Page 411 - Offshore Electrical Engineering Manual

398 CHAPTER 1 Reliability

where regular maintenance is carried out, as a good approximation, it is acceptable to
take the output of an AND gate as the product of the input event failure probability, pro-
vided the MTTRs are very much shorter than the mean time between failures (MTBFs).

RELIABILITY BLOCK DIAGRAMS
If a system is broken down into key components or elements, the failure of which
would have some effect on the system’s availability, a block diagram may be drawn
such that for the continuing operation of the system, a continuous string of elements
must exist from one side of the diagram to the other. An example of such a block
diagram is shown in Fig. 8.1.7. A reliability block diagram produced in this way
provides a clear indication of any critical system components and often can also be
numerically evaluated. In order to carry out this numerical evaluation, it is necessary
to assign a value for failure rate and MTTR for each system element. An availability
may then be calculated for each element as follows:
μ
Availability (A) =
λ + μ
where μ is the reciprocal of the MTTR (in hours) and λ is the failure rate (failures
6
per 10 h). The unavailability is given by
A = 1 − A

and the unavailability of a system of n components in series is then
A s = A 1 + A 2 +⋯ + A n
If the unavailabilities are calculated for each component, they may be added
together where the configuration consists of series components and where the com-
ponent MTBFs are very much larger than their MTTRs.
The MTBF can be obtained by inverting the failure rate and multiplying by 10
6
as follows:
1 6
( failures ) = 10 /λ h/failure
λ 6 h
10
The unavailability of a system of n identical components in parallel, assuming
only one component is required to maintain the system, is
A s = A 1 A 2 ⋯ A n
Where more than one parallel component is required to maintain the system, the
following can be shown to be the combined availability:
n
∑ n j n − 1
A s = j A (1 − A)
j= m
where n is the total number of components and m is the number of components
required to maintain the system.