Some conditional reliability properties of \(k\)-out-of-\(n\) system composed of different types of components with discrete independent lifetimes
type: Item
instance of: scholarly article
title: Some conditional reliability properties of \(k\)-out-of-\(n\) system composed of different types of components with discrete independent lifetimes
zbMATH Open document ID: 1496.62173
author: Krzysztof Jasiński
published in: Metrika
publication date: 2021-11-24T00:00:00Z
review text: A technical system is said to have a \(k\)-out-of-\(n\) structure if it works when at least \(k\) of the \(n\) components operate. The author of this paper considers reliability properties of a \(k\)-out-of-\(n\) system consisting of \(l\) (\(1 \leq l\leq n\)) different types of components with discrete, independent lifetimes. Some conditional survival functions of the lifetime of a used system are obtained, which are used to calculate two conditional failure probabilities for \(k\)-out-of-\(n\) systems. Under some conditions, it is shown that they are equal to the unconditional failure probability of a \(k\)-out-of-\((n-r)\) system for \(r < n-k+1\).
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 7432987
zbMATH Keywords: reliability theory
zbMATH Keywords: not identically distributed random variables
zbMATH Keywords: discrete lifetime distributions
zbMATH Keywords: \(k\)-out-of-\(n\) system
reviewed by: Yuehua Wu
MaRDI profile type: Publication
full work available at URL: s00184-021-00826-1
OpenAlex ID: W3174890878
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DOI: 10.1007/S00184-021-00826-1
description: scientific article; zbMATH DE number 7432987