Data mapping and the prediction of common cause failure probability

General failure event data from various sources are often used to estimate the failure probability for the system of interest, especially when s-dependence exists among component failures, where common cause failure plays an important role. Failure event data from different sources must be reasonably explained, and correctly applied, so that the information about load environment, and component/system property can be used correctly. In estimating the probability for s-dependent system failure, both the load distribution, and component strength distribution are much more important than component failure probability index. Based on the relationship among different multiple failures, this paper presents a data mapping approach to estimating dependent system failure probability through multiple failure event data of other systems with different sizes. The underlying assumption on data mapping is that failures of different multiples (including single) are correlated with each other for a group of components if they are subjected to the same or correlated random load (loads). Taking the situation of a group of s-independent components operating under the same random load as an example, the likelihood of a component failure at a trial depends not only on the strength of the individual component but also on the realization of the random load. The likelihood of a specific multiple failure at a trial is also determined by both the component strengths, and the realization of the random load. Furthermore, if a larger load sample appears, the likelihoods for failure are higher. Conversely, if a smaller load sample appears, the likelihoods of failure are lower. We emphasized in this paper that system failure event data should be interpreted & applied under the principle that various multiple failures are distinguished by their respective failure multiplicity and/or system size, and are inherently interrelated through correlated load environments. The approach starts with determining the load parameter, and component strength parameter according to multiple (including single) failure event data available. Then, these parameters are used to calculate the probability of multiple failures for systems of different sizes. This approach is applicable to predict high multiple failure probability based on low multiple failure event data. Examples of estimating multiple failure probabilities of EDG (emergency diesel generators) with mapped data illustrate that the proposed approach is desirable.