Cost-benefit analysis of a one-server two-unit cold standby system with repair and preventive maintenance

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the type where the operating unit is taken up for PM whenever the other unit is available for operation. Initially, one unit is placed in operation and the other unit is kept as a cold standby. When the operating unit fails while the other unit is under service (repair or PM), the system breaks down. The busy period of the server in a time interval (O, t] is divided into time spent for repair and time spent for PM. By identifying regenerative epochs, suitable expressions for the expected values of these times are obtained. The pointwise availability is also derived. With the assumptions that a revenue is earned linearly with up-time, and repair and PM costs are incurred linearly with repair and PM times, respectively, the net expected revenue for a period (O, t] is derived. A particular case where the time to failure of the operating unit is 2-Erlang and the times for repair and PM are exponential has been analysed.