A general mathematical model for run-time distributions in a passively replicated fault tolerant system

In many systems, passive replication is used as a method for fault tolerance. A problem with using passive replication in real-time systems is that it can be difficult to analyze the time used by the system if a fault should occur. In this paper, we present a general mathematical model for the run-time distribution of a method in a fault tolerant system where a passive replication technique is used. The model gives this distribution as a function of the run-time distribution of the method in a fault-free system. We also demonstrate how this can be used to compute the probability of a missed deadline in a simple fault-tolerant system.