Cost analysis of series systems with different standby components and imperfect coverage

The authors calculate the steady-state availability and the cost-benefit analysis for three different systems with mixed standby (cold standby, warm standby) and imperfect coverage. The coverage factor is the same for an operative-unit failure as that for a warm standby-unit failure. The failure times of the operative unit and the warm standby unit are exponentially distributed while the repair time is arbitrarily distributed. The supplementary variable technique is applied to derive the steady-state availability for three different configurations. For each system, the steady-state availability is calculated according to two different cases for repair time distributions, such as exponential, and k-stage Erlang, where k = 2, 3. The configurations are compared as based on availability and cost/benefit at a special numerical value given to the distribution parameters.