API RP 581 - 3rd Ed.2016 - Add.2-2020 - Risk-Based Inspection Methodology

RISK-BASED INSPECTION METHODOLOGY, PART 2—PROBABILITY OF FAILURE METHODOLOGY 2-111
CUIF
Po 1
n) STEP 16—Calculate the posterior probabilities, p
with 1 CUIF I
, I 2 CUIF CUIF
and I 3 in STEP 13.
CUIF
Po 2
, p
CUIF
Po 3
, and p
, using Equation (2.57)
CUIF
CUIF I1
Po p1
=
CUIF CUIF CUIF
I1 + I2 + I3
CUIF
CUIF I 2
Po p2
=
CUIF CUIF CUIF
I1 + I2 + I3
CUIF
CUIF I3
Po p3
=
CUIF CUIF CUIF
I1 + I2 + I3
(2.57)
o) STEP 17—Calculate the parameters, β 1 CUIF , β 2 CUIF , and β 3 CUIF , using Equation (2.58) and assigning
COV ∆t = 0.20, COV Sf = 0.20, and COV p = 0.05.
β
CUIF
1
=
CUIF
1−D ⋅A 1
rt −SR
S
p
2
2 2 2 2 CUIF 2 2
⋅
1
rt ⋅ t ( 1
1
rt )
( )
S ∆ + − ⋅ ⋅ +
S S f
p ⋅ P
D A COV D A COV SR COV
,
β
CUIF
2
=
CUIF
1−D ⋅A 2
rt −SR
S
p
2
2 2 2 2 CUIF 2 2
⋅
2
rt ⋅ t ( 1
2
rt )
( )
S ∆ + − ⋅ ⋅ +
S S f
p ⋅ P
D A COV D A COV SR COV
,
(2.58)
β
CUIF
3
=
S3
2 2 2
1
S3 rt ∆t
S3
1−D ⋅A −SR
D ⋅A ⋅ COV + −D ⋅A
rt
CUIF
p
( ) 2 2 CUIF 2 2
rt ⋅ COV + ( SR )
S f
p ⋅COVP
.
where D S1 = 1, D S2 = 2, and D S3 = 4. These are the corrosion rate factors for damage states 1, 2, and 3
as discussed in Section 4.5.3 [17] . Note that the DF calculation is very sensitive to the value used for the
coefficient of variance for thickness, COV ∆t . The COV ∆t is in the range 0.10 ≤ COV ∆t ≤ 0.20, with a
recommended conservative value of COV ∆t = 0.20.
p) STEP 18—Calculate
D
CUIF
f
CUIF
D f using Equation (2.59).
( ( )) ( )
( ) ( ( ))
⎡ CUIF 1 1 CUIF CUIF 2 2 CUIF CUIF 3 3
CUIF
Po p Φ − β + Po p Φ − β + Po p Φ −β
⎤
⎢
⎥
= ⎢
1.
56E-04
⎥
⎢
⎥
⎣
⎦
(2.59)
where Φ is the standard normal cumulative distribution function (NORMSDIST in Excel).
16.7 Nomenclature
age
age coat
age tke
A rt
is the in-service time that damage is applied, years
is the in-service time since the coating installation, years
is the component in-service time since the last inspection thickness measurement with respect
to wall loss associated with CUI or service start date, years
is the expected metal loss fraction since last inspection