Calculate Projected Costs with the Cumulative Average Learning Curve Principles of Cost Analysis and Management 11.3

Forrrrrrrre!!! Should I take lessons?

Terminal Learning Objective Action: Calculate Projected Costs with the Cumulative Average Learning Curve Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for international Learners): Describe the Concept of the Cumulative Average Learning Curve.

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

In-Class Activity Appoint one learner as class timekeeper Divide class into teams Instructor issues materials Instructor specifies task All teams start immediately and at the 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

Class Discussion Q1. How did we do? Q2. How can we do it better? Q2a. Was there role confusion? Q2b. Were we over staffed? Q3. How much better can we do it?

Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” “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 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 cost

Cumulative average of 1st event is equal to 1st event 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 Cumulative average of 1st event is equal to 1st event

Applying CALC Theory (Cont.) 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

Let’s See if It Works The best performing four teams continue Repeat the task Did learning occur? What CALC % did each team achieve Team 1st event per-secs Predicted 2nd event Actual 2nd event

The CALC Template Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) 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%) Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% Column 1 is the event number Column 2 is the result for that event Column 3 is the cumulative total for all events Column 4 is the cumulative average for all events

The CALC Template (Cont.) Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) 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%) Cumulative average for Event 1 = cumulative total/1 Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% /1 =

The CALC Template (Cont.) Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) 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%) Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90%

The CALC Template (Cont.) Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) 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%) Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% /2 =

The CALC Template Total per-secs after 2nd event is sum of 1st and 2nd events (300 + 240 = 540) 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%) Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% /2 =

What CALC% Did the Teams Achieve? Complete the table Team 1st event cum avg 2nd event cum avg 2nd event CALC%

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

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 = aX 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) b

However… We can easily calculate the per-secs for the 3rd and 4th event combined We can easily calculate the per-secs for the 3rd and 4th events combined Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% 4 972 243 Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% 4 972 243 Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 300 2 240 540 270 90% 4 972 = 243 assumed same as 2nd 4 * cum avg for 4 90% * 2nd event cum avg Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4: 972 -540 = 432

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 learner 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 learners with the closest prediction WIN

Score Sheet Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 2 3+4 pred 3+4 act Team: Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % 1 2 3+4 pred 3+4 act Team:

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”?

LSA #1 Check on Learning Q1. A 90% CALC means that the time for the second event will be what percentage of the time for the first event? Q1. A 90% CALC means that the time for the second event will be what percentage of the time for the first event? Reminder: Use the 90% learning curve to predict Event 2 A1. (Event 1 + Event 2)/2 = 90% * Event 1 2 * (Event 1 + Event 2) /2 = 2 * 90% * Event 1 Event 1 + Event 2 = 180% * Event 1 Event 2 = (180% * Event 1) – Event 1 Event 2 = 180% * Event 1 – 100% * Event 1 Event 2 = 80%

LSA #1 Summary Throughout this lesson, we covered the very definition of Learning Curve and explored the CALC Theory as well. This was all applied to an in-class activity pitting one team against the other.

Practical Exercises / Review

TLO Check on Learning

TLO Summary Action: Calculate Projected Costs with the Cumulative Average Learning Curve Condition: FM Leaders in a classroom environment working individually and as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion. Standard: With at least 80% accuracy (70% for international Learners): Describe the Concept of the Cumulative Average Learning Curve.