Quantifying the benefit of prognostic information in maintenance decision making

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Oct 23, 2013 (3 years and 7 months ago)

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Quantifying the benefit of prognostic information in maintenance decision
making

A.
Van Horenbeek
* and
L
.
Pintelon
**


*
Celestijnenlaan 300A, 3001 Heverlee, Belgium,

Catholic University Leuven,
Adriaan.vanhorenbeek
@
cib.kuleuven.be

**
Celestijnenlaan 300A, 30
01 Heverlee, Belgium,

Catholic University Leuven,

Liliane.pintelon
@cib.kuleuven.be


Abstract
.
Many models and methodologies to predict the remaining useful life (RUL) of a component or
system are investigated nowadays. However, decision making based on the
se predictions (RUL) is still an
underexplored area in maintenance management. The objective of this paper is to quantify the added value of
this prognostic information (RUL). This is done by constructing a stochastic discrete
-
event simulation
model, which

optimizes maintenance action scheduling, based on prognostic information on the different
components. Cost and availability criteria are taken into account in this optimization model as the objectives.
The added value of the prognostic information is dete
rmined by comparing this
prognostic
maintenance
policy to four other conventional maintenance policies: corrective maintenance, preventive maintenance,
offline condition
-
based maintenance and online condition
-
based maintenance. The benefit of prognostic
in
formation and the stochastic discrete
-
event simulation model are validated by a real life case study on
bearings of manufacturing equipment. Looking at more than one machine, a plant level approach is taken in
the case study.



1.
Introduction

Condition
-
ba
sed maintenance is a well studied field in maintenance management. Many models in literature
indicate that a condition
-
based maintenance policy is capable of reducing cost
,

increasing productivity and

maintaining high equipment reliability and

availability

while at the same time
ensuring
a higher safety level.

Marseguerra et al.
(2002)

uses Monte Carlo simulation and genetic algorithms to determine the optimal
degradation level beyond which a preventive mai
ntenance
intervention

should be taken

by optimizing profit
and availability.

A multi
-
component simulation modeling approach is taken by
Barata et al.
(2002)

to find
the optimal degradation threshold for performing preventive maintenance actions.

Liao
et al.
(2006)

introduces a condition
-
based availability limit policy which achieves the

maximum availability of a system
by optimal
l
y scheduling maintenance actions.
Other papers not only try to find the optimal degradation
threshold, but
at the same time

optimize the

inspection schedule or policy

(Grall et al., 2002)
.

Although
condition
-
based maintenance takes advantage of the known state of components, setting a deg
radation
threshold beyond which preventive maintenance is carried out is not

always

an optimal solution compared to
predictive maintenance. Predictive maintenance uses
current and
prognostic information like the remaining
useful lifetime of components to o
ptimally schedule mainten
ance actions, while condition
-
based
maintenance only uses
current
component state information.
The benefit of
also
using information about
future degradation
over only using currently observed information
is illustrated in differen
t publications

(Camci, 2009, Yang et al., 2008)
.

Proactive maintenance decisions can be made based on the prognostic
information which results in a dynamic maintenance schedule.

The objective of this paper is to qua
ntify the benefit of prognostic information in maintenance decision
making

by performing a real life case study on manufacturing equipment
.
A comparison between different
maintenance policies
is

made

and the optimal maintenance policy
is

determined
. The ma
intenance policies
considered are corrective, preventive, offline condition
-
based, online condition
-
based and prognostic
maintenance.

The optimization will be done by using stochastic simulation and genetic algorithms.

For each
maintenance policy a multi
-
o
bjective optimization is perfomed by considering cost as well as availability
(
or
downtime
)

as the maintenance objectives.

In many cases both cost and availability objectives are
combined

into one
cost
objective function by expressing availability in terms

of downtime cost. The reason to
consider
these as two separate objectives is
that expressing availability in terms of value to the company is
often
difficult.
This value can be for example increased production output or market share.
Moreover, this value
of
increased availability to the company
will change according to the
varying

business environment. In times of
economic
welfare,

when

as high

availability

as possible

is
needed;

an increase in availability will be more

valuable to a company then in a time

of economic downturn

with
fewer orders
.

In the latter case steering on
cost will be more important, because increased availability will not contribute to a higher profit.

The
advantage of performing multi
-
objective rather than single
-
objective optimizatio
n is that a pareto set of
optimal solutions is found. Based on
this set of optimal solutions, the optimal maintenance schedule can be
determined according to the business environment and circumstances at the time of decision making.


