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Modeling a Complex Maintenance
Scenario in BlockSim
Many organizations use
BlockSim to
model and simulate repairable systems in order to obtain
estimates of reliability, availability, number of spares
required, maintenance cost, throughput and other related metrics
for a given mission time. The numerous features available in
BlockSims reliability block diagrams and phase diagrams make
it the software of choice for advanced system analysis. However,
at times the reliability analyst may come across scenarios that
at first seem to be beyond BlockSims modeling
capabilities. This article discusses one such scenario and gives
the solution to implement it in BlockSim.
Inspection Rejection
Probability
In certain industries, in addition to regular corrective
actions on failed components, periodic maintenance actions are
carried out on components to decrease the probability of
failure. These maintenance actions may reveal other components
that are otherwise inaccessible or invisible. If these
components are found to be in a damaged state then a replacement
is carried out. In effect, the periodic maintenance actions on
adjacent components act as inspections for such components and
industries often assign a fixed probability to model the
resulting replacements of the damaged components. The fixed
probability is referred to as the inspection rejection
probability.
In order to use BlockSim
to model a scenario involving the inspection rejection
probability, the following maintenance policies will be
combined:
- Corrective maintenance
upon inspection.
- Preventive maintenance
upon the maintenance of another group item
These features are described in
this months
Reliability Basics article with simple examples to
demonstrate their basic applications. The fan shaft example in
this article illustrates a more complex configuration that
combines these two policies in order to more accurately
represent the actual operation of the component.
Fan Shaft Example
Consider the following example of a fan shaft in one of the
modules of a compressor. We will assume that:
- The probability of failure
due to wearout of the fan shaft follows the Weibull
distribution with beta = 1.5 and eta = 300 hrs. It is
assumed that the wearout failures are immediately detected
because of the adverse effect of the failure (loss of
operation of the fan).
- The fan shaft is replaced
correctively when it fails and the corrective maintenance
(CM) duration is 3 hrs.
- Every 10 hrs, routine
maintenance performed on an adjacent component exposes the
fan shaft, which provides the opportunity to inspect for
damage to the fan shaft that can occur randomly during
operation (e.g. due to debris entering the system).
There is a 10% probability of finding a damaged shaft during
these opportunistic inspections (i.e. a 10%
inspection rejection probability).
- The fan shaft is replaced
preventively when damage is observed and the preventive
maintenance (PM) duration is also 3 hrs.
In order to represent the
actual behavior of the fan shaft, the model must take into
account the corrective replacements (due to the visible failure
of the fan shaft that results from wearout) and the preventive
replacements (due to the hidden damage that occurs randomly and
is discovered during the scheduled maintenance of an adjacent
item).
Figure 1 shows the reliability
block diagram (RBD) that can be used to model this scenario in
BlockSim.
Figure 1: RBD used to model the scenario in BlockSim
The diagram consists of two
blocks:
- The Fan Shaft block
represents the actual behavior of the fan shaft, including
both CM replacements (due to wearout failure) and PM
replacements (due to the discovery of damage).
- The Inspections
block represents the inspection rejection probability and is
used to "trigger" the PMs in the Fan Shaft block at
the appropriate times during the simulation.
The next sections describe how
to configure the block properties and maintenance policies
within BlockSim in order to model the scenario
appropriately.
Configuring a Block to
Represent the Inspection Rejection Probability
As mentioned above, the Inspections block is used to
model the inspection rejection probability and thereby determine
when the fan shaft will be replaced due to damage discovered
during the maintenance of an adjacent item. Specifically, the
following reliability, corrective maintenance and inspection
properties are defined for the Inspections block:
Reliability Properties (Inspections Block)
In order to represent the inspection rejection probability, the
failure distribution defined for the Inspections block
should be such that it returns a 10% probability of failure
every time an inspection takes place. Since this damage occurs
randomly at a fixed rate, it can be modeled with an exponential
distribution where the mean time is such that a 10% probability
of failure (or 90% reliability) is obtained every 10 hrs. This
can be calculated as follows:
where t is the mission
duration, m is the mean life and R(t) is the
reliability at time t. Substituting the value of the
required reliability as 0.9 and the mission duration as 10
returns the mean time:
Figure 2 shows the Failure
Distribution defined for the Inspections block.
Figure 2: Distribution to model the inspection rejection
probability
Corrective Maintenance and Inspection Properties (Inspections
Block)
Since the preventive replacement will be initiated when the
maintenance of an adjacent item reveals damage to the fan shaft
that was not visible until the inspection, this can be treated
as a hidden failure and modeled with the "Upon Inspection"
maintenance policy.
