CLIC-ILC meeting on costs Cost learning curves: from theory to practice Ph. Lebrun Webex meeting 17 July 2009

Theory T.P. Wright, Factors affecting the cost of airplanes, Journ. Aero. Sci. (1936) Unit cost c(n) of nth unit produced c(n) = c(1) n log 2 a with a = « learning percentage », i.e. remaining cost fraction when production is doubled Cumulative cost of first nth units C(n) = c(1) n 1+log 2 a / (1+log 2 a) with C(n)/n = average unit cost of first nth units produced n = number per production line ≠ total number in project

Typical learning percentage values (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%

Reality 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 dipoles

Effect of staff buildup/turnover LHC dipole coils (Jeumont)

Saturation plateau LHC dipole coils (BNN)

LHC components & industrial products

LHC series components Flexible cells, manual work Flexible workshops Automatic chains

Some 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?