The structure of this
paper is as follows. Section 2 describes the discrete
-
event simulation together with
the different maintenance policies that are considered

and how they are handled
.

In section 3 the case
-
study
is introduced, while section 4 summarizes the simulation resul
ts for the different maintenance policies.
Conclusions and future work are discussed in section 5.


2.
Simulation of m
aintenance policies

Markov models have been widely used in condition
-
based maintenance to model the state of a system. The
advantage of u
sing Markov models is that analytic results to the maintenance problem can be found.
However, using Markov models also has some disadvantages. Many simplifying assumptions are made and
the probabilities of the different states in a Markov process are diffi
cult to find. The more realistic and
complex the modeled systems
get

the more difficult and cumbersome it is to describe the system by analytic
models.

This is the main reason to resort to simulation tools to model the manufacturing equipment in this
paper
. Futhermore, simulation
does not require any assumptions on the character of the degradation process

(Yang et al., 2008)
.

In this paper a discrete
-
event Monte Carlo simulation is used to model the dynamic
behavio
u
r
of the manufactu
ring equipment over a finite horizon.

F
ive different maintenance policies are simulated, w
h
ich are corrective, preventive, offline condition
-
based
,

online condition
-
based
and prognostic

maintenance.

The maintenance policies are evaluated based on
the expected value of the distribution of cost a
nd availability.
By doing so the optimal maintenance policy is
determined and the added value of prognostic information is quantified.
In the corrective maintenance case
maintenance is only performed
when a failure
,

which causes machine breakdown
,

of a cer
tain
component
happens.

A fixed maintenance schedule where maintenance is performed in regular time intervals is
considered as preventive maintenance. When a component br
e
aks down before a scheduled maintenance
action corrective maintenance is performed on

the component.
Optimization of the time interval between two

consecutive

maintenance actions on the machine is executed for the preventive maintenance policy.

Offline
condition
-
based maintenance uses inspections (e.g. vibration measurements) to determine
the current state of
a machine or component. Inspections are carried out at regular time intervals. When
the deterioration level,
revealed during the inspection, of a component
exceeds

a well definied threshold
,

preventive maintenance is
carried out.

If th
e deterioration level is below the threshold level the next inspection is scheduled.

Corrective
maintenance is perfomed when a component breaks down between two scheduled inspections

where the
deterioration level was below the threshold level when the firs
t inspection was done
.

Both optimization of
the time between two consecutive inspections and the deterioration level beyond which

preventive

maintenance actions are taken is performed in the simulation model.

Online condition
-
based maintenance
applies onli
ne monitoring of all considered components in the machine.

In this way the state and
deterioration level of each component is continuously known.

When the deterioration level exceeds a set
deterioration
threshold level a preventive maintenance action is
pe
rformed
.

When the online monitoring is
unable to detect an incipient failure corrective m
aintenance is executed at break
down.

For online condition
-
based maintenance the
preventive maintenance action threshold is optimized

in the stochastic simulation
model
.


Prognostic or predictive maintenance
takes advantage of the available predictions of remaining useful
lifetime for components. Based on the remaining useful lifetime distributions for all components an optimal
maintenance schedule can be found which opt
imizes plantwide maintenance operations.
A
Genetic
Algorithm (GA)

(Holland, 1962)

will be used to find this optimal maintenance schedule.
A GA is a heuristic
that mimics the process of
natural evolution and survival of the fittest based on crossover and mutation on
the initial population.
The different maintenance schedules are represented by a chromosome defined as an
array of binary numbers, where one represents scheduled maintenance a
t time t and zero no scheduled
maintenance at time t.
A different number of iterations, referred to as generations
of

the GA, are performed

to

improve the objective
or fitness
function(s).

The choice for GA’s in this paper is based on two major
advantages
or properties of the heuristic
. Firstly, they handle multi
-
objective optimization problems in a fast
and accurate way. Secondly, no analytically tractable objective function is needed to solve the optimization
problem.

By comparing both cost and availabili
ty objectives
for all different
optimal
maintenance policies
the benefit of prognostic information in maintenance decision making is quantified.


3
. Case study

The discrete
-
event simulation is applied to
a real life case study on manufacturing equipment
to
quantify the
added
value of prognostic maintenance.

Focus is on one specific subassembly
of each

machine that consists
of two roller bearings with corresponding bearing housings and a driving axle.

When one bearing breaks
down the other one is replaced
at the same time
.

