Quantifying the benefit of prognostic information in maintenance decision
Celestijnenlaan 300A, 3001 Heverlee, Belgium,
Catholic University Leuven,
Celestijnenlaan 300A, 30
01 Heverlee, Belgium,
Catholic University Leuven,
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
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
policy to four other conventional maintenance policies: corrective maintenance, preventive maintenance,
based maintenance and online condition
based maintenance. The benefit of prognostic
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.
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
while at the same time
a higher safety level.
Marseguerra et al.
uses Monte Carlo simulation and genetic algorithms to determine the optimal
degradation level beyond which a preventive mai
should be taken
by optimizing profit
component simulation modeling approach is taken by
Barata et al.
the optimal degradation threshold for performing preventive maintenance actions.
introduces a condition
based availability limit policy which achieves the
maximum availability of a system
y scheduling maintenance actions.
Other papers not only try to find the optimal degradation
at the same time
inspection schedule or policy
(Grall et al., 2002)
based maintenance takes advantage of the known state of components, setting a deg
threshold beyond which preventive maintenance is carried out is not
an optimal solution compared to
predictive maintenance. Predictive maintenance uses
prognostic information like the remaining
useful lifetime of components to o
ptimally schedule mainten
ance actions, while condition
maintenance only uses
component state information.
The benefit of
using information about
over only using currently observed information
is illustrated in differen
(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
by performing a real life case study on manufacturing equipment
A comparison between different
and the optimal maintenance policy
. The ma
considered are corrective, preventive, offline condition
based, online condition
based and prognostic
The optimization will be done by using stochastic simulation and genetic algorithms.
maintenance policy a multi
bjective optimization is perfomed by considering cost as well as availability
as the maintenance objectives.
In many cases both cost and availability objectives are
objective function by expressing availability in terms
of downtime cost. The reason to
these as two separate objectives is
that expressing availability in terms of value to the company is
This value can be for example increased production output or market share.
Moreover, this value
increased availability to the company
will change according to the
business environment. In times of
an increase in availability will be more
valuable to a company then in a time
of economic downturn
In the latter case steering on
cost will be more important, because increased availability will not contribute to a higher profit.
advantage of performing multi
objective rather than single
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
is introduced, while section 4 summarizes the simulation resul
ts for the different maintenance policies.
Conclusions and future work are discussed in section 5.
Simulation of m
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
the more difficult and cumbersome it is to describe the system by analytic
This is the main reason to resort to simulation tools to model the manufacturing equipment in this
. 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
of the manufactu
ring equipment over a finite horizon.
ive different maintenance policies are simulated, w
ich are corrective, preventive, offline condition
The maintenance policies are evaluated based on
the expected value of the distribution of cost a
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
A fixed maintenance schedule where maintenance is performed in regular time intervals is
considered as preventive maintenance. When a component br
aks down before a scheduled maintenance
action corrective maintenance is performed on
Optimization of the time interval between two
maintenance actions on the machine is executed for the preventive maintenance policy.
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
a well definied threshold
preventive maintenance is
e deterioration level is below the threshold level the next inspection is scheduled.
maintenance is perfomed when a component breaks down between two scheduled inspections
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
maintenance actions are taken is performed in the simulation model.
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
threshold level a preventive maintenance action is
When the online monitoring is
unable to detect an incipient failure corrective m
aintenance is executed at break
For online condition
based maintenance the
preventive maintenance action threshold is optimized
in the stochastic simulation
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.
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
the GA, are performed
improve the objective
The choice for GA’s in this paper is based on two major
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
By comparing both cost and availabili
for all different
the benefit of prognostic information in maintenance decision making is quantified.
. Case study
event simulation is applied to
a real life case study on manufacturing equipment
value of prognostic maintenance.
Focus is on one specific subassembly
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
as new state after maintenance.
Three different maintenance or
scenarios exist both for
preventive and corrective maintenance. In the first
ly replacement of the bearings is
necessary, in the second
scenario replacement of both bearings and bearing housings is
required, while in the third
scenario replacement of the whole subassembly is necessary.
ios are initiated by
preventive replacement or
failure of one of the bearings.
reason a failure probability distribution is fitted to breakdown data of the bearings.
