calculate projected costs with the cumulative average learning curve ©1

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Calculate Projected Costs with the Cumulative Average Learning Curve

Intermediate Cost Analysis and Management

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Forrrrrrrre!!!Should I take lessons?

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Terminal Learning Objective

• Task: Calculate Projected Costs with the Cumulative Average Learning Curve

• Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools 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

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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

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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)Team A B C D E F

People

Seconds

Per-secs

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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?

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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

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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

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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 1Event 1 + Event 2 = 160% * Event 1

Event 2 = (160% * Event 1) – Event 1

• Calculate a predicted second trial for each team

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Team A B C D E F

1st cum avg

2nd cum avg

Predicted 2nd event

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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

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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 %

1 300 300 300

2 240 540 270 90%

Column 1 is the event numberColumn 2 is the result for that eventColumn 3 is the cumulative total for all eventsColumn 4 is the cumulative average for all events

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The CALC Template




Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%/1 =

Cumulative average for Event 1 = cumulative total/1

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The CALC Template




Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%

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The CALC Template




Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%/2 =

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The CALC Template




Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%/2 =

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What CALC% Did the Teams Achieve?

• Complete the table

Team

1st event cum avg

2nd event cum avg

2nd event CALC%

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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

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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

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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

CALC %

1 300 300 300

2 240 540 270 90%

4 972 243 90%assumed same as 2nd

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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

CALC %

1 300 300 300

2 240 540 270 90%

4 972 = 243 90%

90% * 2nd event cum avg

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However,


Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%

4 972 243 90%

4 * cum avg for 4

4x

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However,


Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1 300 300 300

2 240 540 270 90%

4 972 243 90%

Prediction for total of events 3 & 4 is difference between cumulative total for 3 and

cumulative total for 4:972 -540 = 432

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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 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

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Score SheetTrial

NumberEvent

Per-SecsTotal

Per-SecsCumulative

AverageCALC %

1

2

3+4 pred

3+4 act

Trial Number

Event Per-Secs

Total Per-Secs

Cumulative Average

CALC %

1

2

3+4 pred

3+4 act

Team:

Team:

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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”?

calculate projected costs with the cumulative average learning curve ©1

Documents

cumulative average cost

future improvement

learning curve calculation

concept of learning

certain level of improvement

doubling points

constant percentage

doubling of experience