Page 211 - Sustainability in the Process Industry Integration and Optimization

188 Cha p te r E i g h t

Availability is the probability of the successful operation of a
system in a determined period of time. It can be calculated as the
ratio between an equipment’s lifetime and total time between failures
(de Castro and Cavalca, 2006):

A Lifetime Lifetime MTBF (8.1)

Total time Lifetime Repair time MTBF MTTR
where MTBF is the Mean Time Between Failure (the inverse of the
failure rate) and MTTR is the Mean Time To Repair (the inverse of the
repair rate).
In addition, there are three frequently used terms defined
by Ireson, Coombs, and Moss (1996) and elsewhere: inherent,
achieved, and operational availability. The expression for inherent
availability is
MTBF
A (8.2)

i
MTBF MTTR
for achieved availability,
MTBM
A (8.3)
a

MTBM MAMT
and for operational availability,

A MTBM (8.4)
o

MTBM MDT
Further specifications also exist—for example, those given by
Hosford (1960):
• Pointwise availability is the probability that a system will be
able to operate within tolerances at a given instant of time.
• Interval availability is the expected fraction of a given interval
of time that a system will be able to operate within
tolerances.
• A special type of interval availability, called limiting interval
availability, was defined by Barlow and Proschan (1996); it is
the expected fraction of time in the long run that a system
operates satisfactorily.

There are even more specific definitions. For example, the availability
of a redundant system represented by a series of parallel systems is
formulated by de Castro and Cavalca (2006) as
n

A s – [1 (1 A i ) ] (8.5)
y i
i 1