Supplement Learning Curves McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc All rights reserved Supplement 7: Learning Objectives You should be able to: Explain the concept of a learning curve Make time estimates based on learning curves List and briefly describe some of the main applications of learning curves Outline some of the cautions and criticisms of learning curves Estimate learning rates from data on job times Instructor Slides 7S-2 Learning Curves Learning curve The time required to perform a task decreases with increasing repetitions The degree of improvement is a function of the task being done Short, routine tasks will show modest improvement relatively quickly Longer, more complex tasks will show improvement over a longer interval Instructor Slides 7S-3 Learning Instructor Slides 7S-4 The Learning Effect The learning effect is attributed to a variety of factors: Worker learning Preproduction factors Tooling and equipment selection Product design Methods analysis Effort expended prior to the start of work Changes made after production has begun Changes in work methods Changes in tooling and equipment Managerial factors Improvements in planning, scheduling, motivation, and control Instructor Slides 7S-5 Interesting Characteristics of Learning The learning effect is predictable The learning percentage is constant Every doubling of repetitions results in a constant percentage decrease in the time per repetition Typical decreases range from 10 to 20 percent Instructor Slides 7S-6 Learning Curves: On a Log-Log Graph Instructor Slides 7S-7 Learning Percentage 90% learning percent means 10% decrease in unit time with each doubling of repetition 80% learning percent means 20% decrease in unit time with each doubling of repetition Question: What does 100% learning percent imply? Learning Curves nth unit 10 11 12 13 14 15 16 Unit Time (hours) Calculations 10 (.8) x (10) = (.8)1(10) 6.4 (.8)(8) = (.8)(.8)(10) = (.8)2(10) 5.12 (.8)(6.4) = (.8)(.8)(.8)(10) = (.8)3(10) 4.096 (.8)(5.12) = (.8)(.8)(.8)(.8)(10) = (.8) (10) Improvement 1.6 1.28 1.024 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%: Unit Unit Time (hours) Instructor Slides = 100 90(100) = 90 90(90) = 81 90(81) = 72.9 16 90(72.9) = 65.61 32 90(65.61) = 59.049 7S-10 Unit Times: Formula Approach Tn = T1 × n b where Tn = Time for nth unit T1 = Time for first unit ln r b= ln r = learning rate percentage ln stands for the natural logarithm Instructor Slides 7S-11 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? T25 = 100 × 25 ln 90 ln = 100 × 25−.15200 = 61.3068 hours Instructor Slides 7S-12 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) Tn = T1 × Unit time factor Cumulative value, which enables us to compute the total time required to complete a given number of units ∑T n Instructor Slides = T1 × Total time factor 7S-13 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? T25 = 100 × 613 = 61.3 hours How long would it take to complete the first 25 units? ∑T 25 Instructor Slides = 100 × 17.713 = 1,771.3 hours 7S-14 Learning Curves Example S-2 A contract calls for the production of 20 jets The initial unit required 400 days of direct labor The learning percent is 80% Learning Curves Example S-2 Q1: Calculate the time of the 5th unit Approach – using the formula b = ln(.8) / ln(2) = -.3219 b (-.3219) n =5 = 5956 T5 = (400)(.5956) = 238.24 7S-16 Learning Curves Example S-2 Q1: Calculate the time of the 5th unit Approach using the learning Curve Coefficients table (7S-1, page 346) b n = 596 (Unit Time for 85% and n = 5) T5 = (400)(.596) = 238.4 7S-17 Learning Curve Coefficients Unit Number 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 70% Unit Total Time Time 1.000 0.700 0.568 0.490 0.437 0.398 0.367 0.343 0.323 0.306 0.291 0.278 0.267 0.257 0.248 0.240 0.233 0.226 0.220 0.214 0.209 0.204 0.199 0.195 0.191 0.187 0.183 0.180 0.177 0.174 1.000 1.700 2.268 2.758 3.195 3.593 3.960 4.303 4.626 4.932 5.223 5.501 5.769 6.026 6.274 6.514 6.747 6.973 7.192 7.407 7.615 7.819 8.018 8.213 8.404 8.591 8.774 8.954 9.131 9.305 75% Unit Total Time Time 1.000 0.750 0.634 0.563 0.513 0.475 0.446 0.422 0.402 0.385 0.370 0.357 0.345 0.334 0.325 0.316 0.309 0.301 0.295 0.288 0.283 0.277 0.272 0.267 0.263 0.259 0.255 0.251 0.247 0.244 1.000 1.750 2.384 2.946 3.459 3.934 4.380 4.802 5.204 5.589 5.958 6.315 6.660 6.994 7.319 7.635 7.944 8.245 8.540 8.828 9.111 9.388 9.660 9.928 10.191 10.449 