On modeling possibilistic uncertainty in two-state reliability theory

In this paper, we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components. At the same time, we present a thorough study of the incorporation of this possibilistic uncertainty model in classical, two-state reliability theory. The possibilistic reliability of a component or system is introduced and studied. Furthermore, we introduce the important notion of a possibilistic structure function, based upon the concept of a classical, two-valued structure function. Under certain conditions of possibilistic independence, it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components. Finally, we give straightforward methods for determining a possibilistic structure function from its classical, two-valued counterpart. In this way, we intend to show that a possibilistic uncertainty model in two-state reliability theory is formally analogous to, and certainly not more complicated than, a probabilistic uncertainty model.