ABSTRACT
Until section 5, we consider only corrective maintenances. Let {Ti}i≥1 be the successive failure times of a repairable system, starting from T0 = 0. Let Xi = Ti − Ti−1,∀i ≥ 1, be the successive interfailure times and Nt be the number of failures observed up to time t. We assume that a repair is performed after each failure and that repair times are negligible or not taken into account. Then, the failure process is defined equivalently by the random processes {Ti}i≥1, {Xi}i≥1 or {Nt}t≥0 (Lindqvist 2007). The distribution of these processes is completely given by the failure intensity defined as:
∀t ≥ 0, λNt = lim t→0
t P(Nt+t − Nt− = 1 |Ht−)
(1)
where Ht− is the past of the failure process at time t, i.e. the set of all events occurred before t. In most cases, it means that λNt is a function of the number and times of failures occurred before t: Nt ,T1, . . . ,TNt− .
