Analytical solutions for stochastic process of a general view with two states and continuous time as basis event in a Fault Tree - Part 3: Analytical Expressions of Function Expectations

摘要

There is semi-Markov renewal process with two states and arbitrary CDFs (cumulative distribution functions) of a time during which the system S stays in the states. Some random total operating time function represented by a polynomial or, more generally, by some function which looks like element of the PH class (phase type distribution), but with arbitrary parameters (that is not an element of PH class) is considered. With such function it is possible to associate a benefit of an element operation. The way of a calculation of the mean of such function is determined. Then the average number of renewals is calculated. It is possible to associate repair costs with the number of renewals. All received expressions have an analytical form in the Laplace-Stieltjes domain. The way of pre-image calculation of received expressions is specified if a PDF' of a time during which the system S stays in the state are approximated by PDFs from PH class.