Abstract
In this paper, a concept of order uncertain variable is introduced as a main tool in analysis of k-out-of-n system with uncertain lifetimes. Then, by the operational law of uncertain variable, the uncertainty distribution of order uncertain variable is deduced. At last, the k-out-of-n system is studied, and the uncertainty distribution of k-out-of-n system lifetime is given.
Highlights
The real world is filled with indeterminacy
In order to deal with this type of uncertainty, Liu [6] founded an uncertainty theory in 2007, which is a branch of mathematics based on normality, duality, subadditivity, and product axioms
As an application of uncertainty theory, Liu [7] proposed a spectrum of uncertain programming which is a type of mathematical programming involving uncertain variables and applied uncertain programming to system reliability design, facility location problem, vehicle routing problem, project scheduling problem, finance, and so on
Summary
The real world is filled with indeterminacy. randomness and fuzziness are two cases of indeterminacy, behind which probability theory and credibility theory have been proposed. Based on the uncertainty theory, this paper gives a new concept of order uncertain variable, which is used as a tool to analyze k-out-of-n system with (Liu [6]) The set function M is called an uncertain measure if it satisfies the normality, duality, and subadditivity axioms.
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