Prediction of Engine Removals for a Fleet of PW4056 Engines in 2003
Mark Wibben
DES-6620
DISCRETE EVENT SIMULATION
Fall 2002
December 02, 2002
Abstract
Management of an airline’s gas turbine engine fleet is a complicated and costly task.
Decisions made on a daily basis about engine maintenance, configuration, and logistics
management can have an impact of millions of dollars. However, doing the analysis
necessary to make the right decisions takes valuable resources in the form of engineering
labor. Tools that could help airline engineers make these decisions correctly and
efficiently would be valuable assets. The purpose of this project was to attempt to
develop such a tool. Specifically, to create a simulation that would predict how many
engines would be removed from service and have to be routed to an overhaul/repair
facility in a year. A simulation was made based on data provided by an airline for its fleet
of PW4056 engines, and the results it gave were consistently higher by about one
standard deviation when compared against the actual results of past years. However, it
was also found that the addition of increased fidelity into the model would allow it to
give results that were both more accurate and more useful.
Introduction
The responsibility of an airline’s technical operations division is to manage the hardware
used by the airline for its primary business of flying customers around the world. Engine
management is a significant part of this task. The cost of overhauling a PW4056 engine is
approximately two million dollars and takes around two months. Careful planning is
required to ensure the airline can absorb the financial and logistical impact of engine
removals when they occur. Otherwise, it is possible to run out of serviceable engines,
causing hundreds of millions of dollars in aircraft assets to remain on the ground where
they are incapable of generating revenue.
In order to make the right decisions with regards the budgeting of money, labor, and
spare engines, it is important to have an accurate means of forecasting when engines will
be removed. Currently, there are many different methods used by airlines. One such
method is to use previous engine removal data to calculate average removal rates, based
on how many hours the engines flew, and use this along with the number of hours
expected to fly in the coming year to calculate an expected number of removals. This
method has been refined over the years and is reasonably accurate. However using
average rates for everything generates only one number for predicted removals and
provides no information about the confidence in that number.
For this project, it was attempted to develop an engine fleet model based on airline data
which could be run numerous times and calculate predictions for engine removals in a
year on a basis of mean, standard deviation, and 95% confidence interval. The model was
run in a variety of ways to simulate past years and the results were compared against the
actual data to determine which way was most accurate. Then the model was run again to
simulate the upcoming year, 2003, and the results were compared against the prediction
made by the airline that supplied the data. It was found that the mean number of removals
predicted by the simulation was approximately one standard deviation higher than the
actual results as reported by the airline.
Background
Most major airlines operate several fleets of aircraft, each fleet comprised of a specific
model of airplane. There can be several subfleets that are separated out because of
differences in equipment that are significant enough to require it to be maintained
differently. For engines, this is no different. The airline used as the basis for this analysis
operates several models of engines from several different manufacturers. Each has its
own mission, utilization, and failure modes. Because of this, simulating an entire engine
fleet of an airline is unpractical given the scope of this project. Therefore, one particular
engine model, the Pratt & Whitney PW4056, was selected based on the size of the fleet
and the typical number of removals. The results of the project are still useful since
different engine fleets often have separate budgets and resources allocated to them.
The PW4056 is a high bypass turbofan engine that is rated for 56,000 lbs of takeoff
thrust. The airline in question operates it on its fleet of Boeing 747-400 aircraft. The
engines operate an average of 1.49 takeoff/landing cycles per day, which is equivalent to
11.92 flight hours. Currently, the airline operates 64 engines at any given time, along
with 4 or so spares. This is a relatively small fleet with a relatively long in-service life.
Therefore, the number of removals per year is small when compared to other engines,
which makes it ideal for a project of this scope, as there are fewer failure modes and this
takes out some of the complication in analyzing the data and building a model.
A given engine’s life cycle is as follows. When the engine is either new from
manufacture or newly overhauled, it is installed on an aircraft to take the place of an
engine that is being removed. The engine accrues flight cycles and time which result in
wear and tear on it. Eventually it will be removed and sent to and engine shop for
overhaul or repair, and it will start its life cycle over again.
