Calculate Projected Costs With The
Cumulative Average Learning Curve
Principles of Cost Analysis and
Management
© Dale R. Geiger 2011 1

Should I take lessons?
© Dale R. Geiger 2011 2

• 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

• 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

• 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)
A B C D E F Team
People
Seconds
Per-secs
© Dale R. Geiger 2011 5

• 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 (2 nd , 4 th , 8 th , 16 th , 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 (2 nd , 4 th , 8 th , 16 th , 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 (2 nd , 4 th , 8 th , 16 th , 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 (2 nd , 4 th , 8 th , 16 th , 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 (2 nd , 4 th , 8 th , 16 th , etc.)
• Improvement is based on cumulative average cost
© Dale R. Geiger 2011 11

• 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 1 st event is equal to 1 st event
© Dale R. Geiger 2011 12

• 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
1 st cum avg
2 nd cum avg
Predicted
2 nd event
A B C D E F
© Dale R. Geiger 2011
13

• The best performing four teams continue
• Repeat the task
Team
1 st event per-secs
Predicted 2 nd event
Actual 2 nd event
• Did learning occur?
• What CALC % did each team achieve
© Dale R. Geiger 2011 14

• Total per-secs after 2 nd event is sum of 1 st and 2 nd events (300 + 240 = 540)
CALC % Trial
Number
1
2
Event
Per-Secs
300
240
Total
Per-Secs
300
540
Cumulative
Average
300
270 90%
• Cumulative Average after 2 nd event is Total divided by
• number of events in the Total (540/2 = 270)
Column 3 is the cumulative total for all events
CALC% is the ratio between cumulative averages of
2 nd and 1 st events (270/300 = 90%)
© Dale R. Geiger 2011 15

• Total per-secs after 2 nd event is sum of 1 st and 2 nd events (300 + 240 = 540)
CALC % Trial
Number
1
2
Event
Per-Secs
300
240
Total
Per-Secs
300 /1 =
540
Cumulative
Average
300
270 90%
• 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 2011 16

• Total per-secs after 2 nd event is sum of 1 st and 2 nd events (300 + 240 = 540)
CALC % Trial
Number
1
2
Event
Per-Secs
300
240
Total
Per-Secs
300
540
Cumulative
Average
300
270 90%
• 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 2011 17

• Total per-secs after 2 nd event is sum of 1 st and 2 nd events (300 + 240 = 540)
CALC % Trial
Number
1
2
Event
Per-Secs
300
240
Total
Per-Secs
300
540 /2 =
Cumulative
Average
300
270 90%
• 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 2011 18

• Total per-secs after 2 nd event is sum of 1 st and 2 nd events (300 + 240 = 540)
CALC % Trial
Number
1
2
Event
Per-Secs
300
240
Total
Per-Secs
300
540 /2 =
Cumulative
Average
300
270 90%
• 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 2011 19

What CALC% Did the Teams Achieve?
• Complete the table
Team
1 st event cum avg
2 nd event cum avg
2 nd event CALC%
© Dale R. Geiger 2011 20

• 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
4
80
64
8
16
32
51.2
40.96
32.768
© Dale R. Geiger 2011 21

rd
• 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
• b= ln calc%/ln 2
• a = 1 st event per-secs
• X = event number
• y works out to 70.21 for the cum avg after 3 rd event
• (We are only interested in natural doubling in this course)
© Dale R. Geiger 2011 22

• We can easily calculate the per-secs for the 3 rd and 4 th events combined
Trial
Number
1
2
4
Event
Per-Secs
300
240
Total
Per-Secs
300
540
972
Cumulative
Average
300
270
243
CALC %
90%
90% assumed same as 2 nd
© Dale R. Geiger 2011 23

• We can easily calculate the per-secs for the 3 rd and 4 th event combined
Trial
Number
1
2
4
Event
Per-Secs
300
240
Total
Per-Secs
300
540
972
Cumulative
Average
300
270
= 243
90% * 2 nd event cum avg
CALC %
90%
90%
© Dale R. Geiger 2011 24

• We can easily calculate the per-secs for the 3 rd and 4 th event combined
Trial
Number
1
2
4
Event
Per-Secs
300
240
Total
Per-Secs
300
540
972
4x
Cumulative
Average
300
270
243
4 * cum avg for 4
CALC %
90%
90%
© Dale R. Geiger 2011 25

• We can easily calculate the per-secs for the 3 rd and 4 th event combined
Trial
Number
1
2
4
Event
Per-Secs
300
240
Prediction for total of events 3
& 4 is difference between cumulative total for 3 and cumulative total for 4:
972 -540 = 432
Total
Per-Secs
300
540
972
Cumulative
Average
300
270
243
CALC %
90%
90%
© Dale R. Geiger 2011 26

• 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 2011 27

Team:
1
Trial
Number
2
3+4 pred
3+4 act
Event
Per-Secs
Total
Per-Secs
Cumulative
Average
CALC %
Team:
1
Trial
Number
2
3+4 pred
3+4 act
Event
Per-Secs
Total
Per-Secs
Cumulative
Average
CALC %
© 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 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 2011 29

• 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

© Dale R. Geiger 2011 31