Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence

Juan Yin, Lirong Cui and Narayanaswamy Balakrishnan

Reliability Engineering and System Safety, 2022, vol. 224, issue C

Abstract: Multi-state system models are more practical and valuable when describing complex engineering structures than binary-state system models. Modelling of linear consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence is discussed in this work. The proposed model is an extension of both “consecutive-k-out-of-n: F system†and “consecutive-k-out-of-n: F system with shared components between adjacent subsystems†. All the components in the system are assumed to have three states and are non-homogeneous Markov-dependent. Using the method of sum of disjoint products (SDP), the system reliability formula is derived by summing the reliability values for all disjoint cases. The well-known finite Markov chain imbedding approach (FMCIA) is used for deriving the reliability formula for each disjoint case. For the special cases of systems with homogeneous Markov-dependent or independent components, the corresponding results are deduced. Finally, some numerical examples are presented to illustrate all the results developed here.

Keywords: Consecutive system; Multi-state system; Non-homogeneous Markov-dependence; Sum of disjoint products method; Finite Markov chain imbedding approach (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:224:y:2022:i:c:s0951832022002009

DOI: 10.1016/j.ress.2022.108549

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