When an engine is removed, it is considered one of two types of events: a planned
removal or an unplanned removal. Planned removals happen for one or a combination of
three reasons. The first is that a life-limited part (LLP) is about to expire. Rotating parts
on engines have life limits imposed on them by the manufacturer. Adherence to these
limits is required by federal regulations. For the PW4056, these limits are based on the
number of cycles the part has flown. If a part on an airplane has reached it’s life limit, the
aircraft is grounded until it is replaced. The second reason for planned removals is engine
performance. As engines accrue time on wing, wear and tear affect the performance
relative to certain metrics, such as exhaust gas temperature and fuel flow. These
parameters are tracked by an airline and when the engine deteriorates enough it is
removed. Because deterioration is predictable these are considered planned removals. For
the PW4056 engines considered by this project, performance removals almost never
happen. This is due to many factors including engine rating and utilization. The third
reason for a planned removal is simply that it is has a high amount of service time on it
since its shop visit. There are many parts on an engine that are not life-limited but airline
experience has shown that they should be inspected at certain intervals to ensure
reliability. Therefore, once the engine reaches a certain limit, it is removed and sent to the
shop so that these inspections may occur. It should be noted that of these three reasons,
only life limited parts are hard deadlines that cannot be violated. If spares availability or
scheduling requires it, performance and high time removals can always be postponed for
a certain amount of time.
If an engine must be removed due to a failure of some sort before its planned removal
time, it is designated as an unplanned removal. These are obviously undesirable as they
frequently cause service disruptions (such as flight delays and cancellations) and also
cause the airline to use resources (such as money and manpower) to repair the engine that
it did not plan on, and which may have been budgeted for other things.
Data Analysis
The data used to build and validate this model was provided by a major airline that
operates a fleet of 16 Boeing 747-400s each with four PW4056 engines. Specifically,
data was provided for every engine removal since 1989 as well as the fleet configuration
at the beginning of each year since 1996. This way, simulations could be built to
represent several different years and the results could be compared with the actual case in
an attempt to validate the model. The data can be found in spreadsheet form in Appendix
B: Removal Data and Appendix C: Fleet Configuration Data. For removals, the
airline provided information such as reason for removal and time on wing at removal. For
fleet configuration, the airline provided, by engine serial number, the time on wing at the
beginning of each year, as well as the expected days to planned removal due to life
limited parts or high time (as mentioned above, performance removals are not an issue
for the PW4056).
Before the data could be analyzed, it was necessary to develop a strategy for how the
simulation would operate, so that the data could be put in a useful form. It was decided
that the most efficient way to model the fleet, given the way ProModel is laid out, would
be to determine for each engine, at the beginning of the simulation, whether it would be a
planned or unplanned removal and how long it would be on wing. First, the question of
planned versus unplanned was considered. To do this, all the removal data from 1989 was
analyzed and each removal was categorized as planned or unplanned. Then, for each year
a percentage of planned removals was calculated as planned removals divided by total
removals. This percentage could then be used by the simulation, along with a random
number generator, to determine if each engine would be a random or unplanned removal.
Once this is known, each engine’s time on wing until removal is then determined. If the
engine is to be a planned removal, this is simple. Days to planned removal is taken
directly from what the airline has reported. In actuality, the Days to Planned Removal are
not always exactly right. However, it was determined that a few days on either side do
not affect the out come of the simulation a significant amount.
To determine the time on wing for unplanned removals, the removal times for all of the
unplanned removals were grouped by year. Now, an interesting problem was faced. The
engine manufacturer is constantly trying to develop improvements their product is
intended to eliminate unplanned engine removal causes. This results in the removal times
between unplanned removals to increase over time. If the data used to generate the
distributions used by the simulation goes back too far in time, it may include too many
removals that were due to failure modes that are no longer an issue due to service bulletin
improvements. However, if the data does not go back in time far enough it may not
include enough data to get a good representation. To deal with this, for each year to be
simulated, data from the previous 3, 4, and 5 years was input into the STAT::FIT function
in ProModel to determine a statistical distribution to be used by the simulation to
determine the total days on wing of each engine. That way, distributions could be used
from 3, 4, and 5-year rolling averages to determine how much influence the sample size
had on the results.
