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Aki, Sigeo; Hirano, Katuomi

Lifetime distribution and estimation problems of consecutive \(k\)-out-of-\(n\):F systems. (English) Zbl 0857.62094

Ann. Inst. Stat. Math. 48, No. 1, 185-199 (1996).
Summary: An 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 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 the 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.

Cited in 11 Documents

MSC:

62N05 Reliability and life testing
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60K25 Queueing theory (aspects of probability theory)

Keywords:

explicit formula; consecutive-\(k\)-out-of-\(n:F\) system; reliability; failure time; discrete distributions of order \(k\); exponential distribution; Weibull distribution; lifetime distribution; linear combination of distributions of order statistics; Pareto distributions; moment estimator; asymptotic efficiency
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References:

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