Slides calculate projected costs

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 r

Calculate Projected Costs With The Cumulative Average Learning Curve

Principles of Cost Analysis and

Management

Should I take lessons?

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 

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

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)

People

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?

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.)

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

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.)

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

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.)

Applying CALC Theory

• CALC theory posits that the use of resources will drop predictably

event is equal

to 1 st event

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

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

Team

1 st event per-secs Predicted 2 nd event Actual 2 nd event

The CALC Template

• Total per-secs after 2nd event is sum of 1st and 2nd

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 2nd event is sum of 1st and 2nd

The CALC Template

• Total per-secs after 2nd event is sum of 1st and 2nd

The CALC Template

/2 =

The CALC Template

events (300 + 240 = 540)

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 Per-Secs Event Per-Secs Total Cumulative Average CALC %

/2 =

What CALC% Did the Teams Achieve?

• Complete the table

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

Trial Cum Avg

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 = 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)

b

• We can easily calculate the per-secs for the 3rd

and 4th events combined

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

• We can easily calculate the per-secs for the 3rd

and 4th event combined

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

90% * 2 nd event cum avg 90% * 2 nd event cum avg

• We can easily calculate the per-secs for the 3rd

and 4th event combined

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

4 * cum avg for 4

4 * cum avg for 4

4x

• We can easily calculate the per-secs for the 3rd

and 4th event combined

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

Prediction for total of events 3

& 4 is difference between

cumulative total for 3 and

cumulative total for 4:

972 -540 = 432

Prediction for total of events 3

& 4 is difference between

cumulative total for 3 and

cumulative total for 4:

972 -540 = 432

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

Score Sheet

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

1 2 3+4 pred 3+4 act

Trial Number Per-Secs Event Per-Secs Total Cumulative Average CALC %

1 2 3+4 pred 3+4 act Team:

Team:

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”?

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?

Practical Exercises