Once the removal data had been analyzed, the fleet configuration data was used to set up
the model for each year to be simulated. To do this, the time on wing, as reported by the
airline in flight hours and cycles, had to be converted to days. This was complicated by
the fact that not all engines are completely overhauled at the same time. For some shop
visits, a turbine may be overhauled while a compressor is merely inspected. This leads to
some confusion as to the actual time on wing of an engine. For the example of the
overhauled turbine with the repaired compressor, the time before a turbine failure will
adhere to one distribution, while the time before a compressor failure may follow quite
another. Fortunately, this does not happen as often with PW4056’s as with other engine
models, but it is still an issue. For the purposes of this simulation, an engine’s time on
wing at t = 0 was taken as the minimum of compressor or turbine time. Once that was
done, establishing days since install was simply a matter of dividing the cycles since
overhaul by the daily utilization rate of 1.49 cycles per day.
Now that the data was categorized and analyzed, it was possible to build the model.
Model
The objective of this report was to simulate the fleet of engines progressing through their
life cycle for a period of one year, and to see how many of them were removed. To do
this, a model of the fleet was built using ProModel software. The models used can be
found in Appendix A: Models. The basic layout of the model as well as the assumptions
associated with each element will now be described.
Entities:
There were two entities in this model, serviceable engines and unserviceable engines.
Serviceable engines are engines that are either installed on an aircraft accruing service
time or are available as spares. Unserviceable engines are engines that have been
removed from service and have yet to be made serviceable again by visiting the engine
shop. In actuality, it is possible for an engine to be removed and still be serviceable. For
example, an engine may be a planned removal due to high time, but be kept serviceable
for a few days in the case where spares are low. Then when the spare count is up again,
the engine can be inducted into the shop and overhauled. For the purposes of this
simulation, these types of occurrences are not modeled. It was assumed that all engines
removed were unserviceable, and they remained so until they were made serviceable by
the engine shop.
Locations:
The primary location in the model was designated the Fleet. It was decided to model the
entire fleet as one location with a capacity equal to the number of engines in service at a
given time. The other alternative was to model each aircraft in the fleet separately, but
this added a great deal of complexity to the model without adding any benefit. This is
because for the purposes of this simulation, the fleet is intended simply as a place where
serviceable engines accrue service time until they are removed. The use of specific
airplanes for this function has no advantage over using one generic location.
The second location is the Engine Shop. This is the location where unserviceable engines
go to be made serviceable. Several dozen modeling projects could be done on the inner
workings of the engine shop alone. Since the goal of this project is to predict engine
removals, the role the engine shop plays in the system was deliberately kept minimal. To
do this, several assumptions were made. For example, in reality, when an engine enters
the shop it can be either overhauled or repaired. An overhaul involves completely tearing
down the engine to the piece part level for inspection, repairing or replacing any damaged
parts, and reassembling. A repair involves doing just enough work to address a specific
condition, and then returning the engine to service. An overhauled engine is expected to
stay on wing longer than a repaired engine. However, in the case of the PW4056’s
modeled in this project, both overhauls and repairs are expected to stay on for longer than
one year, which is the time span of interest. Therefore, it was assumed all engines that
entered the shop were overhauled. This allowed for a further reduction in complexity, as
the process of deciding whether an engine shall be overhauled or repaired is very
complicated and there is often has a team of people dedicated to just such a purpose.
Another assumption that was made was that the engine shop had infinite capacity. This is
of course not true in reality. However, while the airline studied does maintain many of its
engine fleets in-house, it does not do so with its PW4056’s. Instead, they are sent out to a
vendor with large capacity relative to the number of removals experienced per year. The
possibility that shop capacity issues would affect the number of engine removal in a year
is not significant, so the capacity was assumed to be infinite.
Once an unserviceable engine is made serviceable by the Engine Shop, it is sent to the
Spare Pad. This location also has an infinite capacity and is merely a place where
serviceable engines wait to be sent to the fleet. The spare pad was set up with first in, first
out logic. That is, the first engine to enter the spare pad will be the first one that is sent to
the fleet to replace a removal. In reality, a great deal of thought can be put into which
spare engine is installed on an airplane. Spares are typically kept all over the world in
strategic places and in the case of an unplanned engine removal, the spare that is closest
to the affected airplane is frequently used. Also, engine spares are not necessarily freshly
overhauled engines, and it may be desirable to match them up with specific aircraft based
on expected on-wing life and anticipated aircraft down time. Inputting that type of logic
into a model for a project of this scope is not practical. In addition, because the details of
the fleet such as aircraft routing are not being modeled for this project, these factors were
ignored, and FIFO logic was deemed sufficient.
