Reliability analysis of A combination of (n,f,k) and <n,f,k> systems

• Published in: Reliability engineering & system safety Vol. 249; p. 110191
• Main Authors: Cui, Lirong, Wang, Mengqian, Jiang, Weixin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2024
• Subjects: Combined reliability system; Finite Markov chain imbedding approach; Irreducible structure; Region of system failure; Structure equivalence; Combined reliability system; Structure equivalence; Finite Markov chain imbedding approach; Irreducible structure; Region of system failure
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2024.110191

•Two-kind combined reliability systems are introduced in terms of two reliability systems: (n,f,k) and <n,f,k>.•Some important concepts such as irreducible structure and structure equivalence are introduced.•We present an important criterion: four-class combined reliability systems are needed to be considered in essential.•A coordinate system is introduced for representing the working and failure regions for the combined reliability systems.•A procedure for calculations of the combined reliability systems is given. In the paper, two-element (f,k) and <f,k> combined systems are developed, and two-kind combined reliability systems and some related new concepts such as irreducible structure and structure equivalence are introduced, which can be used not only in real practical situations, but also enrich the reliability contents. We proved that four-class combined reliability systems need to be considered actually, which facilitates the handling of these combined reliability systems. Meanwhile, a coordinate system with two axes, the number of total failed components and the number of maximal consecutive failed components, is introduced in the paper for representing the working and failed areas for the combined reliability systems, which brings out a useful tool for understanding the working and failure mechanisms, and system state transition ways, for the combined reliability systems. To summarize the reliability calculation, a procedure for calculations of the combined reliability systems is presented, which is an efficient guidance for these reliability computations. Finally, two numerical examples are given to illustrate the computation procedure in which the detailed steps, special on using Finite Markov Chain Imbedding Approach (FMCIA), are shown. We believe that the present paper can shed light on researches on combined reliability systems.