Approximation of General Semi-Markov Models Using Expolynomials

Sammanfattning: Safety analysis is critical when developing new engineering systems. Many systems have to function under randomly occurring events, making stochastic processes useful in a safety modelling context. However, a general stochastic process is very challenging to analyse mathematically. Therefore, model restrictions are necessary to simplify the mathematical analysis. A popular simplified stochastic model is the Semi-Markov process (SMP), which is a generalization of the "memoryless" continuous-time Markov chain. However, only a subclass of Semi-Markov models can be analysed with non-simulation based methods. In these models, the cumulative density function (cdf) of the random variables describing the system is in the form of expolynomials. This thesis investigates the possibility to extend the number of Semi-Markov models that can be analysed with non-simulation based methods by approximating the non-expolynomial random variables with expolynomials. This thesis focus on approximation of models partially described by LogNormal and Weibull distributed random variables. The result shows that it is possible to approximate some Semi-Markov models with non-expolynomial random variables. However, there is an increasing difficulty in approximating a non-expolynomial random variable when the variability in the distribution increases.