Modeling an engine fleet for any specific period of time poses many problems. One of
them is that at the beginning of the time period that is being modeled (in this case, one
year) the engines that are in the fleet are all at different points in their life cycle (the time
they have already spent in service is different for each engine). Because of this, it is not
possible to model the engines as generic entities. They must each be tracked individually.
To do so, each engine must be assigned a serial number at the beginning of the
simulation. Because of the way ProModel works, this needed to be done at a location that
the engines would not return to so that they would not be assigned new serial numbers
every time they are removed. To do this task, a dummy location called Arrival was
created. On the first day of a simulation, all of the engines arrive at this location and are
assigned serial numbers and other attributes that are used in calculating times on wing
and, subsequently, removals.
Figure 1: Layout of Model
Variables and Attributes:
For reasons described above, each engine in this simulation had to be tracked separately.
To do this, several attributes needed to be assigned to each entity so that the simulation
can tell them apart and calculate time on wing accordingly. Unfortunately, the student
version of ProModel only allows the use of 5 attributes, which was insufficient for this
task. Therefore, it was necessary to use global variables to track entity specific variables.
To do this, several global variables were created for each desired attribute, one for each
engine serial number in the fleet. That way, only two actual attributes needed to be book
kept by the simulation, serial number (called ENGN) and days to removal (called DTR).
For example, one parameter that each engine needed to have was DOWAI (which
represented the number of days the engine had already been on wing at the beginning of
the simulation). In order to track this for each engine in a fleet of 40, 40 different global
variables were created, with a prefix corresponding to DOWAI, and a suffix
corresponding to the serial number it was attached to (for example DOWAI_ENGN01,
DOWAI_ENGN02, etc.). Then, at each location where logic was executed, a series of IF
and GOTO statements were utilized to ensure the proper logic was executed for the right
global variable. The major attributes and variables used and their meanings are tabulated
below.
Attribute
ENGN
DTR
Description
Engine Serial Number. Used by the simulation to identify and track
specific engines.
Days to Removal. This parameter is calculated by the simulation and
used to determine when the engine will be removed.
Pseudo-Global Variable
(*_XXXXX denotes
attached to specific engine
serial number.
DOWAI_XXXXX
RFR_XXXXX
DTPR_XXXXX
DTRR_XXXXX
Truly Global Variables
REMOVALS
UNPLN_REM
PLN_REM
Description
The days already spent on wing by and engine at the start
of the simulation (t=0).
The Reason for Removal (0 = planned, 1 = unplanned)
Days to Planned Removal. If an engine is to be a planned
removal, how long until this happens.
Days to Random Removal. If an engine is to be an
unplanned removal, how long until this happens.
Description
Total number of removals in simulated year.
Total number of unplanned removal is simulated year.
Total number of planned removals in simulated year.
Processing:
The process that an engine takes in the model is detailed below. At time equals zero, the
engines arrive at the location Arrival and are assigned a serial number. Next, the key
parameters RFR, DTPR, and DTRR are calculated for each engine based on the planned
removal percentage and DOWAI. A random number is generated between 0 and 1. If the
number is less than the planned removal rate for the year being simulated, then the Days
to Removal (DTR) attribute is set equal to DTPR. If not, then DTR is set to equal to
DTRR.
After the Arrival location, the engines are sent to the fleet. Here, they simply wait a
number of days equal to DTR. Then they are removed as unserviceable engines and sent
to the Engine Shop. The move logic from the fleet to the shop includes calculations that
increment total removals, as well as number of planned and unplanned removals, as
appropriate.
Once in the engine shop, the engines wait for an exponentially distributed time with a
mean time of 30 days. This number was chosen from experience and not validated with
data, as detailed simulation of the engine shop was not the goal of this project. However,
this is an area for potential future improvements to the model. Once the engine is made
serviceable by the engine shop it moves to the spare pad. Here, new values of RFR and
DTR are assigned, and the engine waits to be moved back to the fleet once enough
removals have occurred to make room for it.
