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, 3001 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 these 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 determined 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
information 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-based 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 maintenance 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 optimally 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 degradation
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 optimally schedule maintenance 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 different 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 quantify 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 maintenance 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-objective 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 optimization 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 results for the different maintenance policies.
Conclusions and future work are discussed in section 5.
2. Simulation of maintenance policies
Markov models have been widely used in condition-based maintenance to model the state of a system. The
advantage of using 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 difficult 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
behaviour of the manufacturing equipment over a finite horizon.
Five different maintenance policies are simulated, which are corrective, preventive, offline conditionbased, online condition-based and prognostic maintenance. The maintenance policies are evaluated based on
the expected value of the distribution of cost and 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 certain component
happens. A fixed maintenance schedule where maintenance is performed in regular time intervals is
considered as preventive maintenance. When a component breaks 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 the 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 first 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 online 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 performed. When the online monitoring is
unable to detect an incipient failure corrective maintenance is executed at breakdown. For online conditionbased 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 optimizes 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 at 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 availability 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 asgood-as new state after maintenance. Three different maintenance or replacement scenarios exist both for
preventive and corrective maintenance. In the first maintenance scenario only 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 scenarios are initiated by preventive replacement or failure of one of the bearings. For this
reason a failure probability distribution is fitted to breakdown data of the bearings. The fitted Weibull
distribution with its parameters and 95%-confidence interval on the parameters is shown in Figure 1. These
95%-confidence bounds are used to simulate the failure behaviour 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.
1
0.9
0.8
Cumulative probability
WL(9.2023,2.0363)
W(10.0352,2.3571)
0.7
WU(10.9436,2.7286)
0.6
0.5
0.4
0.3
Failure data
Weibull
confidence bounds (Weibull)
0.2
0.1
0
5
10
15
Time To Failure
20
Figure 1. Weibull distribution fitted to the failure data of the bearings with scale 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 parameters.
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:
f ( x; n, p)  (n!/( x1!,..., xk !))( p1x1 ,..., pkxk ), whenik1 xi  n.
(1)
Where x  ( x1 ,..., x k ) gives the number of each of k outcomes in n trials of a process with fixed probabilities
p  ( p1 ,..., p k ) of individual outcomes in any one trial. The vector p has non-negative integer components
that sum to one. The vector p defines the probabilities of the replacement or failure scenarios for both
preventive replacement actions ( p p  ( p1  0.95, p2  0.03, p3  0.02) ) and corrective maintenance
( p c  ( p1  0.1, p 2  0.15, p3  0.75) ) actions. This means that for preventive maintenance 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 holds for the
corrective maintenance actions 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 summary 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.
Duration parameters
Inspection
Waiting
Replacement
Repair
Installation
Secondary damage
Distribution
Triangular
Triangular
Triangular
Triangular
Triangular
Triangular
Min. time
(h)
0,4
23
3,5
3,5
3,5
0,5
Mean time
(h)
0,5
24
4
4
4
1
Max. time
(h)
0,6
25
4,5
4,5
4,5
1,5
Cost parameters
Bearing
Bearing house
Shaft
Transportation
Secondary damage
Working
Cost
(€)
302,5
232,5
1675
120
300
70 €/h
The two objectives considered when optimizing the different maintenance policies are expected cost (€)
and downtime (weeks), which are defined as:
ETotalCost  Cost p  Costc  Costinsp. .
(2)
ETotalDowntime   Downtimep  Downtimec  Downtimeinsp..
(3)
Where Costp is preventive maintenance cost, Costc is corrective maintenance cost, Costinsp. is cost of
inspection, Downtimep is downtime due to preventive maintenance, Downtimec is downtime due to corrective
maintenance and Downtimeinsp. is downtime due to inspection. The cost parameters for preventive
maintenance, corrective maintenance and inspection are defined as followed:
(4)
Cost p  T p  CostW  3i 1 N pi  Cost pi .
Cost c  Tc  Cost W  3i 1 N ci  Cost ci   N SD  Cost SD .
(5)
Costinsp.  Tinsp.  CostW .
(6)
Where Tp, Tc and Tinsp. are respectively the total preventive maintenance, corrective maintenance and
inspection time during the simulation. Npi is the number of preventive maintenance actions for replacement
scenario i. Nci is the number of corrective maintenance actions for failure scenario i. NSD is the number of
times secondary damage occurs. CostW is the cost of working or personnel cost and CostSD is the cost of
secondary damage. Finally, Costpi and Costci 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 value by
using the following formula:
CostDiscounted  kj 0 Cost j / 1  d  j .
(7)
Where k is the number of years simulated, Costj 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 the 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 section 3.
