Reliability of Combined $k{\hbox{-out-of-}}n$ and Consecutive $k_{c}{\hbox{-out-of-}}n$ Systems of Markov Dependent Components

Concepts

EngineeringSystems EngineeringFault-tolerant ComputingFault-tolerant SystemsProbability TheoryDependability MetricsMarkov ChainsMarkov ProcessesMulti-state ModelsReliability ModelingReliable System DesignMarkov Fault ModelsMarkov PropertySystem Reliability Assessment

Abstract

A combined k -out-of- n : F ( G ) & consecutive kc -out-of- n : F ( G ) system fails (functions) iff at least k components fail (function), or at least kc consecutive components fail (function). These models involve two common failure criteria, and can be used in various situations depending on the actual failure criteria involving consecutive components, or all components. Explicit formulas for the reliabilities of these systems are obtained for Markov dependent components using the distribution theory of runs. Some numerical results are also presented.

References

Optimal Reliability Modeling: Principles and Applications

William S. Griffith · Technometrics · 2004 · 504 citations

Engineering, Systems Engineering, Maintenance Engineering +11

Enumerative combinatorics

Choice Reviews Online · 2003 · 228 citations

Reliability of Consecutive-k-out-of-n:F Systems with (k-1)-step Markov Dependence

James C. Fu · IEEE Transactions on Reliability · 1986 · 142 citations

Engineering, Systems Engineering, Fault-tolerant Computing +16

Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components

Serkan Eryılmaz · Reliability Engineering & System Safety · 2008 · 92 citations

Engineering, Computer Engineering, Systems Engineering +14

Reliability evaluation of combined k-out-of-n:F, consecutive-k-out-of-n:F and linear connected-(r, s)-out-of-(m, n):F system structures

Ming J. Zuo, Daming Lin, Yanhong Wu · IEEE Transactions on Reliability · 2000 · 77 citations

Engineering, Computer Engineering, Computer Science +14