# © 2007 Pearson Education Learning Curve Analysis Supplement G.

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© 2007 Pearson Education Learning Curve Analysis Supplement G

© 2007 Pearson Education Learning Curves 0.30 0.30 – 0.25 0.25 – 0.20 0.20 – 0.15 0.15 – 0.10 0.10 – 0.05 0.05 – 0 0 – |||||| 50100150200250300 Learning curve Cumulative units produced Process time per unit (hr)

© 2007 Pearson Education Learning Curves 0.30 0.30 – 0.25 – 0.20 0.20 – 0.15 0.15 – 0.10 0.10 – 0.05 0.05 – 0 0 – |||||| 50100150200250300 Learning curve Cumulative units produced Process time per unit (hr) Learning period Showing the learning period

© 2007 Pearson Education Learning Curves 0.30 0.30 – 0.25 0.25 – 0.20 0.20 – 0.15 0.15 – 0.10 0.10 – 0.05 0.05 – 0 0 – |||||| 50100150200250300 Learning curve Cumulative units produced Process time per unit (hr) Learning period Standard time Showing the learning period and the time when standards are calculated

© 2007 Pearson Education Developing Learning Curves  In developing learning curves we make the following assumptions:  The direct labor required to produce the n + 1 st 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. k n = k 1 n b where k 1 = direct labor hours for the 1 st unit n = cumulative number of units produced b = log r / log 2 r = learning rate

© 2007 Pearson Education 80% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit

© 2007 Pearson Education 90% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit

© 2007 Pearson Education Example G.1 Developing the 80% Learning Curve Manufacturer of diesel locomotives: Labor hours required for first unit = 50,000 Learning rate = 80% 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands)

© 2007 Pearson Education Example G.1 Estimating Direct Labor Requirements 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80%

© 2007 Pearson Education Example G.1 using the formula Labor hours required for 40 th unit k 40 = 50,000(40) (log 0.8)/(log 2) Labor hours required for first unit = 50,000 Learning rate = 80% 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands)

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) k 40 = 50,000(40) -0.322 Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using the formula

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) k 40 = 50,000(0.30488) Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using the formula

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) k 40 = 15,244 hours Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using the formula

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) k 40 = 15,244 hours Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using the formula

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) k 40 = 15,244 hours Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using the formula

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Cumulative average labor hours = Labor hours required for first unit = 50,000 Learning rate = 80% n 11.00000 20.90000 30.83403... 380.43634 390.43304 400.42984 640.37382 1280.30269 80% Learning Rate (n = cumulative production) Example G.1 using Conversion Factors

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Cumulative average labor hours = 50,000(0.42984) n 11.00000 20.90000 30.83403... 380.43634 390.43304 400.42984 640.37382 1280.30269 80% Learning Rate (n = cumulative production) Example G.1 using Conversion Factors

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Cumulative average labor hours = 21,492 hours n 11.00000 20.90000 30.83403... 380.43634 390.43304 400.42984 640.37382 1280.30269 80% Learning Rate (n = cumulative production) Example G.1 using Conversion Factors

© 2007 Pearson Education Labor hours required for first unit = 50,000 Learning rate = 80% 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Second unit = 50,000(80%) Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Second unit = 40,000 hours Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Fourth unit = 40,000(80%) Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) Labor hours required for first unit = 50,000 Learning rate = 80% Fourth unit = 32,000 hours Example G.1 using Unit-doublings

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) The 80% Learning Curve for Example G.1

© 2007 Pearson Education 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||| 4080120160200240280 Cumulative units produced Direct labor hours per locomotive (thousands) The 80% Learning Curve for Example G.1

© 2007 Pearson Education Application G.1 Estimating Direct Labor Requirements The 1 st unit of a new product is expected to take 1,000 hours. The learning rate is 80%, how much time should the 50 th unit take?

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Example G.2 Estimating Labor Requirements Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units n 11.00000 20.95000 30.91540 40.88905 50.86784... 300.69090 640.62043 1280.56069 90% Learning Rate (n = cumulative production)

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,500 n 11.00000 20.95000 30.91540 40.88905 50.86784... 300.69090 640.62043 1280.56069 90% Learning Rate (n = cumulative production) Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,035 n 11.00000 20.95000 30.91540 40.88905 50.86784... 300.69090 640.62043 1280.56069 90% Learning Rate (n = cumulative production) Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 n 11.00000 20.95000 30.91540 40.88905 50.86784... 300.69090 640.62043 1280.56069 90% Learning Rate (n = cumulative production) Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,500 230,000(0.86784) = 26,035 330,000(0.79945) = 23,983 430,000(0.74080) = 22,224 530,000(0.69090) = 20,727 Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,035 330,000(0.79945) = 23,983 430,000(0.74080) = 22,224 530,000(0.69090) = 20,727 Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,983 430,000(0.74080) = 22,224 530,000(0.69090) = 20,727 Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Month 1: Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Month 1:57,000–0= 57,000 hours Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Month 1:57,000–0= 57,000 hours Month 2:130,175–57,000= 73,175 hours Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Month 1:57,000–0= 57,000 hours Month 2:130,175–57,000= 73,175 hours Month 3:239,830–130,175= 109,655 hours Month 4:400,032–239,830= 160,202 hours Month 5:621,810–400,032= 221,778 hours Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Units perCumulative MonthMonthUnits 122 235 3510 4818 51230 Cumulative Average TimeTotal Hours Monthper Unitfor All Units 130,000(0.95000) = 28,50028,500(2)=57,000 230,000(0.86784) = 26,03526,035(5)=130,175 330,000(0.79945) = 23,98323,983(10)=239,830 430,000(0.74080) = 22,22422,224(18)=400,032 530,000(0.69090) = 20,72720,727(30)=621,810 Month 1:57,000–0= 57,000 /150=380 employees Month 2:130,175–57,000= 73,175 /150=488 employees Month 3:239,830–130,175= 109,655 /150=731 employees Month 4:400,032–239,830= 160,202 /150=1068 employees Month 5:621,810–400,032= 221,778 /150=1479 employees Example G.2 Estimating Labor Requirements

© 2007 Pearson Education Application G.2 Estimating Cumulative Labor Hours An example of using the learning model to test budget constraints: A company has a contract to make a product for the first time. The total budget for the 38-unit job is 15,000 hours. The first unit took 1000 hours, and the rate of learning is expected to be 80 percent. Do you think the 38-unit job can be completed within the 15,000-hour budget? How many additional hours would you need for a second job of an 26 additional units?

© 2007 Pearson Education Application G.2 First 38-unit Job