F

c.d.f of a random variable (r.v)

f

p.d.f of an r.v

R( t)

reliability at time t

A( t)

instantaneous availability

M( t)

maintainability

Q, P _S

probability of the top event of a fault tree

A _? or A

asymptotic availability

( t)

average availability over [0, t]

_? or

asymptotic average availability

h( t)

hazard rate at time t

?( t)

instantaneous failure rate

?( t)

instantaneous repair rate

L( t)

mean residual lifetime at time t

T

lifetime of the system

?

duration of mission of the system

Y

duration of the repair

1 _A

indicator function of event A

m _k

k-th centered moment of the random variable X ( k ? ?*)

?( x)

Gamma function: ?( x) = t ^{x -1} e ^{- t}dt.

if x ? ? * then ?( x) = ( x - 1)!

?

set of real numbers:

? = (- ?, + ?) and ? ₊ = [0, + ?)

?

set of natural numbers:

? = {0, 1, 2, } and ?* = ?\{0}

?

structure function of a system

C

set of components of a system

?

state space of a system

? _i

state space of a component i ? C

K