
Volatility of System Instantaneous Availability ◾ 155
=
∈
−+−∈
∞
t
M
tM
t
M
t
M
tMM
tM
2
0, ]
2
2
1, [,2]
1, [2
2
2
2
2
(6.23)
en, substituting Q(t) into the renewal equation (6.18), we can get:
∫
∫∫
∫∫
() ()
() ()
=
−+
−
∈
−
+−
−
+
∈
−
+−
−
+
∞
−
−
−
−
−
At Ft Qt At
t
M
tu
M
Audu
tz
M
Azdz
tz
MM
Azdz tMM
tz
M
Azdz
tz
MM
Azdz tM
t
tM
tM
t
tM
tM
tM
t
1*
1(), 0,
2
2
2
,2,
2
0
22
0
22
2
(6.24)
We take the derivative of Equation 6.24 to obtain the two-order delay differen-
tial equations with piecewise:
)
)
))
)) )
(
(
((
(( (
′′
=
∈
−− ∈
−−+−
∞
At
M
At tM
M
At
M
At
MM
M
At
M
At M
M
At MtM
1
0, ]
12
,2 ]
12 1
2, [2
2
22
22 2
(6.25)
For the delay differential equations with piece