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Transcript of LaRisa Sergent Jeff Sorenson University of Oklahoma School of Chemical, Biological, and Materials...
LaRisa SergentJeff Sorenson
Optimal Preventative Maintenance Scheduling in Process Plants
University of OklahomaSchool of Chemical, Biological, and Materials Engineering
April 29th, 2008
Systematic inspection, detection, and correction of failures either before they occur or before they develop into major defects.
Preventative maintenance (PM) - tests, measurements, adjustments, and parts replacements which prevent faults from occurring.
Corrective maintenance (CM) - care and servicing of failed or damaged equipment to return to satisfactory operating condition.
What is Maintenance?
Favors constant preventative maintenance.Economic trade-offs
Cost of laborLoss of productReplacement costsDowntime for PM
How much preventative maintenance is economically optimal?
30%-50% of a plant’s operating budgetGoals of maintenance scheduling
maximize safetyminimize total cost
Modern Maintenance Philosophy
Parameters to be manipulatedSpare parts policyFrequency of preventative maintenanceLabor resources
Objective function to be minimized: Total maintenance costs (PM + CM)Total economic loss
Our Model
PM takes place on regular intervals (fraction of MTBF)
Time to complete diagnosis of failure negligible
All workers perform every maintenance taskEquipment failures prioritized by severityEmergencies take precedence over scheduled
maintenanceParts not on hand arrive in no more than a
weekRepaired equipment is deemed as good as
new
Assumptions in the Model
Samples failure rate of the equipment and the probability of each failure mode (i.e. electrical, mechanical, etc.)
Associated cost of each failure is calculatedMan hours are assigned first to each needed
CM, then to scheduled PM When the man hours for the week are
expended, no more maintenance takes placeAverage total cost is determined for a large
number of samples (10,000)
Monte Carlo Simulation
Tennessee Eastman plant – 19 pieces of equipment
Time horizon – 2 yearsResults of optimization
Labor: 3Inventory: somePM frequency: 1 x MTBF
Average objective value for no PM and no resource limitations was $1.66 million
Previous Study
Tennessee Eastman Plant
Risk analysisTotal cost versus probability of incidence Consider Value at Risk in addition to Average
Total CostModel applied to larger process
New values determined for:Optimal labor forceOptimal PM interval
Genetic algorithm applied to larger processAll variables manipulated simultaneously
Additions to the previous model
FCC– 153 pieces of equipment 31 pumps (29 with spares)2 compressors4 heaters87 heat exchangers15 vessels (drums, accumulators, etc.)1 catalytic reactor and associated regenerator12 separation columns
Auxiliary systems not considered in the optimization: cooling water system, waste system, steam system, etc.
Time horizon – 10 years
Current Study
Pumps Those with spares do not incur economic loss
upon failing.PM is done on spare following CM on main
pump, and the cost is included in the CM cost.The TNCM includes time for PM on the spare.
ColumnsTwo main columns – if one fails, the other
begins running at max capacity.
Assumptions Specific to the FCC
Vessels and tanksFailure results in loss of throughput for that
tank only; rest of the product throughput is not lost.
Heat exchangersFailure reduces efficiency of the process.Being repaired HE can be bypassed.Bypassed HE causes loss in product relative to
the portion of heat duty lost.Reactors and compressors
Failure results in total throughput lost.
Assumptions Specific to the FCC
Monte Carlo simulation data (aka. The woes and misfortunes of Excel)
0 5 10 15 20 25 30 $40,000,000.00
$45,000,000.00
$50,000,000.00
$55,000,000.00
$60,000,000.00
$65,000,000.00
$70,000,000.00
$75,000,000.00
Effect of Labor on Fitness Function - FCC
Total CostTotal Economic Loss
Labor
Do
llars
over
10
years
Cost of labor: $40,000/year/worker
3 4 5 6 7 8 9 10 110
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
HT = 10 years
xf=1
Total Cost (MM$)
Pro
babil
ity
of
Occu
rren
ce
More risk of high costsLower average total cost
More risk of high costsLower average total cost
Risk Analysis: Total Cost versus Probability of Occurrence
What we expected…
Less risk of high costsHigher average total cost
3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
HT = 10 years
xf=.7xf=1xf=1.2xf=1.5xf=1.8
Total Cost (MM$)
Pro
babil
ity
of
Occu
rren
ce
Risk Analysis: Total Cost versus Probability of Occurrence
What we found…
• Distribution (i.e. shape of the curves) doesn’t change.• No trade-off between risk and average total cost.
Risk and Average Cost – Tennessee Eastman
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.25.2
5.4
5.6
5.8
6
6.2
6.4
0
1
2
3
4
5
6
7
8
Average cost Polynomial (Average cost)Percent above 8MM Polynomial (Percent above 8MM)
PM Interval (x MTBF)
Avera
ge C
ost
(MM
$)
% a
bo
ve $
8 M
M
Try another type of risk analysis…
If at first you don't succeed
…
ENGINEER
Objective – Establish a “fitness function” to consider “value at risk” (VAR) in addition to average total cost.
Purpose – Determine optimal PM conditions that balance trade-off between
Low average total costLower probability of high economic loss
Form: f = ATC + xVAR, 0 ≤ x ≤ 1
VAR is the difference between ATC and the cost defining 95% or less probability.
