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

RISK-BASED INSPECTION METHODOLOGY, PART 5—SPECIAL EQUIPMENT 5-35
(
t 2
bundle
+
maint ) ⋅ ( 1 + ) <
t1
( )
t 2
If Cost Cost ROR EIR then replace the bundle
If Cost + Cost + Hurdle Cost < EIR then replace the bundle
(5.79)
bundle maint t1
The actual inspection costs should be used when available. Maintenance costs to pull the bundles for
inspection should be included in the total inspection costs when using Equation (5.78) and Equation (5.79).
Optimal Bundle Replacement Frequency
Maintenance optimization helps to strike a balance between cost and reliability. The cost per day of a "run to
failure" strategy shows low costs early in the life of the equipment and increasing costs as reliability
decreases. By overlaying the costs of an associated preventative maintenance to address the failure mode,
initial costs are high, but costs per unit time decrease as time progresses. This optimization occurs at a point
where the total cost function (sum of the two cost functions) is at a minimum. The time at which the minimum
occurs is the optimum time to perform maintenance [5] .
The optimum replacement frequency is calculated comparing the cost associated with a bundle failure
(increasing with increasing replacement frequency) to the replacement cost associated with periodic planned
shutdowns to replace the bundle (decreasing with increasing replacement frequency). The point where the
two costs reach a minimum value is the optimum replacement frequency.
The methodology in Shultz, 2001 [6] described below is recommended to determine the optimum bundle
replacement frequency.
a) Increasing Risk Cost of Unplanned Outage
A planned replacement time frequency is defined by the variable, tr
n
, and the risk cost associated with
an unplanned failure to replace the bundle (including business interruption and bundle replacement
costs) is calculated using Equation (5.80).
( ) ( )
Risk tr = C ⋅ P tr
(5.80)
tube tube tube
f n f , unplan f n
tube
Where C
f , plan
is defined in Equation (5.81).
Rate
C ⎛
⎞
= ⎜Unit ⋅ ⋅D ⎟⋅ Outage + Cost + ( Cost ⋅ matcost)
+ Cost
⎝ 100 ⎠
tube
red
f , unplan prod sd , unplan mult env bundle maint
(5.81)
Note that Equation (5.81) is similar to Equation (5.69) but uses the unplanned outage time, D .
sd , unplan
tube
The consequence of an unplanned frequency due to a tube bundle failure, C , includes business
f
interruption, the number of days required for bundle replacement during an unplanned outage, D sd , unplan
and environmental impact, Cost
env
. The risk cost due to bundle failure increases with time since the
tube
P tr , increases with time.
POF, ( )
f
n
b) Decreasing Cost of Bundle Replacement
The bundle replacement costs as a function of planned replacement frequency, tr , is calculated using
Equation (5.82).
tube
tube
( ) = ⋅⎡
− ( )
Cost tr C ⎣ P tr
pbr n f , plan
1
f n
tube
Where C
f , plan
is defined in Equation (5.83).
⎤
⎦
C ⎛ Rate ⎞
= ⎜Unit ⋅ ⋅D ⎟⋅ Outage
⎝ 100 ⎠
+ Cost + ( Cost ⋅ matcost)
+ Cost
tube
C = Cost + ( Cost ⋅ matcost)
+ Cost
tube
red
f , plan prod sd , plan mult env bundle maint
f , plan env bundle maint
(5.82)
(5.83)