Study of the beta-factor model application for common cause failure modeling

Abstract

Aim. Common cause failures (CCFs) are dependent failures of groups of certain elements that occur simultaneously or within a short period of time (i.e. almost simultaneously) due to a single common cause (e.g. a sudden change of climatic operating conditions, flooding of premises, etc.). A dependent failure is a multiple failure of several elements of a system, whose probability cannot be expressed as a simple product of the probabilities of unconditional failures of individual elements. ССА probabilities calculation uses a number of common models, i.e. the Greek letter model, alpha, beta factor and their variants. The beta-factor model is the most simple in terms of simulation of dependent failures and further dependability calculations. Other models, when used in simulation, involve combinatorial enumeration of dependent events in a group of n events that becomes labour-intensive if the number n is high. For the selected structure diagrams of dependability, the paper analyzes the calculation method of system failure probability with CCF taken into account for the beta-factor model. The Aim of the paper is to thoroughly analyze the beta-factor method for three structure diagrams of dependability, research the effects of the model parameters on the final result, find the limitations of beta-factor model applicability. Methods. The calculations were performed using numerical methods of solution of equations, analytical methods of function studies. Conclusions. The paper features an in-depth study of the method of undependability calculation for three structure diagrams that accounts for CCF and uses the beta-factor model. In the first example, for the selected structure diagram out of n parallel elements with identical dependability, it is analytically shown that accounting for CCF does not necessarily cause increased undependability. In the second example of primary junction of n elements with identical dependability, it is shown that accounting for CCF subject to parameter values causes both increased and decreased undependability. A number of beta factor model parameter values was identified that cause unacceptable values of system failure probability. These sets of values correspond to relatively high model parameter values and are hardly practically attainable as part of engineering of real systems with highly dependable components. In the third example, the conventional bridge diagram with two groups of CCFs is considered. The complex ambivalent effect of beta factor model parameters on the probability of failure is shown. As in the second example, limitations of the applicability of the beta-factor model are identified.