7152

Summary: Suppose that a system consists of $n$ independent components and that the lifelength of the $i$\,th component is a random variable $X_i$ $(i=1,2,\dots, n)$. For $k\in \{1,2,\dots ,n - 1\}$, denote by $X_1^{(k)},X_2^{(k)},\dots ,X_{n-k}^{(k)}$ the residual lifelengths of the remaining functioning components following the $k$\,th failure in the system. We discuss the joint distribution of these exchangeable random variables. In addition, we identify the conditions sufficient to guarantee the independence of the residual lifelengths.
MSC 2000:
*62N05 Reliability, etc. (statistics)
62E15 Exact distribution theory in statistics

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