Report

Calculate Projected Costs With The Cumulative Average Learning Curve Principles of Cost Analysis and Management © Dale R. Geiger 2011 1 Forrrrrrrre!!! Should I take lessons? © Dale R. Geiger 2011 2 Terminal Learning Objective • Task: Calculate Projected Costs With The Cumulative Average Learning Curve • Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors • Standard: with at least 80% accuracy • Describe the concept of learning curve • Identify the key variables in the learning curve calculation • Solve for missing variables in the learning curve calculation © Dale R. Geiger 2011 3 What is the Learning Curve? • Learning is an important part of continuous improvement • Learning curve theory can predict future improvement as experience grows • Learning occurs most rapidly with the first few trials and then slows • Cumulative learning curve percentage conveys the factors by which the cumulative average adjusts with every doubling of experience © Dale R. Geiger 2011 4 In-Class Activity • • • • • • • Appoint one student as class timekeeper Divide class into teams Instructor issues materials Instructor specifies task All teams start immediately and at same time Timekeeper records time each team finishes task Instructor converts time into resource consumption (person seconds) Team A B C D E F People Seconds Per-secs © Dale R. Geiger 2011 5 Class Discussion • How did we do? • How can we do it better? • Was there role confusion? • Were we over staffed? • How much better can we do it? © Dale R. Geiger 2011 6 Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” • Expect a certain level of improvement with each repetition • Absolute improvement is marginal and will decrease over many repetitions • Assume a consistent percentage of improvement at Doubling Points (2nd, 4th, 8th, 16th, etc.) • Improvement is based on cumulative average cost © Dale R. Geiger 2011 7 Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” • Expect a certain level of improvement with each repetition • Absolute improvement is marginal and will decrease over many repetitions • Assume a consistent percentage of improvement at Doubling Points (2nd, 4th, 8th, 16th, etc.) • Improvement is based on cumulative average cost © Dale R. Geiger 2011 8 Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” • Expect a certain level of improvement with each repetition • Absolute improvement is marginal and will decrease over many repetitions • Assume a consistent percentage of improvement at Doubling Points (2nd, 4th, 8th, 16th, etc.) • Improvement is based on cumulative average cost © Dale R. Geiger 2011 9 Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” • Expect a certain level of improvement with each repetition • Absolute improvement is marginal and will decrease over many repetitions • Assume a consistent percentage of improvement at Doubling Points (2nd, 4th, 8th, 16th, etc.) • Improvement is based on cumulative average cost © Dale R. Geiger 2011 10 Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” • Expect a certain level of improvement with each repetition • Absolute improvement is marginal and will decrease over many repetitions • Assume a consistent percentage of improvement at Doubling Points (2nd, 4th, 8th, 16th, etc.) • Improvement is based on cumulative average cost © Dale R. Geiger 2011 11 Applying CALC Theory • CALC theory posits that the use of resources will drop predictably as experience doubles • Let’s assume an 80% learning rate • Cumulative average = Sum of all events # of events • 80% learning rate means: Event 1 + Event 2 2 = 80% * Event 1 © Dale R. Geiger 2011 Cumulative average of 1st event is equal to 1st event 12 Applying CALC Theory • Use the 80% learning curve to predict Event 2 (Event 1 + Event 2)/2 = 80% * Event 1 2 * (Event 1 + Event 2) /2 = 2 * 80% * Event 1 Event 1 + Event 2 = 160% * Event 1 Event 2 = (160% * Event 1) – Event 1 • Calculate a predicted second trial for each team Team A B C D E F 1st cum avg 2nd cum avg Predicted 2nd event © Dale R. Geiger 2011 13 Let’s See if It Works • The best performing four teams continue • Repeat the task Team 1st event per-secs Predicted 2nd event Actual 2nd event • Did learning occur? • What CALC % did each team achieve © Dale R. Geiger 2011 14 The CALC Template • Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 CALC % 90% nd event is Total divided by •Column Cumulative Average after 2 1 is the event number