Counting Failure Events for a Support System

An initiating event is a departure from a desired operational envelope to a system state where a control response is required either by human or machine intervention. In the case of a support system such as a cooling water or electrical distribution system, failure of this system represents the departure from normal operating conditions. Initiating event frequencies for probabilistic risk assessments are generally based on data collection. For rare, but potentially high consequence initiators representing the failure of support systems, this approach has a number of shortcomings. For example, since events are rare, there may not be any complete system failure events in the available data sets. Consequently, there is a desire to model system failures of initiating events since component-level failure events in the support systems are more frequent. Therefore, what is needed is a suitable method for calculating the initiating event frequency (expected number of system failures over some operating mission) from the relatively well known component failure rates. In this paper, we explore ways to develop and quantify models that represent the rates of failures for support systems. These failures of repairable systems can be represented by focusing on observables. Specifically, we can either count the number of failures in time t or count the times of failure. As part of the analysis, we will describe and evaluate a couple of typical redundant support systems. Included in the analysis will be considerations of dependent failure mechanisms.