Minimal Cut Vectors (MCVs) are an important concept in reliability analysis because they describe situations in which a repair of any failed component of a failed system results in a repair of the system. Knowledge of these situations allows us to propose maintenance procedures of the system, estimate its availability or analyze importance of system components. However, one of the key problems in reliability analysis based on MCVs is their efficient identification. One of the interesting approach to solve this problem is based on logic differential calculus. According to this approach, MCVs can be identified by computing so-called Direct Partial Boolean Derivatives (DPBDs), which describe situations in which a repair (failure) of the system is caused by a repair (failure) of a specific system component. In this paper, we further develop this approach assuming that DPBDs are expressed in a compact graphical form that is known as a Binary Decision Diagram (BDD). This form is very useful for computer representation of structure of systems that are composed of many components because it has less memory demands and can be processed on a computer faster than other representations. More specifically, in this paper we present special operations for manipulation with DPBDs that allow us to combine several DPBDs expressed in a form of a BDD into one BDD that will represent all MCVs of the system.