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

2. Forrrrrrrre!!!
Should I take lessons?

3. 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.

4. 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

5. 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

6. 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?

7. 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

8. 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

9. 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

10. 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

11. The CALC Template
Total per-secs after 2nd event is sum of 1st and 2nd events ( = 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

12. The CALC Template (Cont.)
Total per-secs after 2nd event is sum of 1st and 2nd events ( = 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 =

13. The CALC Template (Cont.)
Total per-secs after 2nd event is sum of 1st and 2nd events ( = 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%

14. The CALC Template (Cont.)
Total per-secs after 2nd event is sum of 1st and 2nd events ( = 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 =

15. The CALC Template
Total per-secs after 2nd event is sum of 1st and 2nd events ( = 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 =

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

17. 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

18. 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 for the cum avg after 3rd event
(We are only interested in natural doubling in this course) b

19. 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:
= 432

20. 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

21. 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:

22. 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”?

23. 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%

24. 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.

25. Practical Exercises / Review

26. TLO Check on Learning

27. 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.