
Volatility of System Instantaneous Availability ◾ 165
Similar to the method for judging the existence of volatility in Section 6.3.1.2,
the steps to judge the volatility can be given according to eorem 6.7.
Step one:
Calculate the steady-state availability A.
From the Formulas 6.20 and 6.44, we can calculate
2
A
M
=
λ+
.
Step two:
Judge whether the extreme point of A(t) exists when t ∈ [0,M]. Because
At
ee
tt
=
β−β
λ+
λ
∈
ββ
()
4
,[0, ],
12
2
12
solve the extreme point of A(t).
Namely,
′
=β
At ee
()
1
2
2
2
Get the stagnation point:
=
β−β
β
β
=
λ+
λ
λ+ λ+
λ
+
t
M
M
M
2
1n
2
4
1n
4
2
2
0
12
2
1
2
2
(6.51)
We easily can prove A′(t) < 0, t < t
0
; A′(t) > 0 t > t
0
, so t
0
is the ex ...