New algorithm for calculation of Fussell-Vesely importance with application of direct partial logic derivatives

Abstract

Fussell-Vesely Importance (FVI) is one of the most commonly used importance measures. It is based on the concept of Minimal Cut Sets (MCSs), and it quantifies the contribution of a system component to system failure. In paper (Kvassay et al. 2015), the algorithm for identification of all system MCSs based on Direct Partial Logic Derivatives (DPLDs) has been considered. These MCSs are then used to compute the FVI. However, the FVI of a system component depends only on MCSs that contain the considered component, i.e. it is not necessary to identify all MCSs of the system. This implies that it is useful to develop algorithms that will identify not all system MCSs but only those in which a specific component occurs. Such algorithms can be used to compute the FVI without a priori knowledge of MCSs. In this paper, a new algorithm for this task is proposed. The algorithm is based on a relation between DPLDs and MCSs that is also considered in this paper. of algorithms for identification or generation of MCSs of investigated system. These algorithms are developed mainly on the basis of applied fault trees (Sinnamon & Andrews 1997, Vatn 1992) or networks (Emadi & Afrakhte 2014, Rebaiaia & Ait-Kadi 2013). Another algorithm for identification of system MCSs has been considered in paper (Kvassay et al. 2015). This algorithm is based on tools of logical differential calculus, and it can be used for systems of any type (not only for systems presented as networks or for systems described by fault trees). Logical differential calculus has been developed for analysis of dynamic properties of logic functions. Direct Partial Logic Derivatives (DPLDs) are essential part of this tool (Tapia et al. 1991). Their use in reliability analysis has been considered in several papers (Zaitseva 2003, Zaitseva 2012, Zaitseva et al. 2015). These papers have showed that DPLDs are very appropriate for identification of situations in which failure/repair of a system component results in system failure/repair. This fact has been used to develop algorithms for defining system boundary states and for calculation of some measures that can be used to evaluate system reliability. In this paper, we develop ideas presented in paper (Kvassay et al. 2015) to propose an algorithm that identifies not all system MCSs but only MCSs in which a specified component is presented. Such MCSs are useful in computation of FVI of the considered component. As a result new method for calculation of this IM is developed. This method is