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5 Annexe A - Relationship between Proof Testing and
Reliability
A SIS is considered to be a number of physical components that are each subject to
random hardware failures. The reliability of a SIS is a function of the proof test interval
(i.e. the time between proof tests), the failure rates of the individual components and time
of operation, as follows:
For a demand mode systems, the reliability of a system is normally expressed as the
probability of system failing to operate on demand (PFD). PFD increases over time in an
exponential fashion (although for relatively short proof test intervals, it is often
approximated to a linear relationship).
For example, if a fully operating system is put into operation at a particular time, its PFD is
zero, since we know that it is a fully operating system. As time increases, un-revealed
failures are expected to occur to the system components in a random fashion and
therefore the PFD of the system increases. The rate at which the PFD increases over time
will depend upon the failure rates of the components.
The purpose of proof testing is to reveal all undetected dangerous failures that would
prevent the system performing its designed functionality (i.e. PFD
AV
with respect to the
safety function is back to zero). This should occur before the PFD gets higher than the
target PFD.
Once a test interval is known, then the average PFD (PFD
AV
) across the test interval
period can easily be calculated and compared against the target PFD. This can then form
part of the demonstration that the SIS provides the necessary risk reduction.
2
i
D
AV
T
PFD
Where:
Interval
Test
Proof
)
(Dangerous
Rate
Failure
i
D
T
[Equations taken from BS EN 61508-6:2001 B2.2.1 and assuming mean time to repair is
small relative to the proof test interval.
Note these equations have been simplified for the purposes of demonstration of particular
issues.
These equations are suitable for low demand modes of operation only, i.e. where demand
frequency ≤ 1 per year and ≤ 2 x proof test frequency – BS EN 61508:-4:2001 3.5.12
.
This equation is an approximation that is only valid when
1
2
i
D
T
, and typically < 0.2]
So if the failure rate of a particular component was 0.02 per year then with a 1 year proof
test interval the PFD
AV
would be 0.01. Similarly for 2 year interval the PFD
AV
would be
0.02. By running the equation in reverse, if a PFD
AV
of 0.001 was required then the proof
test interval would be 0.1 years (about 36 days).