Specifically, Figure 3 shows
the Corrective Maintenance properties for the Inspections
block, which indicate that a CM will be recorded within the
simulation each time the block is found to be "failed" at the
time of the inspection (i.e. damage is visible). Each
replacement will take 3 hrs and the restoration factor of 1
indicates that the component will be "as good as new" after the
replacement.
In addition, Figure 4 shows the
Inspection properties, which indicate that the inspections will
occur every 10 hrs.
Figure 3: CMs will be recorded for the Inspections block if
it is found to be damaged upon inspection
Figure 4: Inspections will occur every 10 hrs
As you can see in both figures,
an Item Group # of 1 has been assigned to this block. By
assigning the same Item Group # to both blocks in the
BlockSim diagram, it will be possible to use the inspection
rejection probability modeled by the Inspections block to
"trigger" preventive maintenance actions on the Fan Shaft
block, as described next.
Configuring a Block to
Represent the Actual Behavior of the Fan Shaft
Now that we have used the Inspections block to model the
inspection rejection probability, the next step is to configure
the Fan Shaft block to represent the actual behavior of
the fan shaft, taking into account both the CMs due to wearout
failure and the PMs that occur when damage is discovered during
the routine maintenance of an adjacent item. Therefore, the
following reliability, corrective maintenance and preventive
maintenance properties are defined for the Fan Shaft
block:
Reliability Properties (Fan Shaft Block)
Figure 5 shows the Failure Distribution defined for the Fan
Shaft block. It is the probability that the fan shaft will
fail due to wearout (i.e. Weibull with Beta = 1.5 and Eta
= 300 hrs).
Figure 5: The probability of
failure due to wearout
Corrective Maintenance Properties (Fan Shaft Block)
Figure 6 shows the Corrective Maintenance properties defined for
the Fan Shaft block, which indicate that CMs will occur
upon failure due to wearout. As before, each replacement will
take 3 hrs and the restoration factor of 1 indicates that the
fan shaft will be "as good as new" after it is replaced.
Figure 6: Corrective maintenance of the Fan Shaft will occur
upon failure due to wearout
Preventive Maintenance Properties (Fan Shaft Block)
Figure 7 shows the Preventive Maintenance properties defined for
the Fan Shaft block, which indicate that the PM will
occur "Upon Maintenance of another Group Item." Since the
Inspections block described previously has the same Item
Group # as the Fan Shaft block, this means that each time
a CM for the Inspections block occurs in the simulation,
a PM for the Fan Shaft block will also occur. In other
words, each time a damaged fan shaft is discovered (the
Inspections block fails), a preventive replacement of the
fan shaft is carried out (the Fan Shaft block gets a PM).
Figure 7: Preventive
maintenance of the Fan Shaft block will occur upon maintenance
of the other block with the same Item Group # (i.e. the
Inspections block)
Model Illustration
With the above settings, the model for the inspection rejection
probability is simulated in BlockSim. One hundred
simulations are run with an end time of 1000 hrs and a seed of
1. Figure 8 shows the Block Up/Down plot obtained for the
simulation. The plot shows the fan shaft getting damaged at
392.912 hrs. No action is taken at this time because the damage
is hidden. The next inspection at 400 hrs detects this damage
and a corrective maintenance is carried out on the
Inspections block. At the same time this corrective
maintenance triggers a preventive replacement of the Fan
Shaft block. Therefore, at 400 hrs a new fan shaft is
installed in place of the damaged fan shaft. A wearout failure
then occurs at 473.780 hrs. This failure is immediately detected
and a corrective maintenance replaces the fan shaft. Again the
fan shaft starts new at 476.780 hrs.
Figure 8: Block Up/Down plot for the inspection rejection
probability model
Results
Results from running 100 simulations of the model are discussed
next.
Figure 9 gives the results for
the Inspections block. The results show that there are 99
inspections during the simulation (No. of Inspections = 99).
Roughly 10% of these inspections detect a damaged shaft as
indicated by 9.46 corrective maintenance actions (No. of CMs =
9.46). Therefore, this demonstrates that the inspection
rejection probability of 10% is modeled well by the
Inspections block.
Figure 9: Results for the
Inspections block indicate that the inspection rejection
probability of 10% occurs during the simulation
Figure 10 gives the results for
the Fan Shaft block. The results show that there are
11.44 replacements of the fan shaft (No. of Downing Events =
11.44). Out of these, 2.06 replacements are corrective
replacements due to wearout failures of the fan shaft (No. of
CMs = 2.06). The remaining 9.38 replacements are preventive
replacements when a damaged shaft is discovered by the
inspections (No. of PMs = 9.38).
Figure 10: Results for the Fan
Shaft block
Conclusion
This article illustrated how the maintenance properties and
policies available in BlockSim can be combined to model
complex maintenance activities. The Block Up/Down plot can be
used as a tool to quickly examine the functioning of such models
before implementing them in the final system reliability block
diagram. |
