Answer/Explanation:
SIL1, SIL2, and SIL3 ratings with PFDs of 10-2, 10-3, and 10-4, respectively.
PFD is the failure probability denoted as P.
Let's define R as its inverse.
Therefore, R = 1 - P
The failure Rate f is given by
f = - In R.
The mean time between failures (MTBF), 1/f
For SIL1,
P = 2/10 = 0.2
R = 1 - 0.2 = 0.8
failure rate f = -In(0.8) = 0.2231
MTBF = 1/f = 4.481
For SIL2,
P = 3/10 = 0.3
R = 1 - 0.3= 0.7
failure rate f = -In(0.7) = 0.3367
MTBF = 1/f = 2.804
For SIL3,
P = 4/10 = 0.4
R = 1 - 0.4 = 0.6
failure rate f = -In(0.6) = 0.5108
MTBF = 1/f = 1.9576
