Fault Tree Analysis with Multistate Components

A general analytical theory has been developed which allows one to calculate the occurrence probability of the top event of a fault tree with multistate (more than two states) components.It is shown that, in order to correctly describe a system with multistate components, a special type of boolean algebra is required. This is called “boolean algebra with restrictions on variables” and its basic rules are the same as those of the traditional boolean algebra with some additional restrictions on the variables. These restrictions are extensively discussed in the paper.Important features of the method are the identification of the complete base and of the smallest irredundant base of a boolean function which does not necessarily need to be coherent. It is shown that the identification of the complete base of a boolean function requires the application of some algorithms which are not used in today’s computer programmes for fault tree analysis.The problem of statistical dependence among primary components is discussed. The paper includes a small demonstrative example to illustrate the method. The example includes also statistical dependent components.