1. McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Supplement 7 Learning Curves

2. 7S-2 LC estimates (SLOPE): Every doubling of repetitions results in a constant percentage decrease in the time per repetition Typical decreases range from 10 to 20 percent  10% of Improvement Rate = 90% of Learning Curve Slope = 90% of Learning Percent

3. 7S-3 LC estimates (SLOPE): T 2n = Learning Percent x T n  T 22 = Learning Percent x T 11  T 11 = T 22 / Learning Percent  Learning Percent = T 22 / T 11 T n = Time for n th unit

4. 7S-4 Learning

5. 7S-5 The Learning Effect

6. 7S-6 Learning Curves: On a Log-Log Graph

7. 7S-7 The Learning Effect

8. 7S-8 Learning Illustrated Each time cumulative output doubles, the time per unit for that amount should be approximately equal to the previous time multiplied by the learning percentage. If the first unit of a process took 100 hours and the learning rate is 90%: UnitUnit Time (hours) 1= 100 2.90(100)= 90 4.90(90)= 81 8.90(81)= 72.9 16.90(72.9)= 65.61 32.90(65.61)= 59.049

9. 7S-9 Unit Times: Formula Approach

10. 7S-10 Example: Formula Approach If the learning rate is 90%, and the first unit took 100 hours to complete, how long would it take to complete the 25 th unit? Or, Check table 7s.1 (PAGE 255) T 25 = T 1 x ( ).90, 25 T 25 = 100 x.613 = 61.3 hours

11. 7S-11 Unit Times: Learning Factor Approach The learning factor approach uses a table that shows two things for selected learning percentages: –Unit value for the number of repetitions (unit number) –Cumulative value, which enables us to compute the total time required to complete a given number of units.

12. 7S-12 Example: Learning Factor Approach If the learning rate is 90%, and the first unit took 100 hours to complete, how long would it take to complete the 25 th unit? How long would it take to complete the first 25 units?

13. 7S-13 eg : learning rate is 80%, T 1st Jet = 400 Days a.Estimate the expected number of labor days of direct labor for the 20th jet. T 20 = T 1 x ( ).80, 20 T 20 = 400 x.381 = 152.4 Days b.Estimate the expected number of labor days of direct labor for all 20 jets. T 1-20 = T 1 x ( ).80, 1-20 T 1-20 = 400 x 10.485 = 4194 Days Avg Days/Jet = 4194 days / 20jets = 209.7 days/jet

14. 7S-14 Eg : learning rate is 80, T 1st Jet = 400 Days c.If the company expects a contribution to overhead & profit of $150/day on top of a labor cost $200/day, what should be the Total Price Quote? T 1-20 = 4194 Days Charge per day=150+200=350 Total price quote = $350 x 4194days = $1467900 d.If the company expects a contribution to overhead & profit of $150/day on top of a labor cost $200/day, what should be the Unit Price Quote? Unit price quote = $1467900 / 20jets = $73395

15. 7S-15 Eg : learning rate is 80, T 1st Jet = 400 Days e.Estimate the expected number of labor days of direct labor for jet 10 through jet 15. T 1-15 – T 1-9 = T 1 x ( ).80, 1-15 – T 1 x ( ).80, 1-9 = 400 x 8.511 – 400 x 5.839 = 400 x (8.511 – 5.839) = 1068.8 Days

16. 7S-16 Eg : learning rate is 80, T 1st Jet = 400 Days f.If the total labor cost of 20 jets is $1467900, what should be the total labor cost for 30 jets and the average cost per unit? T 1-20 = 4194 Days $1467900 /4194days = $350/day T 1-30 = 400 x 14.020 = 5608 Days Total labor cost =$350 x 5608days=$1962800 Avg cost/unit =$1962800/30Jets=$65426.70