In order to find the transient probabilities that reflect the behaviour of a large electrical-power system or any other system, a suitable technique is needed. Before calculating the transient probabilities for the overall electrical power-system, which consists of a number of sub-systems (such as generators), the failure and repair rates of each generator are needed. These two coefficients can form a transition rate matrix which represent each sub-system. In the present study, the Kronecker technique is used to form the overall system: this is the first part of the current study. The second part is to find the transient probabilities following the fourth-order Runge-Kutta method. A number of examples related to the State of Bahrain are considered. In addition, by applying the new technique under investigation, we describe the behaviours of electric-power stations.