1. Calculate Projected Costs with the Cumulative Average Learning Curve
Intermediate Cost Analysis
and Management
Show Slide #1: Calculate Projected Costs with the Cumulative Average Learning Curve
Title: Calculate Projected Costs with the Cumulative Average Learning Curve
References: Handouts, Excel Spreadsheets
Facilitator Material and Student Material: Dry erase markers, white boards, access to Excel spreadsheets, case-studies
Facilitator Material: Each primary facilitator should possess a lesson plan, slide deck, course handouts, practical exercises, access to Excel spreadsheets, case-studies All required references and technical manuals will be provided by the local Command.
Student Material: Students should possess course handouts, practical exercises, access to Excel spreadsheets, case-studies and standard classroom supplies.
The 21st Century Soldier Competencies are essential to ensure Soldiers and leaders are fully prepared to prevail in complex, uncertain environments. This lesson reinforces the following 21st Century Soldier Competencies:
Communication and Engagement (Oral, written, and negotiation)
Critical thinking, intergovernmental, and multinational competence
Tactical and Technical Competence
Throughout the lesson discussion seek opportunities to link the competencies with the lesson content through the student’s experiences.
10.3

2. Forrrrrrrre!!! Should I take lessons?
Show Slide #2: Concrete Experience: Why taking lessons could save time and money
Facilitator’s Note: (Concrete Experience 10 minutes) Present students the slide statements Ask students what their thoughts are on “ Is taking lessons worth it?”
Facilitator’s Note: (Publish and Process 10 minutes) The critical portion of this part of the ELM process is to force the students to reflect. Ask a series of thought influencing questions.
Facilitator’s Note: Introduction: We are seldom perfect on the first try, and even after two or three tries we are still finding ways to get better. We learn about using the proper tools (I think our friend in the picture could use some help in this regard!) and other ways to improve performance.

3. Terminal Learning Objective
Action: Calculate Projected Costs with the Cumulative Average Learning Curve
Condition: You are training to become an ACE with access to ICAM course handouts, readings, spreadsheet tools, and awareness of Operational Environment (OE) 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 
Show Slide #3: TLO
Action: 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 
Safety Requirements: In a training environment, leaders must perform a risk assessment in accordance with DA PAM , Risk Management. Leaders will complete a DD Form 2977 DELIBERATE RISK ASSESSMENT WORKSHEET during the planning and completion of each task and sub-task by assessing mission, enemy, terrain and weather, troops and support available-time available and civil considerations (METT-TC). Local policies and procedures must be followed during times of increased heat category in order to avoid heat related injury. Consider the work/rest cycles and water replacement guidelines IAW TRADOC Regulation
Environmental Considerations: Environmental protection is not just the law but the right thing to do. It is a continual process and starts with deliberate planning. Always be alert to ways to protect our environment during training and missions. In doing so, you will contribute to the sustainment of our training resources while protecting people and the environment from harmful effects. Refer to FM Environmental Considerations and GTA ENVIRONMENTAL-RELATED RISK ASSESSMENT.
INSTRUCTIONAL LEAD-IN. Learning is an important part of continuous improvement…next slide

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
Show Slide #4: Introduction
Facilitator Note: 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 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)
Show Slide #5: Demonstrate the learning curve
Learning Step/Activity #1 Demonstrate the learning curve
Method of Instruction: DSL (large or small group discussion)
Facilitator to Student Ratio:
Time of Instruction: 2.0 (Total)
Media: Power Point Presentation, Printed Reference Materials
Facilitator’s Note: Appoint one student as class timekeeper. Divide class into teams
Instructor issues materials:
Each group requires: 40 sheets of paper (20 each of “page 1” and “page 2”), 15 envelopes, a stapler. Pages 1 and 2 may be different color pages, or just marked in some way to indicate they are different.
Instructor specifies task
Each group must collate and staple page 1 and 2 together, fold and stuff into envelopes (do not seal the envelopes.)
[Don’t give the groups a lot of time to get organized. Hand out the materials, define the task, and have them start. Learning will come later. The task is completed when all 15 envelopes are stuffed. The extra paper is part of the learning process. Students may find that they wasted effort stapling papers that didn’t need to be stapled. ]
All teams start immediately and at same time
Timekeeper records time each team finishes task (to nearest whole second)
Instructor converts time into resource consumption (person seconds) Number of people in the group * number of seconds to complete the task.
Team A B C D E F
People
Seconds
Per-secs
© Dale R. Geiger 2011

6. 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?
Show Slide #6: Demonstrate the learning curve (Cont.)
Facilitator Note: How did we do?
How can we do it better?
Was there role confusion? Perhaps we can better define the roles.
Were we over staffed? Maybe we need to fire someone.
How much better can we do it? Make a guess as to what your time in person-seconds will be next time.

7. Cumulative Average Learning Curve (CALC) Theory
Expect a certain level of improvement with each repetition
Absolute decrease over many repetitions
Assume a consistent percentage of improvement at Doubling Improvement is based on cumulative average cost
The Cumulative Average per Unit
Decreases by a Constant Percentage
Show Slide #7: Demonstrate the learning curve (Cont.)
Facilitator Note: There are really three key pieces to the theory:
First it is the cumulative average per unit, NOT the value of each new unit, that decreases.
Second: Decreases by a Constant Percentage - this percentage is new cumulative average/old cumulative average. Examples 80%, 95%, etc. (as opposed to the percentage of the change: 20%, 5%, etc.)
Third: Each Time the Number of Iterations Doubles – the constant percentage is not applied with each iteration, but only at the doubling points.
Each Time the Number of Iterations Doubles

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
Show Slide #8: Demonstrate the learning curve (Cont.)
Facilitator Note: 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 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
Show Slide #9: Demonstrate the learning curve (Cont.)
Facilitator Note: 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

