Consider a parallel redundant system modeled in a probabilistic risk assessment. The system fails when every unit fails (there is no repair capability). This system is likely to be subject to both independent and common cause failures. The goal of this paper is to find the expected time to failure of the system given that the system fails before the mission is complete. That is, suppose there is a parallel system of size two and that there is a cold standby unit ready to be used if the primary system fails. To model the failure probability of the cold standby unit, the failure time of the primary system is required to determine how much mission time is remaining.

Traditionally, the time to failure of the primary system has been taken to be the total mission time divided by two, provided the failure rate of the system is low. This paper will explain how to calculate a more accurate failure time of the for a primary system, with equations derived for primary systems with two to four redundant units.