### Learning Curve

```Calculate Projected Costs With The
Cumulative Average Learning Curve
Principles of Cost Analysis and
Management
1
Forrrrrrrre!!!
Should I take lessons?
2
Terminal Learning Objective
• Task: Calculate Projected Costs With The Cumulative
Average Learning Curve
• Condition: You are a cost advisor technician with
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
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
4
In-Class Activity
•
•
•
•
•
•
•
Appoint one student as class timekeeper
Divide class into teams
Instructor issues materials
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
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?
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
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
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
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
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
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
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
13
Let’s See if It Works
• The best performing four teams continue
Team
1st event per-secs
Predicted 2nd event
Actual 2nd event
• Did learning occur?
• What CALC % did each team achieve
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%)
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%)
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%)
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%)
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%)
19
What CALC% Did the Teams Achieve?
• Complete the table
Team
1st event cum avg
2nd event cum avg
2nd event CALC%
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
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)
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
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
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
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
26
Finishing Up
• The team with the best 2nd event time and the
team with the best CALC% will complete the
• 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
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
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
“come down the learning curve”?