L z -Transform for a Discrete-State Continuous-Time Markov Process and its Applications to Multi-State System Reliability

Anatoly Lisnianski ()
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Anatoly Lisnianski: The Israel Electric Corporation Ltd.

Chapter Chapter 6 in Recent Advances in System Reliability, 2012, pp 79-95 from Springer

Abstract: Abstract During last years a specific approach called the universal generating function (UGF) technique has been widely applied to MSS reliability analysis. The UGF technique allows one to algebraically find the entire MSS performance distribution through the performance distributions of its elements. However, the main restriction of this powerful technique is that theoretically it may be only applied to random variables and, so, concerning MSS reliability, it operates with only steady-states performance distributions. In order to extend the UGF technique application to dynamic MSS reliability analysis the paper introduces a special transform for a discrete-states continuous-time Markov process that is called L Z -transform. The transform was mathematically defined, its main properties were studied, and numerical example illustrating its benefits for dynamic MSS reliability assessment is presented.

Keywords: Discrete-state continuous-time Markov process; Universal generating function; Multi-state system; Reliability (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:ssrchp:978-1-4471-2207-4_6

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DOI: 10.1007/978-1-4471-2207-4_6

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