Learning Curves
There is often a systematic
relationship between experience
in performing a task and the time
required to do it.
The average time per task declines
by a constant percentage each time
the quantity of tasks done doubles.
1
Types of Learning Curves
Cumulative Average-Time Learning Model – •
cumulative average time per unit declines by a
constant percentage each time the cumulative
quantity of units produced doubles
Incremental Unit-Time Learning Model – •
incremental time needed to produce the last unit
declines by a constant percentage each time the
cumulative quantity of units produced doubles
2
Effect of Learning on Cost Behavior
Berry Co. makes products requiring labor that
follows an 80 percent learning rate. If the
first unit of such a product requires 10 hours,
what is the average time for 16 units of this
product?
An 80 percent learning rate:
the average time required to make 2 units is 80 percent
of the time for 1 unit and the average time for 4 units is
80 percent of the time for 2 units, etc.
3
Cumulative Average-Time Learning Model
Number
of Units
1
2
4
8
16
Average
Labor Time
per Unit
1 × 10 = 10
.80 × 10 = 8
.80 × 8 = 6.4
.80 × 6.4 = 5.12
.80 × 5.12 = 4.096
Total Time:
Average x Units
1 × 10 = 10
2 × 8 = 16
4 × 6.4 = 25.6
8 × 5.12 = 40.96
16 × 4.096 = 65.536
The graphic presentation of the learning
phenomenon is called the learning curve.
4
Learning Curve
Average Labor
Time per Unit
Learning effects
are large initially.
Learning effects
become smaller, eventually
reaching expected final time.
Cumulative Production Output
5
Average Labor
Time per Unit
This is used to help
determine investment required.
This is used to estimate
ongoing results.
Cumulative Production Output
6
Learning Curve Formula
Cumulativeaveragelabor timeper unit
 DLH to produce unit 1
 Cumulativeno.of units produced
learning factor
ln learningrate% in decimalform
Learningfactor
ln 2
7
Question for Discussion 2 
Time to produce the first unit = 100 minutes
Learning factor = ln(0.80)/ln2 = -0.32193
•
•
What is the cumulative average time to produce .1
5 units?
What is the total time to produce 5 units? .2
What is the time it took to produce the 5th unit? .3
8
Incremental Unit-Time
Learning Model
Using the example of Berry Co. and using
the incremental unit-time learning model
Number
of Units
1
2
3
4
5
Individual Unit Time
for X-th Unit
1 × 10 = 10
0.80 × 10 = 8
7.02
0.80 × 8 = 6.40
5.96
Cum.
Cumulative
Ave. Time
Total Time
Per Unit
10
10
10 + 8 = 18
9
18 + 7.02 = 25.02
8.34
25.02 + 6.40 = 31.42
7.86
31.42 + 5.96 = 37.38
7.48
9