1. Learning Curves Chapter 19 Sections: Learning Curve Theory
Why the Learning Curve Occurs
Determining the Learning Rate
Factors Affecting the Learning Curve
Learning Curve Applications
Time Standards Versus the Learning Curve
Chapter 19
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

2. Learning Curve Phenomenon
Reduction in cycle time that occurs in a repetitive work activity as the number of cycles increases
An important topic in time study
When a worker accomplishes a task over and over, the time required for each successive cycle decreases as he or she learns the task
At first the learning effect is rapid, and the cycle time decreases significantly
As more and more cycles are completed, the cycle time reduction becomes less and less
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

3. Learning Curve Theory
According to theory, there is a constant learning rate that applies to a given repetitive task
Learning rate = the proportion by which the dependent variable (e.g., task time) is multiplied every time the number of task cycles doubles
Rate of improvement is the proportion by which the dependent variable is reduced every time the number of units doubles IR = 1-LR
Example: If T1 = 10 hr and LR = 80%, then
T2 = 0.80(10) = 8.0 hr,
T4 = 0.80(8.0) = 6.4 hr
T8 = 0.80(6.4) = 5.12 hr
and so on
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

4. Learning Curve for LR = 80%
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

5. Log-Linear Model
When learning curve time data are plotted on log-log coordinates, the plot yields a straight line with slope m
y = kxm
where y = dependent variable(usually the time or cost of a task cycle or work unit), k = constant representing the value of the dependent variable for the first work cycle, x = number of work units completed, and m = slope
m = and LR = 2m
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

6. Same Learning Curve in Log-Log Plot
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

7. Two Widely Used Log-Linear Models
Crawford Model
Dependent variable is unit time TN
Wright Model
Dependent variable is cumulative average time
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

8. Crawford Model Most widely used learning curve model in industry today
Example: T1 = 10 hr, LR = 80%, how long will it take to complete the 20th work unit?
m = ln(0.80)/ln 2 =
T20 = 10(20) = 3.81 hr
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

9. Crawford Model
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

10. Crawford Model Cumulative average time
Cumulative average time between two values of N
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

11. Cumulative Total Time for Crawford Model
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

12. Solution: (a) Given T7 = 45 min and T7+10 = T17 = 30 min
A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes. Given this information, (a) what is the percent learning rate and (b) what is the total cumulative time to produce all 17 welded assemblies? Use the Crawford learning curve model.
Solution: (a) Given T7 = 45 min and T7+10 = T17 = 30 min
T7 = T1(7)m = 45
T17 = T1(17)m = 30
T1 = 45/7m = 30/17m
45/30 = 7m/17m = (7/17)m
1.5 = ( )m
ln 1.5 = m ln
= m m =
LR = = = 72.9%
(b) T1 = 45/ = hr
E(TT17) = 109.5{( – )/( )}
E(TT17) = 109.5{( )/ } = min = hr
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

13. Wright Model First learning curve model to be published
Based on cumulative average time per unit
= T1Nm
Total cumulative time:
TTN = N
or TTN = T1Nm+1
Unit time:
TN = TTN - TTN-1
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

14. Advantage of Log-Linear Model
In some cases, a log-linear model turns out not to be the best model to use and several alternatives to log-linear formula are explored. The trouble with other alternative learning curve equation is that they have more complex forms and require valuation of more parameters than the log-linear model
Log-linear model Consists of only two parameters:
The time associated with the first unit
The slope m, from which can be derived the learning rate LR
Conversely, if LR is known, the slope m can be deduced
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

15. Determine the Learning Rate
(a) Crawford model: E(TT50) = 2,347 = 72{(50.5m+1 – 0.5m+1)/(m+1)}
2,347/72 = = (50.5m+1 – 0.5m+1)/(m+1)
Trial and error solution required.
Try m = -0.30
= ( – )/(0.7) = 21.36
Try m = -0.20
= ( – )/(0.8) = 28.09
Try m = -0.15
= ( – )/(0.85) = 32.34
Try m = -0.14
= ( – )/(0.86) = 33.27
Interpolating, ( – 32.34)/(33.27 – 32.34) = 0.276
Try m = – 0.276(0.01) =
= ( – )/(0.853) = (Close enough)
LR = = = 90.3%
Read Example 19.6 page 493
The unit time for the first unit of production is 72 hr and the total cumulative time for 50 units is 2,347 hr. Determine the learning rate for (a) the Crawford learning curve model and (b) the Wright learning curve model.
(b) Wright model: 2,347 = 72(50)m+1
= (50)m+1
(m+1) ln 50 = ln
3.912 m = 3.484
3.912 m = m =
LR = = = 92.7%
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

16. Comparison of Crawford and Wright
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

17. Why the Learning Curve Occurs
Contributions of the worker
Worker becomes familiar with the task - the worker learns the task
Worker makes fewer mistakes as the task is repeated
Hand and body motions become more efficient, and there is a rhythm and pattern developed
Minor adjustments in workplace layout to reduce distances
Fewer delays that interrupt the operation
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

