Open AccessThe reliability of systems with stair-type consecutive minimal cuts
Author(s) -
Yi-Chih Hsieh,
Ta-Cheng Chen
Publication year - 2007
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor0702235h
Subject(s) - linear programming , reliability (semiconductor) , integer programming , component (thermodynamics) , limit (mathematics) , mathematics , set (abstract data type) , type (biology) , simple (philosophy) , mathematical optimization , integer (computer science) , product (mathematics) , algorithm , computer science , mathematical analysis , power (physics) , ecology , physics , philosophy , geometry , epistemology , quantum mechanics , biology , thermodynamics , programming language
This paper considers the component system with stair-type consecutive minimal cuts. The system consists of n components and the set of minimal cuts can be linearly ordered. The proposed system generalizes the typical consecutive-k-out-of-n: F systems. By using integer linear programming, this paper shows that such a system can be converted into the consecutive-k-out-of-n: F systems with the insertion of artificial "broken-down" components. Then the system reliability can be obtained by the product form of component reliability matrices and the limit behavior of system could be easily analyzed. Additionally, we show that the integer constraints of the linear programming can be relaxed due to the total unimodularity. Thus, a general linear programming can be used to solve the problem. Numerical examples show the simple and effective new approach
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