How can we calculate the Expected energy not supplied in a network because of network component failure?
How to calculate the probability of each event?
Dear Alireza Soroudi
Everything depends on the structure of both - the reliability and/or the energy transfer
(a graph showing how the energy is supplied and then sent between users, etc.).
Moreover, some probabilistic characteristics are required, like rate of failure
of each verices and/or edges, the power sent via each connectio, possibilities of the service and repairs, . . . ) Even simplest models need careful analysis, beginning at the stage of construction of the model, through the calculations or simulations of the evolution of the whole system, especially in the case if some perturbances caused by e.g. destruction appear. Unfortunately, I am familiar only with some elementary examples, which give answer to questions on the reliability of the system. Seemigly the methods can be applied to other features, for instance - the asked by you Expected energy not supplied to/between (?). Frankly, it would be simpler to answer if some detailes about your problem were known :)
Sincerely, Joachim Domsta
PS. Let me suggest the following basic book on life testing from the point of view of reliability:Statistical theory of reliability and life testing: probability models
Quoted from internet:
RE Barlow, F Proschan - 1975 - DTIC Document
Abstract: This is the first of two books on the statistical theory of reliability and life testing. The present book concentrates on probabilistic aspects of reliability theory, while the forthcoming book will focus on inferential aspects of reliability and life testing, applying the probabilistic ... JoD
PS2: Also, it is worth to know, that some processes calculating the probability distribution of the total time of staying in chosen states is a strong tool for such problems, see eg.
Maintenance Theory of Reliability, by Toshio Nakagawa
where semiMarkov processes (= Markov renewal processes) are presented with applications. For an examplary paper on closed problems and methods cf.
http://www.jaqm.ro/issues/volume-5,issue-3/pdfs/grabski.pdf
JoD
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