ITEM TOOLKIT

216 ITEM ToolKit Getting Started Guide
t
⎡
⎤
r = ∑ ∑ ⎢∫
Pr( xi; τ) ⋅λx Pr( ; ) ( )
i→y ⋅ dτ
+
j
∑ xi tk ⋅Px i→y t
j k ⎥
ix : i∈X jy : j∉ X⎣τ
= 0
k
⎦
t
⎡
⎤
f = ∑ ∑ ⎢∫
Pr( yj; τ) ⋅λy Pr( ; ) ( )
j→x ⋅ dτ
+
i
∑ yj tk ⋅Pyj→x t
i k ⎥
ix : i∈X jy : j∉ X⎣τ
= 0
k
⎦
where t k , k = 1,…,n is the set of times t k < t at which discrete transitions take place. Note that this definition excludes
transitions that take place between states that belong to group X, as well as transitions that take place between states that do
not belong to group X.
Unreliability
Unreliability represents the probability of one or more system failures over a specified period of time. The number of
expected system failures (W) provides a good approximation for system unreliability for cases where W