10.704 10.955 11.202 11.446 80% Unit Total Time Time 1.000 0.800 0.702 0.640 0.596 0.562 0.534 0.512 0.493 0.477 0.462 0.449 0.438 0.428 0.418 0.410 0.402 0.394 0.388 0.381 0.375 0.370 0.364 0.359 0.355 0.350 0.346 0.342 0.338 0.335 1.000 1.800 2.502 3.142 3.738 4.299 4.834 5.346 5.839 6.315 6.777 7.227 7.665 8.092 8.511 8.920 9.322 9.716 10.104 10.485 10.860 11.230 11.594 11.954 12.309 12.659 13.005 13.347 13.685 14.020 85% Unit Total Time Time 1.000 0.850 0.773 0.723 0.686 0.657 0.634 0.614 0.597 0.583 0.570 0.558 0.548 0.539 0.530 0.522 0.515 0.508 0.501 0.495 0.490 0.484 0.479 0.475 0.470 0.466 0.462 0.458 0.454 0.450 1.000 1.850 2.623 3.345 4.031 4.688 5.322 5.936 6.533 7.116 7.686 8.244 8.792 9.331 9.861 10.383 10.898 11.405 11.907 12.402 12.892 13.376 13.856 14.331 14.801 15.267 15.728 16.186 16.640 17.091 90% Unit Total Time Time 1.000 0.900 0.846 0.810 0.783 0.762 0.744 0.729 0.716 0.705 0.695 0.685 0.677 0.670 0.663 0.656 0.650 0.644 0.639 0.634 0.630 0.625 0.621 0.617 0.613 0.609 0.606 0.603 0.599 0.596 1.000 1.900 2.746 3.556 4.339 5.101 5.845 6.574 7.290 7.994 8.689 9.374 10.052 10.721 11.384 12.040 12.690 13.334 13.974 14.608 15.237 15.862 16.483 17.100 17.713 18.323 18.929 19.531 20.131 20.727 95% Unit Total Time Time 1.000 0.950 0.922 0.903 0.888 0.876 0.866 0.857 0.850 0.843 0.837 0.832 0.827 0.823 0.818 0.815 0.811 0.807 0.804 0.801 0.798 0.796 0.793 0.790 0.788 0.786 0.784 0.781 0.779 0.777 1.000 1.950 2.872 3.774 4.662 5.538 6.404 7.261 8.111 8.954 9.792 10.624 11.451 12.274 13.092 13.907 14.717 15.525 16.329 17.130 17.929 18.724 19.517 20.307 21.095 21.881 22.665 23.446 24.226 25.003 Learning Curves Example S-2 Q2 – Expected time for the 20th jet T20 = (400) X (.381) = 152.4 labor days Q3 – Expected total time for all 20 jets T1-20 = (400) X (10.485) = 4,194 labor days Q4 – Average time per jet: Average time = 4,194/20 = 209.7 labor days Learning Curves Example Given T2 = 10 and 80% learning percent, find the expected time for th the unit T2 = 10 = T1 X (.8) T1 = 10 / = 12.5 T5 = 12.5 X 0.596 = 7.45 Learning Curve Applications Useful application areas: Manpower planning and scheduling Negotiated purchasing Pricing new products Budgeting, purchasing, and inventory planning Capacity planning Instructor Slides 7S-21 Cautions and Criticisms Learning rates may differ from organization to organization and by type of work Base learning rates on empirical studies rather than assumptions where possible Projections based on learning curves should be regarded as approximations of actual times Because time estimates are based on the first unit, care should be taken to ensure that the time is valid It is possible that at some point the curve might level off or even tip upward Instructor Slides 7S-22 Cautions and Criticisms Some of the improvements may be more apparent than real: improvements in times may be caused by increases in indirect labor costs In mass production situations, learning curves may be of initial use in predicting how long it will take before the process stabilizes The concept does not usually apply because improvement in time per unit is almost imperceptible Instructor Slides 7S-23 Cautions and Criticisms Users of learning curves fail to include carryover effects from previous experiences Shorter product life cycles, flexible manufacturing, and cross-functional workers can affect the ways in which learning curves may be applied Instructor Slides 7S-24 Operations Strategy Learning curves have strategic implications for: Market entry when trying to rapidly gain market share As volume increases, operations is able to move quickly down the learning curve Reduced cost improved competitive advantage Useful for capacity planning Can lead to more realistic time estimates, thus leading to more accurate capacity needs assessment Instructor Slides 7S-25 ... applications of learning curves Outline some of the cautions and criticisms of learning curves Estimate learning rates from data on job times Instructor Slides 7S-2 Learning Curves Learning curve ... 7: Learning Objectives You should be able to: Explain the concept of a learning curve Make time estimates based on learning curves List and briefly describe some of the main applications of learning. .. Slides 7S-6 Learning Curves: On a Log-Log Graph Instructor Slides 7S-7 Learning Percentage 90% learning percent means 10% decrease in unit time with each doubling of repetition 80% learning percent