On some optimal switching strategies

Systems of components with increasing failure rates are considered. Switching from an operating component on standby can be performed at each instant of time. Optimal switching strategies, maximizing the time to the first failure of a component and to the total failure of a system are investigated. A new type of strategy: the limit strategy is introduced. It is proved that this strategy is optimal, when there is no additional information on the state of the system. Some simple examples are considered.