On the Reliability of Systems with Warm Redundancy and Unreliable Switching Equipment

The reliability of two contrary reconfiguration circuitries for computer systems with warm redundancy are compared by using renewal-theoretical methods. Buricius et al. demonstrated in their summarizing paper [BUR] the sensitiveness of dynamic replacement computers to their coverage, i.e. the conditional probability that the system recovers after a failure occured. In our model the procedure of failure recognization, -location, repair, roll back and restart,for short the process of recovery will be thought of successfully switching in a spare unit whenever the activ unit fails. A similar model has been examined in [ARN]. Amongst others [REN] emphasizes the importance of the coverage-factor c for the systems reliability. In our model all life times are assumed to be distributed exponentially. The switch is operating independently of the state of the rest of the system (for a discussion of this assumption compare [REN]). The two reconfiguration structures to be discussed are shown below: (S stands for (the same) realization of the switch.) In [RIS] the following renewal equations for the two models are developed: (s indicates the number of spares and the parameter c the probability of the switches correct operation) These recursive equations are solved in [RIS] and system reliability and mean life time are computed as functions of different failure rates of the active unit and the spares. The limit behavior for t→ ∞, s→ ∞, and/or special combinations of parameter values and the influence of the coverage are discussed. In the limit case the connection to known reliability structures (comp. [STO]) are deduced. Another criterion for the comparison of the two models is used when measuring how sensitive the mean life times are to changes of the coverage factor (compare [REI]).