In this paper, we show how a possibilistic uncertainty model can be us
ed to represent and manipulate uncertainty about the states of a syste
m and of its components. At the same time, we present a thorough study
of the incorporation of this possibilistic uncertainty model in class
ical, two-state reliability theory. The possibilistic reliability of a
component or system is introduced and studied. Furthermore, we introd
uce 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 calc
ulate the possibilistic reliability of a system in terms of the possib
ilistic reliabilities of its components. Finally, we give straightforw
ard methods for determining a possibilistic structure function from it
s classical, two-valued counterpart. In this way, we intend to show th
at a possibilistic uncertainty model in two-state reliability theory i
s formally analogous to, and certainly not more complicated than, a pr
obabilistic uncertainty model.