Column 2 is the result for that event number of events in the Total (540/2 = 270) Column 3 is the cumulative total for all events 4 is theiscumulative average for all events •Column CALC% the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%) © Dale R. Geiger 2011 15 The CALC Template Cumulative average for Event nd event is sum of 1st and 2nd • Total per-secs after 2 1 = cumulative total/1 events (300 + 240 = 540) Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 /1 = 300 2 240 540 270 CALC % 90% • Cumulative Average after 2nd event is Total divided by number of events in the Total (540/2 = 270) • CALC% is the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%) © Dale R. Geiger 2011 16 The CALC Template • Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 CALC % 90% • Cumulative Average after 2nd event is Total divided by number of events in the Total (540/2 = 270) • CALC% is the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%) © Dale R. Geiger 2011 17 The CALC Template • Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 /2 = 270 CALC % 90% • Cumulative Average after 2nd event is Total divided by number of events in the Total (540/2 = 270) • CALC% is the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%) © Dale R. Geiger 2011 18 The CALC Template • Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 /2 = 270 CALC % 90% • Cumulative Average after 2nd event is Total divided by number of events in the Total (540/2 = 270) • CALC% is the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%) © Dale R. Geiger 2011 19 What CALC% Did the Teams Achieve? • Complete the table Team 1st event cum avg 2nd event cum avg 2nd event CALC% © Dale R. Geiger 2011 20 Can We Get Better? • Of course! There is always a better way • However, learning curve theory recognizes that improvement occurs with doubling of experience • Consider the 80% CALC Trial Cum Avg 1 100 2 80 4 64 8 51.2 16 40.96 32 32.768 © Dale R. Geiger 2011 21 Can We Predict the 3rd Event • Yes – but this gets more complicated • Because the 3rd event is not a doubling of experience from the 2nd event • There is an equation: y = aXb • • • • b= ln calc%/ln 2 a = 1st event per-secs X = event number y works out to 70.21 for the cum avg after 3rd event • (We are only interested in natural doubling in this course) © Dale R. Geiger 2011 22 However… • We can easily calculate the per-secs for the 3rd and 4th events combined Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 90% 972 243 90% 4 © Dale R. Geiger 2011 CALC % assumed same as 2nd 23 However, • We can easily calculate the per-secs for the 3rd and 4th event combined Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 90% 972 = 243 90% 4 CALC % 90% * 2nd event cum avg © Dale R. Geiger 2011 24 However, • We can easily calculate the per-secs for the 3rd and 4th event combined Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 90% 243 90% 4 972 4x CALC % 4 * cum avg for 4 © Dale R. Geiger 2011 25 However, • We can easily calculate the per-secs for the 3rd and 4th event combined Trial Number Event Per-Secs Total Per-Secs Cumulative Average 1 300 300 300 2 240 540 270 90% 972 243 90% 4 CALC % Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4: 972 -540 = 432 © Dale R. Geiger 2011 26 Finishing Up • The team with the best 2nd event time and the team with the best CALC% will complete the task two additional times • Each student should calculate a prediction for the best total time for 3rd and 4th event • The team with the best 3rd and 4th event time and the three students with the closest prediction WIN © Dale R. Geiger 2011 27 Score Sheet Team: Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 2 3+4 pred 3+4 act Team: Trial Number 1 2 3+4 pred 3+4 act © Dale R. Geiger 2011 28 Applications for Learning Curve • Learning effects all costs and can be a major factor in evaluating contract bids • How many per-secs did the winning team save after four events compared to their 1st event time without learning? • Learning curve effects are very dramatic over the first few events • Consider the effect on new weapons systems developments • What are the advantages of a contractor who has already “come down the learning curve”? © Dale R. Geiger 2011 29 Check on Learning • A 90% CALC means that the time for the second event will be what percentage of the time for the first event? © Dale R. Geiger 2011 30 Practical Exercises © Dale R. Geiger 2011 31