200 ◾ System Instantaneous Availability
7.5.2 Description of Discrete-Time Models
Suppose the system has only one unit, and its failure time X follows the general
probability distribution F(t). After the system fails, it is repaired immediately. Its
repair time is Y. Considering it has a repair delay, suppose the repair delay time is
W, where X, Y, and W are independent of each other, and all follow the general
discrete distribution.
In order to differentiate among the different conditions of the system, its states
are defined as
Zt k
Zt kk
Zt k
=
=
System normal at time point
System repaired afterfailureattimepoint
System beingrepairedattimepoint
() 0
()
,1,2, ...
() 2
e system failure rate function and repair rate function are λ(k) and μ(