Simulation Validation
Once the model was built it was run to simulate the years 1999, 2000, 2001, and 2002.
Each simulation involved 50 runs that were 1 year long each. In addition, runs for each
year were performed using random removal distributions determined from data from the
previous 3, 4, and 5 years. Both unbounded and lower value bounded weibull
distributions were used. The distributions used are shown in Appendix D: Random
Removal Distributions. The mean, standard deviation, and 90% confidence interval
were compared for each run versus the actual number of removals that year. The results
are tabulated below.
Distribution
Mean
Removals
Standard
Deviation
Min-Max
90% Conf
Interval
3 Year
Avg.
Bounded
W(2.11,97
7)
16.96
3 Year Avg.
Unbounded
4 Year Avg.
Bounded
4 Year Avg.
Unbounded
W(2.27,1040
)
16.14
W(2.25,997)
16.84
W(2.44,106
0)
16.08
2.95
3.16
2.51
11-17
16.2517.67
9-23
15.38-16.90
12-24
16.24-17.44
5 Year
Avg.
Bounded
W(2.1,945)
5 Year Avg.
Unbounded
18.14
W(2.42,1060
)
16.14
2.90
2.76
2.47
10-24
15.38-16.78
12-25
17.4818.80
11-21
15.55-14.16
Table 1: Results for Simulation of 1999 (Actual Removals:13 Planned:1 Unplanned:12)
3 Year Avg.
Bounded
3 Year Avg.
Unbounded
4 Year Avg.
Bounded
4 Year Avg.
Unbounded
5 Year Avg.
Bounded
Distribution
W(2.25,913)
W(1.71,709)
W(2.18,956)
W(2.3,977)
Mean
Removals
Standard
Deviation
Min-Max
95% Conf
Interval
21.16
22.72
20.26
W(2.27,989
)
19.28
20.28
5 Year
Avg.
Unbounded
W(2.41,103
0)
19.5
3.47
2.60
2.83
2.63
2.91
2.20
10-30
20.33-21.99
18-28
22.09-23.34
14-27
19.58-20.94
12-25
18.65-19.91
14-27
19.57-20.98
14-25
18.97-20.03
Table 2: Results for Simulation of 2000 (Actual Removals: 14 Planned: 2 Unplanned:12 )
Distribution
Mean
Removals
Standard
Deviation
Min-Max
95% Conf
Interval
3 Year Avg.
Bounded
3 Year Avg.
Unbounded
4 Year Avg.
Unbounded
5 Year Avg.
Bounded
W(3.72,107
0
25.62
4 Year
Avg.
Bounded
W(2.53,99
6
25.28
W(2.1,844
W(2.39,1010
27.84
24.92
5 Year
Avg.
Unbounded
W(2.66,110
0
23.84
W(3.46,103
0
26.18
2.48
2.83
3.29
2.89
2.89
3.37
21-31
25.58-26.77
17-31
24.94-26.30
15-33
24.49 26.07
21-35
27.15 -28.53
18-32
24.23 - 25.61
16.30
23.03-24.65
Table 3: Results for Simulation of 2001 (Actual Removals: 21 Planned: 6 Unplanned:15 )
Distribution
Mean
Removals
Standard
Deviation
Min-Max
95% Conf
Interval
3 Year Avg.
Bounded
3 Year Avg.
Unbounded
4 Year Avg.
Bounded
4 Year Avg.
Unbounded
5 Year Avg.
Unbounded
29.96
W(5.1,1850
)
17.26
5 Year
Avg.
Bounded
W(2.17,10
10)
30.14
W(2.21,106
0)
29.62
W(8.65,317
0)
14
W(2.4,1030)
2.93
0
3.55
1.44
3.43
2.85
28.91-30.32
14-14
29.11-30.81
16.91-17.61
29.3120.50
25.19-26.84
W(2.88,1250
)
26.02
Table 4: Results for Simulation of 2002 (Actual Removals: 19 Planned: 8 Unplanned:11 )
The results show that in general, the simulation consistently predicts more removals than
the data. In some cases the actual results were within one standard deviation of the
predicted results, but in many they were not. It is also apparent that the predictions made
with unbounded weibull distributions seem very inconsistent in many cases. Therefore, it
was decided to consider bounded weibull distributions only when trying to predict the
number of removals for 2003.
