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Optimal Repair Strategy for Rotables during Phase-out of an Aircraft Fleet
NAME:
Jan Block, Support & Services, Luleå University of Technology
DATE:
2010-10-19
Presentation Outline
Introduction.
• Research project – Swedish National Aeronautics Research Programme No.4-5.
• Background and problem description.
Methodology.
• Main principal - Minimal margin.
• • Short about the mathematical model.
Numerical example.
Conclusions.
Further research.
Questions.
Enhanced Life Cycle Assessment for Performance-Based Logistics
The goal of the project is to develop methodologies and software tools for data mining of operational data and to improve and streamline existing methodologies for follow-up and analysis of the aircraft system and support systems throughout their respective life cycles. This will enable better decision-support when predicting and reviewing a variety of business solutions in both the military and civil aerospace sector • Highly capital-intensive systems.
• Very long operational lifecycles. • Necessary operational and performance characteristics during whole lifecycle.
Research project – Empirical data
Aims to develop methodologies for analysis and information extraction from data collected during design, operation, maintenance and monitoring of aircraft.
Empirical data: A/C 37 VIGGEN 330 Aircraft.
615,000 Flight Hours.
1977-2006.
5 Main versions.
• Strike (AJ) • Dual conversion/EW (SK) • Sea control (SH) • Reconnaissance (SF) • Fighter (JA)
SK60 – A PBL Project…
Example of Performance-Based Logistics (PBL).
”The principle is that the A/C (SK 60) shall be ready for flying at a certain time with 95 % probability.”
(Eva Wenström 2009-09-01) http://upphandling24.idg.se/ • Right functionality.
• Right technical availability.
• On right place.
• On right time.
SK60 – A Phasingout Project…
Degree Project: Maintenance optimization RM 15.
• 40 A/C, 2 engines per A/C.
• Minimize of ”Check 3” and change of engines (minimize cost).
• Find optimal time to send engines for “Check 3”.
• Options to consider: • Decisions gates. • Stop flying 2014 alt. 2015.
• Extend flying time.
Problem Description
Optimizing of maintenance resources during parallel phase-out and phase-in of different versions of aircraft, rotables and support equipment, while simultaneously ensuring the contracted availability at a reasonable Life Cycle Cost (LCC) and Life Support Cost (LSC).
This is a critical capability when offering, contracting and implementing performance-based business solutions, such as Performance-Based Logistics (PBL).
Start of discarding Aircraft Maintenance stop Stop collecting units Number of Aircraft Collected items from Aircraft Maintenance occasions Items
Different stages for a repairable unit
How to find a maintenance stop point?
In order to determine the optimal time to stop repair the concept of Minimal Margin is introduced. The Minimal Margin is defined as the minimum difference between Units Available (UA) and Units Required (UR) which is not less than zero, i.e. no shortage should occur.
Eq.1 Minimal Margin
=
Min
(
UA − UR
)
.
Discarded units during repair from functional systems
P d
(
N
(
t
)
N Max
)
i N
Max
0 [
W
(
t
)]
i e
W
(
t
)
i
!
Discarded units from phased-out systems during repair Discarded units without repair from functional systems
P d
(
N
(
t
)
N
(
t s
)
N Max
)
i N
Max
0 [
W
(
t
)]
i e
W
(
t
)
i
!
Discarded units from phased-out systems without repair
N d f
1 ( 0 ,
t
)
n t
0 ( 1 )
p
(
s
)
P f
(
s
)
ds N d f
1 ( 0 ,
t
)
n t s t
( 1 )
p
(
s
)
ds
0 Repair
t
t s S
(
t s
)
S
0
nN m
0
N d S
1 ( 0 ,
t s
)
N f d
1 ( 0 ,
t s
)
t s
No-Repair
t s
T S
(
t s
)
N S d
2 (
t s
,
t
)
N d f
2 (
t s
,
t
) More information: Paper, Optimal Repair for Repairable Components during Phase out an Aircraft Fleet.
Minimal Margin
From this nonlinear programming formulation the optimal time to stop repair
ts
can be obtained.
Where
t s
and t are the decision variables.
Min
{
S
0
nN m
0
N s
1
d
( 0 ,
t s
)
N s d
2 (
t s
,
t
)
N f d
1 ( 0 ,
t s
)
N d f
2 (
t s
,
t
)
nN m
(
t
)}
t N m
0
t s
0
T
p
(
t
)
dt t s
0
t s
T
0
Numerical Example
Assume that the phase-out rate of systems is linear with the constant rate
p
This gives that the instantaneous number of remaining systems is:
N m
(
t
)
N m
0
p
(
t
) In-data:
S
0
N m
0 5 20
n
2 2 .
5 200
p
1 0 .
5
P d
0 .
95
Numerical Example
How the repair stop time varies with repair rate and shape parameter.
Example from end life management of A/C 37 Viggen
Total demand Stock Stock exceed demand Stop reuse Shortage EXAMPLE
Conclusions
The model only handles with operational time measured as calendar time, which implies that all systems and units age are at a similar rate.
Need to consider more parameters: • Calendar/Operational and cycle maintenance intervals.
• • • • Storage maintenance.
Modification programs.
PM history on the A/C.
Etc.
Costly process to ignore.
Further Work
Building a simulation model to be able to deal with all parameters that influences the different maintenance flow on a complex system. The model should be able to deal with parallel phase-out and phase-in scenarios.