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Guideline – Demonstrating Prior Use v4
Page 24 of 30
Calculations
There are many sources and techniques for performing reliability calculations. Various formulae
and techniques can be found in BS EN 61508 and BS EN ISO 14224, to name just two. There are
also many technical publications on Reliability Assessments which provide further calculations.
For the purpose of this example, two techniques have been demonstrated, the first example
utilising a Mean Time between Failure calculation and the second utilising formulae within BS EN
61508 for a 1oo1 system.
Calculation Method 1 - Failure Data MTBF Calculation for 1oo1
Total number of dangerous failures = 1
See Footnote
7
Thus the MTBF is
!"# $
years = 960 years
Basic Formula for converting MTBF to failure rate
λ
=
$ &'()
Converting MTBF to dangerous failure rate (
λ
DU
) =
$ &'()
=
$ !"#
per year = 1.04 x 10
-3
per year
Simplified PFD Calculation
See Footnote
8
Approximate PFD
(avg)
=
λ
DU
x
'* +
(Where TI is the proof test interval in years)
For this case, assuming TI = 1 year then:
PFD
(avg)
= (1.04 x 10
-3
) x (
$ +
)
PFD
(avg)
= 5.2 x 10
-4
Complete PFD Calculation
PFD
(avg)
= 1 - (
$ ,-.
x TI ) x (1-e
- (
λ
DU x TI)
)
= 1 – (
$ $.#0
x 10
-3
) x (1 - e
-(1.04 x 10-3)
)
= 1 – (961.5 x (1-0.99896))
PFD
(avg)
=
5.19 x 10
-4
7
Note – Calculation will not work if there are no dangerous failures recorded and is only valid when repair
rate is much greater than failure rate.
8
The theory behind the formula is developed in Reliability, Maintainability and risk by David J Smith and
based upon algebraic simplifications of Markov models.