In particular, the year 2000 looks especially poor, as the model predicts on average 5-6
more removals per year than what actually happened. A review of the unplanned/planned
results shows that the simulation is over predicting the number of unplanned removals
per year. By definition, the planned/unplanned split that is assigned to the fleet at the
beginning of the simulation should hold to the input value obtained from the data. The
total number of planned removals is close to the data, but too many unplanned removals
are occurring each year. A closer review of the data offers an explanation of what is
happening. The times on the unplanned removals in general are not as high as the
unplanned removals. This is because engines are typically planned off the wing before
they have a chance to fail at high time. In other words, if all engines were allowed to be
on wing until they failed, the distributions for unplanned removals would lean towards
higher time of removals.
This problem results in the distributions of removal times for unplanned removals
looking artificially low. The simulation is in turn calculating the right split of unplanned
vs. planned removals, but since the time to removal of the unplanned removals is
artificially low, more of them are getting moved up into the year currently being
simulated. Because the simulation chooses if an engine will be a planned or unplanned
removal right away, it is forcing the unplanned removals to adhere to a distribution that is
biased towards lower time.
The ideal way to deal with this problem would be to let all engines run till failure in the
real world, and use the distributions generated from that data in the simulation. That is
obviously not possible, however. Another way to deal with this problem might be to
change the basic strategy of the simulation. It could install all of the engines in the fleet
without choosing a reason for removal or removal time. Then, each day the simulation
would predict whether engines have failures that drive unplanned removals on that day
based on daily unplanned removal rates. If this does not occur before engine’s planned
removal time, then it will be a planned removal. It would take significant effort to modify
the simulation to work like this, especially given the way ProModel is structured. For
now, it is left as a way to potentially improve the simulation in the future.
Results and Discussion
Once the simulation was checked against actual results, it was ran for the upcoming year
of 2003 and check against the predictions made by the airline. Note that only simulations
with bounded weibull distributions were run (using data from the preceding 3, 4, and 5
years, respectively).
Distribution
Mean
Removals
Standard
Deviation
Min-Max
95% Conf
Interval
3 Year Avg. Bounded
2.15,1150
23.98
4 Year Avg. Bounded
2.17,1090
25.3
5 Year Avg. Bounded
2.31,1050
25.48
2.87
2.86
2.73
19-29
23.29-24.66
19-31
24.61-25.99
19-33
24-82-26.14
Table 5: Results for Simulation of 2003 (Airline Predicted Removals: 29 )
The spread sheet used by the airline to forecast removals for 2003 is attached as
Appendix E: Airline Removal Forecast. The airlines method is as follows. The days to
planned removal for engines are reviewed and any engines that are intended to come off
next year are noted. Then, the airline predicts the number of random removals by
multiplying the historical removal rate based on flight hours by the number of hours the
fleet expects to fly the following year. Then, a historical average of unplanned removals
that would have come of as planned removals in the same year is applied to generate an
overlap number. The overlap is subtracted from the planned removal prediction. Then,
the planned and unplanned removals are added up to generate the final prediction. As is
seen in Appendix E, this resulted in 29 predicted removals for the year 2003. It is
interesting to note that this prediction is approximately one standard deviation above the
mean removals predicted by the simulation. When compared to the historical data, the
simulation was predicting more removals. In this case, it predicts less. After talking to the
airline, it was discovered that because of an industry surge problem, the airline is
predicting more planned removals next year as part of a management plan. The days to
planned removal for this plan were not reflected in the rank lists supplied by the airline,
so they did not make it into the model. This accounts for approximately 6 additional
removals, which would make the simulation high by about 2-3 removals (depending on
which random removal distribution is used). This could seem to be more consistent with
the model as compared to historical data.
Conclusion
The simulation developed for this project is found to predict a higher number of engine
removals then the historical value by approximately one standard deviation. It was
determined that this was due to the models methodology of predicting whether an engine
would be a planned or unplanned removal up front, combined with the fact that
unplanned removal distributions are biased toward lower times on wing because they are
generated from data that has high time engines removed before they can fail. It is felt that
if the model’s basic methodology were changed, and daily removal rates were applied
every simulation day to predict removals, the simulation results would improve and
become more in line with historical data.