Calculate Projected Costs With The Cumulative Average Learning Curve © Dale R. Geiger 20111

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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 20113

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 20114

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) © Dale R. Geiger TeamABCDEF People Seconds Per-secs

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 20116

Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” © Dale R. Geiger 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 (2 nd, 4 th, 8 th, 16 th, etc.) Improvement is based on cumulative average cost

Cumulative Average Learning Curve (CALC) Theory © Dale R. Geiger 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 (2 nd, 4 th, 8 th, 16 th, etc.) Improvement is based on cumulative average cost

Cumulative Average Learning Curve (CALC) Theory © Dale R. Geiger 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 (2 nd, 4 th, 8 th, 16 th, etc.) Improvement is based on cumulative average cost

Cumulative Average Learning Curve (CALC) Theory © Dale R. Geiger 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 (2 nd, 4 th, 8 th, 16 th, etc.) Improvement is based on cumulative average cost

Cumulative Average Learning Curve (CALC) Theory “The Cumulative Average per Unit Decreases by a Constant Percentage Each Time the Number of Iterations Doubles” © Dale R. Geiger 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 (2 nd, 4 th, 8 th, 16 th, etc.) Improvement is based on cumulative average cost

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

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 © Dale R. Geiger TeamABCDEF 1 st cum avg 2 nd cum avg Predicted 2 nd 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 © Dale R. Geiger Team 1 st event per-secs Predicted 2 nd event Actual 2 nd event

The CALC Template Total per-secs after 2 nd event is sum of 1 st and 2 nd events ( = 540) Cumulative Average after 2 nd event is Total divided by number of events in the Total (540/2 = 270) CALC% is the ratio between cumulative averages of 2 nd and 1 st events (270/300 = 90%) © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % 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 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 Total per-secs after 2 nd event is sum of 1 st and 2 nd events ( = 540) Cumulative Average after 2 nd event is Total divided by number of events in the Total (540/2 = 270) CALC% is the ratio between cumulative averages of 2 nd and 1 st events (270/300 = 90%) © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % /1 = Cumulative average for Event 1 = cumulative total/1

The CALC Template Total per-secs after 2 nd event is sum of 1 st and 2 nd events ( = 540) Cumulative Average after 2 nd event is Total divided by number of events in the Total (540/2 = 270) CALC% is the ratio between cumulative averages of 2 nd and 1 st events (270/300 = 90%) © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % %

The CALC Template Total per-secs after 2 nd event is sum of 1 st and 2 nd events ( = 540) Cumulative Average after 2 nd event is Total divided by number of events in the Total (540/2 = 270) CALC% is the ratio between cumulative averages of 2 nd and 1 st events (270/300 = 90%) © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % /2 =

The CALC Template © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % /2 =

What CALC% Did the Teams Achieve? Complete the table © Dale R. Geiger Team 1 st event cum avg 2 nd event cum avg 2 nd 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 © Dale R. Geiger TrialCum Avg

Can We Predict the 3 rd Event Yes – but this gets more complicated Because the 3 rd event is not a doubling of experience from the 2 nd event There is an equation: y = aX b= ln calc%/ln 2 a = 1 st event per-secs X = event number y works out to for the cum avg after 3 rd event (We are only interested in natural doubling in this course) © Dale R. Geiger b

However… We can easily calculate the per-secs for the 3 rd and 4 th events combined © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % % assumed same as 2 nd

However, We can easily calculate the per-secs for the 3 rd and 4 th event combined © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % 4972= 24390% 90% * 2 nd event cum avg

However, We can easily calculate the per-secs for the 3 rd and 4 th event combined © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % % 4 * cum avg for 4 4x

However, We can easily calculate the per-secs for the 3 rd and 4 th event combined © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % % % Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4: = 432 Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4: = 432

Finishing Up The team with the best 2 nd 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 3 rd and 4 th event The team with the best 3 rd and 4 th event time and the three students with the closest prediction WIN © Dale R. Geiger

Score Sheet © Dale R. Geiger Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % pred 3+4 act Trial Number Event Per-Secs Total Per-Secs Cumulative Average CALC % pred 3+4 actTeam:

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 1 st 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

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

Practical Exercises © Dale R. Geiger