Estimation of common cause factors from systems with different numbers of channels

The paper gives a resume of the Multiple Beta Factor Model, being a rather simple extension of the beta factor model for common cause failures. In this new model, a number of beta factors are introduced, defined as the probability that one specific channel (element) has failed, given that j specific channels have failed. Here the system\´s constant hazard function due to common cause failures will be the product of the channels\´ hazard function, the beta factor, and finally a "configuration factor". The configuration factor is introduced to distinguish between the performances of various system configurations, and if data are not available some generic values could be used for these. The main topic of the present paper is the estimation of the parameters in this model. An overall estimator for the configuration factors is provided, using data from systems with different numbers of channels. This approach utilizes the so-called data mapping. The beta factor estimator of the new model is compared to the commonly used estimator in the beta factor model, and this standard estimator is found to be somewhat inconsistent. Some special cases of the new model are also considered.