18. Why the Learning Curve Occurs
Contributions of the larger organization
Methods improvements by the IE Department
Fine-tuning of machinery and tooling
Development of special tooling
Technological improvements
Product design improvements
Improved quality of starting materials
Better scheduling
Improved logistical support
Better motivation of workers
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

19. Contributions to the Learning Curve
Contributions to learning by the worker and the organization
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

20. Typical Learning Rates (Crawford)
Type of work LR, %
Assembly
Prototype assembly 65
Clerical ops
Inspection
Machining
Welding
Industry LR, %
Aerospace
Complex machines
Construction
Electronics mfg
Machine shop
Shipbuilding
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

21. Determining the Learning Rate
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

22. Solution: Two solutions: (1) Note the doubling effect:
A metal fabrication shop would like to know what the learning rate is for a certain section of the plant that makes welded assemblies. In one case study, a total of four assemblies were completed. Records were kept for units 1 and 4, and the times were 60 hours and 48.6 hours, respectively. Unfortunately, the times for units 2 and 3 were lost. Use the Crawford learning curve model to determine the learning rate indicated by the data?
Solution: Two solutions:
(1) Note the doubling effect:
48.6 = 60(LR)(LR) = 60(LR)2
LR2 = 48.6/60 = 0.81
LR = = 0.90 = 90%
(2) Use the log-linear equation:
T4 = T1(N)m
48.6 = 60(4)m
0.81 = 4m
m ln 4 = ln 0.81
m = m =
LR = = 0.90 = 90%
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

23. Worker-Machine Systems
Learning in a work-machine system will be a composite of the learning rates of the two components of the system
LRw-m = pw LRw + pm LRm
where pw = proportion of cycle time controlled by worker, and pm = proportion of cycle time controlled by machine
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

24. Interruptions in the Learning Curve
Learning curve effect tends to be disrupted by interruptions in production
Possible reasons for interruptions:
Batch production, in which there are extended periods between repeat orders
Labor strikes
Vacations
Raw material shortages
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

25. Learning Loss due to Interruption
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

26. Learning Loss due to Interruption
Assumptions
If the duration of the interruption exceeds 12 months, then resuming production after the break would be the same as starting over for the first time
If the duration of the interruption is less than one month, therefor no effect on remission.
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

27. Learning Loss due to Interruption-
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

28. Other Factors Affecting Learning
Product complexity
More opportunities for learning - higher T1 and lower LR
Preproduction planning
Fewer opportunities for learning - lower T1 and higher LR
Labor turnover - slower learning (higher LR)
Plateau model - learning curve consists of two phases:
Start-up - log-linear model applies
Steady state - no further improvement
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

29. Plateau Learning Curve Model
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

30. Why the Plateau Model Occurs
In a worker-machine system, worker is finally limited by the speed of the machine
No incentives for workers to make further improvements
Management is unwilling or unable to invest in newer production technologies that would sustain the learning curve
Management does not believe that learning can continue indefinitely, and this becomes a self-fulfilling prophecy
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

31. Learning Curve Applications
Accident prevention
Capacity planning
Cost accounting
Cost estimating
Cost reduction
Contract administration
Failure analysis
Labor requirements estimation
Make-or-buy decisions
Methods analysis
New product introduction
Pricing negotiations
Pricing strategies
Product design changes
Productivity analysis
Quality control
Reliability analysis
Safety
Vendor selection
Wage incentives
Warranty maintenance
Worker performance analysis
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

32. Time Standards vs. Learning Curve
Apparent contradiction:
A time standard is a constant value that is defined under the following conditions:
Standard method
Standard work units
Performed by a trained average worker
Task is performed at 100% performance
But the learning curve predicts that the actual time for the work cycle will decrease over time
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

33. How to Reconcile the Contradiction
Although the standard time is a constant, the actual cycle time for a manual task is a variable
The time varies from one cycle to the next
One of the reasons why the cycle time varies is because the worker learns the task
The cycle time is gradually reduced as the number of repetitions increases, as predicted by learning curve theory
As long as there are no changes in methods or work unit, it seems fair to give credit to the worker for reductions in cycle time due to improvements in skill, effort, pace, etc.
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

34. Standard Reference Quantity (SRQ)
In batch production, it can be argued that the quantity of the production run should influence the value of the time standard
Surely a worker must be given an opportunity to learn a task before he or she is measured against the time standard
SRQ = the discrete quantity of production (e.g., 10, 100, 1000 units) for which the standard time for the task is applicable
If the actual quantity of production is different from the SRQ, then an adjustment in the time standard is appropriate
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

35. SRQ Adjustment Ratio
Work Systems and the Methods, Measurement, and Management of Work
by Mikell P. Groover, ISBN
©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.