The fitted W
ion with its parameters and 95%
confidence interval o
n the parameters is shown in Figure 1.
confidence bounds are used to simulate the failure behavio
r of the bearings.
It is assumed that this
Weibull reliability curve correctly reflects the
evolution in time of the
vibration measurement on bearings) and predicted remaining useful lifetime based on these measured
for the condition
based and prognostic maintenance policies
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
Weibull lower bound and Weibull upper
bound to form the 95% confidence interval on both scale and shape parameter
Replacement of the bearing housings and axle are
modeled by a probability of
having one of the three
when failure of a bearing happens
or a preventive maintenance action is performed
Probabilities for the
scenarios are different for preventive and corrective maintenance
bearing breaks down probability of replacing the bearing housing and axle are bigger than when a preventive
maintenance action is performed.
a multinomial distribution:
gives the number of each of
trials of a process with fixed probabilities
of individual outcomes in any one trial. The vector
negative integer components
at sum to one.
defines the probabilities of the
failure scenarios for both
and corrective maintenance
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
corrective maintenance ac
tions except that the probabilities of the failure scenarios change
when a failure
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.
mary of the
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
optimizing the different maintenance policies are expected cost
, which are defined as:
is preventive maintenance cost,
is corrective maintenance cost,
is cost of
is downtime due to preventive maintenance,
downtime due to corrective
is downtime due to inspection.
The cost parameters for
are defined as
are respectively the total preventive maintenance, corrective mainten
inspection time during the simulation.
is the number of preventive maintenance actions for replacement
is the number of corrective maintenance actions for failure scenario
is the n
times secondary damage occurs.
is the cost of working or personnel cost
is the cost of
are the cost for a preventive action of replacement scenario
and the cost for a corrective action of failure scenario
over several years, discounting of costs can have a big influence on the final results of
(van der Weide et al., 2010)
. For this reason costs are discounted to their present v
using the following formula:
is the number of years simulated,
is the total cost in year
is the discount rate which
equals the Weighted Average Cost of
of 10% of the company.
For all maintenance policies the discrete
event simulation is run over a finite time horizon of 200 weeks with
The number of individuals in each population for the GA is set to
number of generations is
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.
objective functions considered are earlier defined in formula (2) and (3) of secti
Corrective and preventive maintenance
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
cost and downtime functions a fixed schedule of preventive actions can be determined.
The optimal time
between two preventive maintenance actions is 7 weeks when the total expected cost
optimized and 5 weeks when the total expected dow
The deterioration threshold beyond which preventive maintenance is
two parameters that are optimized for the offl
based maintenance policy.
downtime curves can be seen in Figure 3.
Figure 3. Isocost and
downtime curves for offline condition
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
based maintenance policy.
The results are shown in Figure 4.
Figure 4. Expected total cost and downtime for online condit
Prognostic maintenance makes use of the predictions of the remaining useful lifetime of components, which
makes it possible to react to the real deterioration
each component in different machines.
population of the GA together with the Pareto optimal front
given in Figure 5.
Figure 5. Expected cost and downtime for prognostic maintenance using GA.
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
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.
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
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
maintenance at every time instant while taking into account the business environment of the company.
Comparison of maintenance policies based on expected cost and downtime per machine.
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
of prognostic information on
cost and downtime
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
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
, C. G., M
, E. (2002) Simulation modelling of repairable multi
nt deteriorating systems for '
on condition' maintenance optimisation.
Engineering & System Safety,
, F. (2009) System Maintenance
IEEE Transactions on
, A., D
, L., B
, M. (2002) Continuous
for a deteriorating system.
IEEE Transactions on
, J. H. (1962)
Adaptation in natural and artificial systems
University of Michigan: Ann Arbor, MIT
, H., E
, E. A.
Y. (2006) Maintenance of con
tinuously monitored degrading systems.
European Journal of Operational Research,
, M., Z
, L. (2002) Condition
based maintenance optimization by means of
genetic algorithms and Monte Carlo simulation.
ty Engineering & System Safety,
an Der Weide
, J. A. M., P
, M. D.
, J. M. (2010) Discounted cost model for
based maintenance optimization.
Reliability Engineering & System Safety,
, Z. M., D
, J. (2008) Maintenance scheduling in manufacturing systems based on
predicted machine degradation.
Journal of intelligent manufacturing,