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Is it necessary to install a downhole safety valve in a subsea oil/gas well?
5.4 Unavailability calculations
The average unavailability of a safety function is often called Mean Fractional Dead Time
(MFDT). MFDT can be given two different meanings; the percentage of time where we are
unprotected by the safety function, or the probability that the safety function will fail on
demand for it. The most important well barriers have “hidden” critical failure modes and are
thus function tested regularly. The interval between two consecutive tests may be denoted by τ.
The MFDT formulas are based on a number of assumptions. The most distinctive are:
The failure rate of components is constant
All failures are detected during testing
The barrier failures are independent of each other
Production unavailability during testing and repair is neglected
5.4.1 The Mean Fractional Dead Time calculation model
The theory and all equations used in this section are found in reference [8].
If based on the fault tree analysis, the Mean Fractional Dead Time (MFDT) of the different cut
sets determines the probability of the ‘TOP’-event.
The MFDT of a single barrier i is given by its unavailability qi(t). A single well barrier is tested
with regular intervals of length τ, and a constant failure rate λi. The general formula is given:
1 τ
−λ
1
iu −τλi
MFDTi(t)= qi
(t) = (1-
∫ e du)
= 1−
( 1−
e )
τ 0
λ τ
i
Equation 5-1
The unavailability of the safety barrier may also be calculated using the approximation formula
below. This approximation is based on Taylor series development of Equation 5-1. Practical
calculations often make use of this approximation. A rule of thumb is that when λ⋅τ is small
(λ⋅τ