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.