Risk Analysis – Fitness Function
Optimizing with a Fitness Function - FCC
$6.00
$6.60
$7.20
$7.80
$8.40
0 0.5 1 1.5 2 2.5
Fitn
ess
Func
tion
Val
ue (i
n m
illio
ns)
PM Interval (fraction of MTBF)
Fitness Factor as a Function of PM Interval
Fitness Factor
Average Total Cost
FF XaXb Optimized
ATC XaXb Optimized
• Changes in VAR are insignificant compared to magnitude of ATC. • Result: fitness function parallels ATC.
Final Monte Carlo Results for FCCOptimal labor force: 5 workers
Actual number employed by refinery for FCC: 5
Optimal PM interval1.7x MTBF
Fitness functionSame results weighing VAR in with ATC
Average objective function with no PM $6.34 million per year
Evaluate a specific component at varied PM interval by simulations with all other PM schedules constant.
Determine optimal PM frequency for the chosen component.
Lower average costLower probability of high economic loss
Run “optimized” simulation using optimal value for each specific component.
Compare values of economic loss to those obtained using a single “x-factor” to vary overall PM frequency.
PM Optimization by Component
Evaluates multiple variables simultaneously.
Each variable becomes a “gene” on the maintenance model “chromosome.”
A population of chromosomes is randomly generated.
Each chromosome (model) is evaluated to determine its “fitness” in comparison to others in the population.
More “fit” chromosomes more likely to reproduce and continue to exist in new generations.
Crossover and mutation exist.
Genetic Algorithms
“Parents” chosen randomly from reproduction poolOffspring are identical to parents UNLESS
Crossover occurs: offspring “swap” one gene. (random)
Mutation occurs: offspring has one gene (random) replaced with a new value.
Crossover and mutation prevent premature convergenceReduce likelihood of optimizing to a “local
minimum.”
Fitness of parents and offspring evaluated.“Best” chromosome automatically enters new
generation
Genetic Algorithms
Operation of Genetic Algorithm
Define range of values for parameter generation.PM intervals set between 0.5 and 1.6 for non-
interfering pieces of equipment.PM intervals set between 0.3 and 1.1 for
interfering pieces of equipment.
Specify population size, crossover probability, mutation probability, and number of generations.
Complication: Each generation takes 48-65 minutes to evaluate. Running the algorithm literally takes days.
Genetic Algorithms
Genetic Algorithm ResultsGenetic Algorithm Conditions:8 parameters (7 equipment groups,
labor)2 variables per parameter (PM interval,
initial PM time)Population size: 40Iterations (# of generations): 40 (~2 day
run time)Crossover probability: 100% Mutation probability: 30%
Genetic Algorithm ResultsVariable Category
Run 1 Run 2
initial time
PM frequenc
y
initial time
PM frequenc
y
Group 1 (pumps) 1.2 0.45 0.7 0.8
Group 2 (compressors) 1.1 0.1 0.3 0.15
Group 3 (heaters) 0.7 0.85 1 1.3
Group 4 (exchangers) 0.3 1.5 1.4 1.15
Group 5 (vessels) 0.1 1.15 0.8 0.5
Group 6 (reactor/regenerator)
0.6 0.8 0.8 0.9
Group 7 (columns) 0.6 1.1 0.5 1.6
Labor 5 4
Average Total Cost $5,403,620 $5,590,003
Issues with Results:• Different optimal values• No common terms between optimal solutions
Greater Convergence Required!
Genetic Algorithm ResultsImproving the Algorithm:Reduce number of equipment groups
Combine similar equipments in same groups
Fewer groups (5 instead of 7)Change range of PM intervals for
parametersRemove low values shown to be inefficient
in Monte Carlo SimulationsChange Labor Cost to $100,000/unit
Information provided by plant w/ FCC unit.Faster evaluation and convergenceAllow for more generations (200, max.)
Genetic Algorithm ResultsVariable Category
Run 1 Run 2 Run 3
initial time
PM frequenc
y
initial time
PM frequen
cy
initial time
PM frequen
cy
Group 1 (pumps) 1.4 1.0 0.6 0.9 1.3 0.65
Group 2 (compressors) 0.8 0.45 0.2 0.4 0.2 0.4
Group 3 (heaters & exchangers)
1.0 1.4 1.4 0.9 0.9 1.15
Group 4 (vessels) 1.3 0.5 1.1 1.5 0.7 1.1
Group 5 (reactors & columns)
0.3 1.2 0.6 1.1 0.0 1.4
Labor 4 5 4
Iterations to Convergence* 96 62 105
Average Total Cost $5,767,811 $5,786,233 $5,756,541
Average Value: $5,770,195Standard Deviation: $14989 (0.26%)
* GA is considered to converged after 50 iterations without finding a more optimal value
Genetic Algorithm: Further Work
Separate equipment groups for more optimal PM interval of each component.
Longer computation time required for each generation
Slower convergence to optimal PM policy
Modify mutation and crossover probability to reduce risk of local minimums being found as optimal solutions.
More generations required for convergence to optimal policy
Refine data used in analysisMore accurate, process-specific data will increase
value of PM solutions obtained by algorithm.
Optimal Preventative Maintenance Scheduling in Process Plants
LaRisa SergentJeff Sorenson
Thank you.