4.1 Corrective and preventive maintenance
For 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 optimization of
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 (65757.11€) is
optimized and 5 weeks when the total expected downtime (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 offline condition-based maintenance policy. The
isocost and –downtime curves can be seen in Figure 3.
0.15
0.2
Threshold level
0.25
4
3.5
3
0.1
0.3
3.27
3.
51
3.36
3.2
7
3.
18
0.15
3.48
3.2
73.2
31
3.3 3.3 .18
93
.36
3.2
4
3.4
2
3.4 3
5 .33
21
3.
3.5
3.4 1
3.4 8
3.4 5
2
3.3
9
0.2
Threshold level
3.33
6
0.1
0
62622524505000
662 70
4.5
4
3.2
1
3.2
61 650
61 800
61 950
62 100
6.5
0
61 65
61 500
5
3.3
61200
61350
5.5
39
3.
3.39
0
7 61 50
6
3.24
7.5
3.1
2
.3
3 machine
36
Expected total downtime per
3.
3.33
61650
61 500
0
61 35
3.21
3.54
8
3.
18
6.5
3.
18 3 3.12 3.09
.1
5
8.5
63 0
63 7590
0
Time between inspections (weeks)
9
7
64 35
64machine
200 0
Expected total cost per
64 05
0
3.63.57
63600
63450
63300
63150
63000
62850
62700
62550
62400
62250
62100
61950
61800
3.15
Time between inspections (weeks)
10
9.5
0.25
0.3
Figure 3. Isocost and –downtime curves for offline condition-based maintenance.
The deterioration of the components is monitored continuously which makes the 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.
9.5
x 10
4
4.5
Expected total downtime per machine
Expected total cost per machine
Online CBM
9
8.5
8
7.5
7
6.5
6
5.5
0
0.2
0.4
0.6
Threshold level
0.8
Online CBM
4
3.5
3
2.5
1
0
0.2
0.4
0.6
Threshold level
0.8
1
Figure 4. Expected total cost and downtime for online condition-based maintenance.
4.3 Prognostic maintenance
3.3
Expected total downtime per machine (weeks)
Expected total downtime per machine (weeks)
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.
Final population of GA
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
5.8
6
6.2
6.4
6.6
6.8
Expected total cost per machine
7
x 10
4
2.68
Pareto optimal front
2.66
2.64
Steering on cost
2.62
Steering on downtime/availability
2.6
2.58
2.56
5.8
5.82
5.84
5.86
5.88
5.9
Expected total cost per machine
Figure 5. Expected cost and downtime for prognostic maintenance using GA.
5.92
x 10
4
4.4 Comparison of all maintenance policies
A comparison between all considered optimal maintenance 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. Moreover,
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.
Cost (€)
Maintenance policy
Improvement (%)
Downtime (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
8028,60
13,94%
3,0104
0,5078
28,92%
Prognostic maintenance
58109,22
2766,60
16,11%
2,5664
0.1453
39,40%
5. Conclusions and future work
A real life case study is performed on manufacturing equipment to quantify the benefit of prognostic
information in maintenance decision making. It shows that the influence of prognostic information on total
cost and downtime is substantially valuable in comparison to the other investigated maintenance policies.
Moreover, the simulation makes clear that the optimal maintenance 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
optimization 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.
References
Barata, J., Soares, C. G., Marseguerra, M. and Zio, E. (2002) Simulation modelling of repairable multicomponent deteriorating systems for 'on condition' maintenance optimisation. Reliability
Engineering & System Safety, 76, 255-264.
Camci, F. (2009) System Maintenance scheduling with prognostics information using genetic algorithm.
IEEE Transactions on Reliability, 58, 539-552.
Grall, A., Dieulle, L., Berenguer, C. and Roussignol, M. (2002) Continuous-time predictive-maintenance
scheduling for a deteriorating system. IEEE Transactions on Reliability, 51, 141-150.
Holland, J. H. (1962) Adaptation in natural and artificial systems. University of Michigan: Ann Arbor, MIT
Press.
Liao, H., Elsayed, E. A. and Chan, L.-Y. (2006) Maintenance of continuously monitored degrading systems.
European Journal of Operational Research, 175, 821-835.
Marseguerra, M., Zio, E. and Podofillini, L. (2002) Condition-based maintenance optimization by means of
genetic algorithms and Monte Carlo simulation. Reliability Engineering & System Safety, 77, 151165.
Van Der Weide, J. A. M., Pandey, M. D. and Van Noortwijk, J. M. (2010) Discounted cost model for
condition-based maintenance optimization. Reliability Engineering & System Safety, 95, 236-246.
Yang, Z. M., Djurdjanovic, D. and Ni, J. (2008) Maintenance scheduling in manufacturing systems based on
predicted machine degradation. Journal of intelligent manufacturing, 19, 87-98.