Components are always replaced and are restored to the as
-
good
-
as new state after maintenance.
Three different maintenance or
replacement

scenarios exist both for
preventive and corrective maintenance. In the first
maintenance

scenario on
ly replacement of the bearings is
necessary, in the second
maintenance

scenario replacement of both bearings and bearing housings is
required, while in the third
maintenance

scenario replacement of the whole subassembly is necessary.

All
maintenance

scenar
ios are initiated by
preventive replacement or
failure of one of the bearings.

For th
is
reason a failure probability distribution is fitted to breakdown data of the bearings.
The fitted W
eibull
distribut
ion with its parameters and 95%
-
confidence interval o
n the parameters is shown in Figure 1.

These
95%
-
confidence bounds are used to simulate the failure behavio
u
r of the bearings.

It is assumed that this
Weibull reliability curve correctly reflects the
evolution in time of the
monitored
physical
parameters (
e.g.
vibration measurement on bearings) and predicted remaining useful lifetime based on these measured
parameters

for the condition
-
based and prognostic maintenance policies
.

Figure 1.
Weibull distribution
fitted
to the failure data of the bearings with s
cale parameter η = 10.0352
and shape parameter β = 2.3571
.
WL and WU are respectively
the
Weibull lower bound and Weibull upper
bound to form the 95% confidence interval on both scale and shape parameter
s
.


Replacement of the bearing housings and axle are
modeled by a probability of
having one of the three
maintenance

scenarios

when failure of a bearing happens

or a preventive maintenance action is performed
.

Probabilities for the
maintenance

scenarios are different for preventive and corrective maintenance
.

When a
bearing breaks down probability of replacing the bearing housing and axle are bigger than when a preventive
maintenance action is performed.
The
maintenance

scenarios

are

sampled

from

a multinomial distribution:




(1)

Where
gives the number of each of
k

outcomes in
n

trials of a process with fixed probabilities
of individual outcomes in any one trial. The vector
p

has non
-
negative integer components
th
at sum to one.

The vector
p

defines the probabilities of the
replacement or
failure scenarios for both
preventive

replacement actions
(
)

and corrective maintenance

(
)

actions
.
This means that for preventive mai
ntenance 95% of the
actions consist of only replacing the bearings, 3% consists of replacing bearings and bearing housings, and in
2% of the cases a replacement of the entire subassembly is necessary.

The same logic hold
s

for the
corrective maintenance ac
tions except that the probabilities of the failure scenarios change
when a failure

of

one of the bearings happens
.
Failure of a bearing will induce secondary damage to other parts of the
machine, like for example the cover, with a probability of 0.8.

A sum
mary of the
other
data and parameters
used in the simulation is provided in Table 1.



Table 1. Parameters and data used in the discrete
-
event simulation for all maintenance policies.


The two objectives considered
when

optimizing the different maintenance policies are expected cost

(€)

and downtime

(weeks)
, which are defined as:



(2)


(3)

Where
Cost
p

is preventive maintenance cost,
Cost
c

is corrective maintenance cost,
Cost
insp.

is cost of
inspection,
Downtime
p

is downtime due to preventive maintenance,
Downtime
c

is

downtime due to corrective
maintenance and
Downtime
insp.

is downtime due to inspection.

The cost parameters for
preventive
maintenance
, corrective
maintenance
and
inspection

are defined as

followed
:





(4)




(5)


(6)

Where
T
p
,
T
c

and
T
insp.

are respectively the total preventive maintenance, corrective mainten
ance and
inspection time during the simulation.

N
pi

is the number of preventive maintenance actions for replacement
scenario
i
.
N
ci

is the number of corrective maintenance actions for failure scenario
i
.
N
SD

is the n
umber of
times secondary damage occurs.
Cost
W

is the cost of working or personnel cost

and
Cost
SD

is the cost of
secondary damage
.
Finally,
Cost
pi

and
Cost
ci

are the cost for a preventive action of replacement scenario
i

and the cost for a corrective action of failure scenario
i
.

When simulating

over several years, discounting of costs can have a big influence on the final results of
the simulation
(van der Weide et al., 2010)
. For this reason costs are discounted to their present v
alue by
using the following formula:






(7)

Where
k

is the number of years simulated,
Cost
j

is the total cost in year
j

and
d

is the discount rate which
equals the Weighted Average Cost of
Capital
(WACC)
of 10% of the company.


4
.
Results

For all maintenance policies the discrete
-
event simulation is run over a finite time horizon of 200 weeks with
5000 replications.

The number of individuals in each population for the GA is set to
700

and th
e maximal
number of generations is
200.

