Learning Curve AnalysisLearning CurvesSlide 3Slide 4Developing Learning Curves80% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit90% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per UnitExample G.1 Developing the 80% Learning CurveExample G.1 Estimating Direct Labor RequirementsExample G.1 using the formulaSlide 11Slide 12Slide 13Slide 14Example G.1 using the formulaExample G.1 using Conversion FactorsSlide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Application G.1 Estimating Direct Labor RequirementsSlide 28Example G.2 Estimating Labor RequirementsSlide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Application G.2 Estimating Cumulative Labor HoursApplication G.2 First 38-unit JobApplication G.2 Second additional 26-unit Job© 2007 Pearson EducationLearning CurveAnalysisSupplement GSupplement G© 2007 Pearson EducationLearning Curves0.30 0.30 –0.25 0.25 –0.20 0.20 –0.15 0.15 –0.10 0.10 –0.05 0.05 –0 0 –| | | | | |5050100100150150200200250250300300Learning curveLearning curveCumulative units producedCumulative units producedProcess time per unit (hr)Process time per unit (hr)© 2007 Pearson EducationLearning Curves0.30 0.30 –0.25 –0.25 –0.20 0.20 –0.15 0.15 –0.10 0.10 –0.05 0.05 –0 0 –| | | | | |5050100100150150200200250250300300Learning curveLearning curveCumulative units producedCumulative units producedProcess time per unit (hr)Process time per unit (hr)Learning periodShowing the learning period© 2007 Pearson EducationLearning Curves0.30 0.30 –0.25 0.25 –0.20 0.20 –0.15 0.15 –0.10 0.10 –0.05 0.05 –0 0 –| | | | | |5050100100150150200200250250300300Learning curveLearning curveCumulative units producedCumulative units producedProcess time per unit (hr)Process time per unit (hr)Learning Learning periodperiodStandard timeShowing the learning period and the time when standards are calculated© 2007 Pearson EducationDeveloping Learning Curves In developing learning curves we make the following assumptions:The direct labor required to produce the n + 1st unit will always be less than the direct time of labor required for the nth unit.Direct labor requirements will decrease at a declining rate as cumulative production increases.The reduction in time will follow an exponential curve. kn = k1nbwhere k1 = direct labor hours for the 1st unit n = cumulative number of units produced b = log r / log 2 r = learning rate© 2007 Pearson Education80% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit© 2007 Pearson Education90% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit© 2007 Pearson EducationExample G.1 Developing the 80% Learning CurveManufacturer of diesel locomotives:Labor hours required for first unit = 50,000Learning rate = 80%50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)© 2007 Pearson EducationExample G.1 Estimating Direct Labor Requirements50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)Labor hours required for first unit = 50,000Learning rate = 80%© 2007 Pearson EducationExample G.1 using the formula Labor hours required for 40th unitk40 = 50,000(40)(log 0.8)/(log 2)Labor hours required for first unit = 50,000Learning rate = 80%50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)k40 = 50,000(40)-0.322Labor hours required for first unit = 50,000Learning rate = 80%Example G.1 using the formula© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)k40 = 50,000(0.30488)Labor hours required for first unit = 50,000Learning rate = 80%Example G.1 using the formula© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)k40 = 15,244 hoursLabor hours required for first unit = 50,000Learning rate = 80%Example G.1 using the formula© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)k40 = 15,244 hoursLabor hours required for first unit = 50,000Learning rate = 80%Example G.1 using the formula© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)k40 = 15,244 hoursLabor hours required for first unit = 50,000Learning rate = 80%Example G.1 using the formula© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| | | | | | |40408080120120160160200200240240280280Cumulative units producedCumulative units producedDirect labor hours per locomotive Direct labor hours per locomotive (thousands)(thousands)Cumulative average labor hours =Labor hours required for first unit = 50,000Learning rate = 80%n1 1.000002 0.900003 0.83403. .. .. .38 0.4363439 0.4330440 0.4298464 0.37382128 0.3026980% Learning Rate(n = cumulative production)Example G.1 using Conversion Factors© 2007 Pearson Education50 50 –40 40 –30 30 –20 20 –10 10 –0 0 –| |