A Fast and Accurate Failure Frequency Approximation for k -Terminal Reliability Systems

This paper considers the problem of approximating the failure frequency of large-scale composite <inline-formula> <tex-math notation="LaTeX">\boldsymbol{k}</tex-math></inline-formula>-terminal reliability systems. In such systems, the nodes (<inline-formula>&l...

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Vydáno v:IEEE transactions on reliability Ročník 67; číslo 3; s. 933 - 950
Hlavní autoři: Heidarzadeh, Anoosheh, Sprintson, Alex, Singh, Chanan
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.09.2018
Témata:
<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX"> boldsymbol{k}</tex-math> </inline-formula>-terminal reliability systems
Approximation algorithms
Failure probability and failure frequency
Maintenance engineering
minimum cutsets and near-minimum cutsets
polynomial-time approximation algorithms
Probability
Random processes
Reliability
Simulation
Steady-state
ISSN:0018-9529, 1558-1721
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Shrnutí:This paper considers the problem of approximating the failure frequency of large-scale composite <inline-formula> <tex-math notation="LaTeX">\boldsymbol{k}</tex-math></inline-formula>-terminal reliability systems. In such systems, the nodes (<inline-formula><tex-math notation="LaTeX">\boldsymbol{k}</tex-math></inline-formula> of which are terminals) are connected through components, which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the <inline-formula><tex-math notation="LaTeX"> \boldsymbol{k}</tex-math></inline-formula> terminals together. We assume that each component's up times and down times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this paper, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all the nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). Our simulation results confirm that the proposed method is much faster and more accurate than the standard Monte Carlo simulation technique for approximating the failure frequency.
ISSN:0018-9529
1558-1721
DOI:10.1109/TR.2018.2825232