Optimal replacement policies for a two-unit system with failure interactions

This paper considers a two-unit system with the following two failure interactions: When unit 1 fails, (i) unit 2 fails with probability αj and (ii) unit 1 causes damage with distribution G(z) to unit 2. Expected cost rates of two models are derived when the system is replaced at failure of unit 2 or at N-th failure of unit 1. Optimal replacement numbers N* to minimize expected costs are discussed. Finally, an extended model of model 2 is introduced.