Applications

Abstract

A probabilistic model for the stochastic behaviour of a transmission network system is developed based on the imbedded Markov chain. While the process is at state i, there is an immediate expected gain q_i which reflects the relative worth of the i-th state. Let us note that q_i must include the revenue of the system at state i, the repair costs for restoring service, and any other penalty costs that may be associated with each particular state. The system reliability is defined as:

$$\mathcal{R} = \frac{{\sum\limits_{{i = 0}}^{M} {{{q}_{i}}{{\phi }_{i}}} }}{{{{{\bar{q}}}_{0}}}} $$

(7.1)

where ${{\bar{q}}_{0}}$ is the system gain in monetary units per unit of time if all components had zero probability of failure, or the system could not leave state zero.