Fluctuation Mechanism and Control on System Instantaneous Availability

28 ◾ System Instantaneous Availability

3.2.2 Physical Significance of Instantaneous

Availability Approximate Solution

According to Reference [8],

A(t) = P{Z(t) = 0 | System is new at the time of 0}. (3.12)

In the formula, Z(t) stands for system status given by (3.6).

Record XX

i

= X

i

+ W

i

+ Y

i

, i = 1, 2, …, in which X

i

, Y

i

, and W

i

refer to failure

time, repair time, and logistic delay time, respectively, of a system in cycle i. en,

the following formula can be obtained through the total probability formula:

∑∑ ∑

∑∑∑

() ()

()

=≤<+ =





















++≤< =





















=

+∞

=

+

=

+

=

+

==

+∞

,0

|0

,0

|0

.

01

1

0

1

0

1

10

At PXXt XX XZtSystemisnew at thetimeof

PXXX tXXZtSystemisnew at thetimeof

j

i

i

j

ij

i

j

ij i

i

j

i

j

j

In the second term, when

∑

∑

+≤<

+

=

+

=

XX Xt XX

ij

i

i

j

i

j

1

1

1

1

, the system must ...