Scattered crossover is selected as the crossover function with a crossover
fraction of 0.8. This crossover fraction specifies the fraction of individuals in the next generation that are
created by crossover. Mutation

produces the remaining individuals in the next generation

by using a
Gaussian mutation function
.

A tournament selection function is used as the parent selection method.

The
objective functions considered are earlier defined in formula (2) and (3) of secti
on 3.



4.1
Corrective and preventive maintenance

F
or preventive maintenance the time between two consecutive preventive maintenance actions is optimized,
in fact this is an optimization of the block
-
based preventive maintenance policy.

Based on optimizati
on of
cost and downtime functions a fixed schedule of preventive actions can be determined.
The optimal time
Duration parameters

Distribution

Min. time
(h)

Mean time
(h)

Max. time
(
h)

Cost parameters

Cost
(€)

Inspection

Triangular

0,4

0,5

0,6

Bearing

302,5

Waiting

Triangular

23

24

25

Bearing house

232,5

Replacement

Triangular

3,5

4

4,5

Shaft

1675

Repair

Triangular

3,5

4

4,5

Transportation

120

Installation

Triangular

3,5

4

4,5

Secondary damage

300

Secondary damage

Triangular

0,5

1

1,5

Working

70 €/h


between two preventive maintenance actions is 7 weeks when the total expected cost
(
65757
.
11
€)

is
optimized and 5 weeks when the total expected dow
ntime

(
3.
18 weeks)

is minimized.


4.2
Offline
and online
condition
-
based maintenance

The deterioration threshold beyond which preventive maintenance is
triggered

together with

the inspection
schedule are

the

two parameters that are optimized for the offl
ine condition
-
based maintenance policy.

The
isoc
ost and

downtime curves can be seen in Figure 3.

Figure 3. Isocost and

downtime curves for offline condition
-
based maintenance
.


The deterioration of the components is monitored continuously which makes th
e deterioration threshold
beyond which a preventive maintenance action is taken the only parameter to optimize in the online
condition
-
based maintenance policy.

The results are shown in Figure 4.

Figure 4. Expected total cost and downtime for online condit
ion
-
based maintenance
.


4.
3

Prognostic maintenance

Prognostic maintenance makes use of the predictions of the remaining useful lifetime of components, which
makes it possible to react to the real deterioration
of

each component in different machines.

The
last
population of the GA together with the Pareto optimal front
is

given in Figure 5.

Figure 5. Expected cost and downtime for prognostic maintenance using GA.


4.
4

Comparison of all maintenance policies

A comparison between all considered optimal maintena
nce policies can be made based on the objectives of
total cost and downtime (Table

2).

This comparison makes clear that the added value of prognostic
information is substantial. It even has a major impact on downtime reduction in this specific case.
Moreov
er,
the analysis in the previous sections makes clear that
a different optimal maintenance policy is found based
on the separate objectives of cost and downtime.
The business environment at the time of decision making
defines the value of availability to a

company.
Considering both cost and downtime as two separate
maintenance objectives makes dynamic maintenance scheduling possible based on the value of availability at
the time of decision making.

This approach not only optimizes maintenance over time, but

optimizes
maintenance at every time instant while taking into account the business environment of the company.


Table 2.

Comparison of maintenance policies based on expected cost and downtime per machine.

Maintenance policy

Cost (€)

Improvement (%)

Downti
me (weeks)

Improvement (%)



Mean

SD



Mean

SD



Corrective maintenance

69266,64

7640,30


4,2352

0,4084


Preventive maintenance

65757,11

9337,30

5,07%

3,1888

0,5390

24,71%

Offline CBM

61017,70

8258,50

11,91%

3,0646

0,5486

27,64%

Online CBM

59607,64

80
28,60

13,94%

3,0104

0,5078

28,92%

Prognostic maintenance

58109,22

2766,60

16,11%

2,5664

0.1453

39,40%


5. Conclusion
s

and future work

A real life case study is performed on manufacturing equipment to quantify the benefit of prognostic
information in main
tenance decision making.
It shows that the
influence

of prognostic information on
total
cost and downtime

is substantial
ly valuable

in comparison to the other investigated maintenance policies.

Moreover, the simulation makes clear that the optimal maintena
nce policy is different according to both
objectives of cost and downtime.
According to the business environment and circumstances at the time of
decision making the optimal maintenance policy can be determined based on the presented multi
-
objective
optimi
zation model.

Future work will be on incorporating more components of the machine into the analysis,
together with the effect of imperfect maintenance and inspections, and constraints on spare parts and
manpower.


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