clic-ilc meeting on costs cost learning curves: from theory to practice ph. lebrun webex meeting 17...
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CLIC-ILC meeting on costsCLIC-ILC meeting on costsCost learning curves: from theory to Cost learning curves: from theory to
practicepractice
Ph. Lebrun
Webex meeting17 July 2009
TheoryTheory
• T.P. Wright, Factors affecting the cost of airplanes, Journ. Aero. Sci. (1936)
• Unit cost c(n) of nth unit producedc(n) = c(1) nlog
2a
with a = « learning percentage », i.e. remaining cost fraction when production is doubled
• Cumulative cost of first nth unitsC(n) = c(1) n1+log
2a / (1+log2a)
with C(n)/n = average unit cost of first nth units produced
• n = number per production line ≠ total number in project
Typical learning percentage Typical learning percentage valuesvalues
(NASA Learning Curve Calculator)(NASA Learning Curve Calculator)
• R. Stewart, Cost estimators reference manual, Wiley (1995)• Structure of manufacturing mix
– 75% hand assembly/25% machining = 80% learning – 50% hand assembly/50% machining = 85% – 25% hand assembly/75% machining = 90%
• Technology domain – Aerospace 85% – Shipbuilding 80-85% – Complex machine tools for new models 75-85% – Repetitive electronics manufacturing 90-95% – Repetitive machining or punch-press operations 90-95% – Repetitive electrical operations 75-85% – Repetitive welding operations 90% – Raw materials 93-96% – Purchased parts 85-88%
RealityReality
• Learning percentage a integrates effects of different nature– Labour efficiency and on-the-job training (for stable staff
population!)– Standardization of production process and method improvement– Technology-driven learning and increase in equipment productivity– Changes in the resource mix– Product redesign– Value chain effects– Network building, shared-experience effects
• Exponential curve « too smooth to be true »– New products– Technology breakthroughs– Abrupt changes in production process– Staff turnover– Saturation plateau for finite production series
RHIC dipolesRHIC dipoles
Effect of staff Effect of staff buildup/turnoverbuildup/turnover
LHC dipole coils LHC dipole coils (Jeumont)(Jeumont)
Saturation plateauSaturation plateauLHC dipole coils LHC dipole coils (BNN)(BNN)
LHC dipole collared coil productionBNN
0
1
2
3
4
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111
collared coil no.
Lear
ning
fact
or
Expected Learning CurveActualTarget
Not including manufacturing hours for breakdowns, repairs and interruptionsIncluding estimation for started but not yet completed dipole-magnets
LHC components & industrial LHC components & industrial productsproducts
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1 10 100 1000
Number of variants
Max
. nu
mbe
r of
uni
ts p
er v
aria
nt Superconductors
Magnet components
Magnets
Power converters
Cryolines
Vacuum
LHC series componentsLHC series components
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1 10 100 1000
Number of variants
Max
imum
num
ber
of u
nits
per
var
iant Superconductors
Magnet components
Magnets
Power converters
Cryolines
Vacuum
Flexible cells, manual work
Flexible workshops
Automatic chains
Some questionsSome questions
• Validity of single-exponent model for limited-series production– Dual-exponent?– Plateau?– Change of regime: absolute number or fraction of total number?
• Values of learning factor for accelerator components– Experience of previous projects?– Comparison with and scaling from other technological products?– ILC approach?– Assumption on number of parallel production lines?