10. 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
Show Slide #10: Demonstrate the learning curve (Cont.)
Facilitator Note: Use the 80% learning curve to predict Event 2
(Event 1 + Event 2)/2 = 80% * Event 1
Multiply both sides of the equation by 2
2 * (Event 1 + Event 2) /2 = 2 * 80% * Event 1
Event 1 + Event 2 = 160% * Event 1
This means that, in order to yield and 80% learning curve, the total of Events 1 and 2 must equal 160% of the time of Event 1
Subtract “Event 1” from both sides of the equation, giving us:
Event 2 = (160% * Event 1) – Event 1
Although this calculation isn’t shown on the slide, Event 2 = 60% of Event 1
Calculate a predicted second trial for each team in person-seconds
Team A B C D E F
1st cum avg
2nd cum avg
Predicted 2nd event

11. 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
Show Slide #11: Demonstrate the learning curve (Cont.)
Facilitator Note: The best performing four teams continue
Repeat the task and record the time in person-seconds as on slide 5
Did learning occur? What did you do differently? Did it help? Any decrease in person-seconds represents learning.
What CALC % did each team achieve

12. 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
Show Slide #12: Demonstrate the learning curve (Cont.)
Facilitator Note:
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

13. The CALC Template (Cont.)
Cumulative average for Event 1 = cumulative total/1
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%
/1 =
Show Slide #13: Demonstrate the learning curve (Cont.)
Facilitator Note: Cumulative average for Event 1 = cumulative total/1
300/1 = 300

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%
Show Slide #14: Demonstrate the learning curve (Cont.)
Facilitator Note: Total per-secs after 2nd event is sum of 1st and 2nd events ( = 540)

15. 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 =
Show Slide #15: Demonstrate the learning curve (Cont.)
Facilitator Note: Cumulative Average after 2nd event is Total divided by number of events in the Total (540/2 = 270)

16. 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 =
Show Slide #16: Demonstrate the learning curve (Cont.)
Facilitator Note: CALC% is the ratio between cumulative averages of 2nd and 1st events (270/300 = 90%)
Notice that, although the second event’s time equaled 80% of the first event’s time, this represents a 90% Cumulative Average Learning Curve, not 80%

17. What CALC% Did the Teams Achieve?
Complete the table
Team
1st event cum avg
2nd event cum avg
2nd event CALC%
Show Slide #17: Demonstrate the learning curve (Cont.)
Facilitator Note: Students should fill in the table with the actual data from the class exercise.

18. 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
Show Slide #18: Demonstrate the learning curve (Cont.)
Facilitator Note: Of course! - there is always a better way
However, learning curve theory recognizes that improvement occurs with doubling of experience.
Consider the 80% CALC
Large improvements are realized quickly at the beginning of the learning process. Later improvements are smaller and come more gradually.

19. 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
Show Slide #19: Demonstrate the learning curve (Cont.)
Facilitator Note: 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 3d event
We are only interested in natural doubling in this course and will not require calculation of the interim events.

20. 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 2
240
540
270
90% 4
972
243
assumed same as 2nd
Show Slide #20: Demonstrate the learning curve (Cont.)
Facilitator Note: When we were calculating the CALC% we worked left to right. Now, to calculate predictions for future events, we will work right to left on the table.
We start by assuming the same learning curve that was achieved after event 2

21. However (Cont.)
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 2
240
540
270
90% 4
972
= 243
Show Slide #21: Demonstrate the learning curve (Cont.)
Facilitator Note: Moving right to left, we next calculate the new cumulative average, which is 90% * old cumulative average.
90% * 2nd event cum avg

22. However (Cont.)
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 2
240
540
270
90% 4
972
243 4x
Show Slide #22: Demonstrate the learning curve (Cont.)
Facilitator Note: Once again moving right to left, multiply the new cumulative average * 4 to get cumulative total for events 1 through 4
4 * cum avg for 4

23. However (Cont.)
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 2
240
540
270
90% 4
972
243
Show Slide #23: Demonstrate the learning curve (Cont.)
Facilitator Note: Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4:
= 432
The underlying algebra for this calculation is included below:
(E1 + E2 + E3 + E4)/4 = 90%*(E1 + E2)/2
(E1 + E2 + E3 + E4)/2 = 90%*(E1 + E2)
(E1 + E2 + E3 + E4) = 180%*(E1 + E2)
(E3 + E4) = 180%*(E1 + E2) – (E1 + E2)
Prediction for total of events 3 & 4 is difference between cumulative total for 3 and cumulative total for 4:
= 432

24. 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
Show Slide #24: Demonstrate the learning curve (Cont.)
Facilitator Note: 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
Prizes may be: cup of coffee, bag of pretzels, etc.

25. 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
Show Slide #25: Demonstrate the learning curve (Cont.)
Facilitator Note: Add the scores from both teams
Team:

26. 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”?
Show Slide #26: Summarize the learning curve concept
Facilitator Note: 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”?
(This is a considerable advantage over contractors who are starting from scratch. They have already learned the shortcuts and improved their processes through experience. Most companies closely guard these trade secret to maintain their competitive advantage.

27. Practical Exercises
Show Slide #27: Summarize the learning curve concept
Facilitator Note: Practical Exercise

28. TLO Summary
Action: Calculate Projected Costs with the Cumulative Average Learning Curve
Condition: You are training to become an ACE with access to ICAM course handouts, readings, spreadsheet tools, and awareness of Operational Environment (OE) 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 
Show Slide #28: TLO Summary
Action: 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 
“Or”
Facilitator's at this time, have one learner from each group to explain the most important take away to them from this lesson. Facilitate a discussion on each answer.