Chapter 7 Supplement: Lurning Curves
Learning usually occurs when humans are involved; this is a basic consideration in the design of work systems.
It is important to be able to predict how learning will affect task times and costs. This supplement addresses
THE CONCEPT OF LEARNING CURVES
Workers exhibit pattern of learning in manufacturing operations through experience. The time to manufacture a
product drops as more units are produced to a point then the curve levels off.
The degree of improvement and the number of tasks needed to realize the major portion of the improvement is a
function of the task being done. If the task is short and somewhat routine, only a modest amount of
improvement is likely to occur, and it generally occurs during the first few repetitions. If the task is fairly
complex and has a longer duration, improvements will occur over a longer interval (i.e., a larger number of
repetitions). Therefore, learning factors have little relevance for planning or scheduling routine activities, but
they do have relevance for complex repetitive activities.
“Learning” effect: time per unit decreases as the number of units produced increases
- first noted by T.P. Wright in 1936; he created a “learning curve” math model
- Used to estimate aircraft production labor in WW II, and since then to estimate many kinds of repeated
- First example of true parametric estimating??
At first, learning was attributed to increased motor skills in the workers as they repeated their tasks
- Later it was realized that management also could contribute to learning with better tools and processes
- This led to new names being applied to the curves, e.g., improvement, progress, startup, efficiency, etc.
- As people repeat a task again and again, the time it takes to do the task gradually decreases due to
- Rate of learning is greatest at first when “ignorance” is greatest; rate of learning decreases as ignorance
This graph illustrates the basic relationship between units produced and a decreasing time per unit. It should be
noted that the curve will never touch the horizontal axis; that is, the time per unit will never be zero. Experts agree that the learning effect is the result of other factors in addition to actual worker learning.
- Some of the improvement can be traced to preproduction factors, such as selection of tooling and
equipment, product design, methods analysis, and, in general, the amount of effort expended prior to the
start of the work.
- Other contributing factors may involve changes after production has begun, such as changes in methods,
tooling, and design. In addition, management input can be an important factor through improvements in
planning, scheduling, motivation, and control.
Changes that are made once production is under way can cause a temporary increase in time per unit until
workers adjust to the change, even though they eventually lead to an increased output rate. If a number of
changes are made during production, the learning curve would be more realistically described by a series of
scallops instead of a smooth curve. Nonetheless, it is convenient to work with a smooth curve, which can be
interpreted as the average effect.
An 80% Learning Curve
An activity is known to have an 80-percent learning curve. It has taken a worker 10 hours to produce the first
unit. Determine expected completion times for these units: the 2nd, 4th, 8th, and 16th (note successive doubling
of units). Each time the cumulative output doubles, the time per unit for that amount should be approximately
equal to the previous time multiplied by the learning percentage (80 percent in this case). Thus:
Unit Unit Time (hours)
1 . . . . 10
2 . . . . 0.8(10) 8
4 . . . . 0.8(8) 6.4
8 . . . . 0.8(6.4) 5.12
16 . . . 0.8(5.12) 4.096
From this, you can see that time reduction per unit becomes less and less as the number of units produced
increases. However, how are times computed for values such as three, five, six, seven, and other units that don’t fall into
this pattern? There are two ways to obtain the times. One is to use a formula; the other is to use a table of
yx= kx Where
x = unit number
yx= man-hrs. to produce x unit
k = hrs. to produce first unit
n = log b / log 2
b = learning rate (80%, etc.) expressed as decimal (.8, etc.)
Example: For 80% LC , b = .80 n = log .80 / log 2 = -.3219 Assume k = 1000
y1= 1000 (1) = 1000 (1) = 1000 y4= 1000 (4) = 1000 (.6400) = 640 y100= 1000
(100) -.321= 1000 (.2270) = 227
The table shows two things for some selected learning percentages.
- One is a unit value for the number of units produced (unit number). This enables us to easily determine
how long any unit will take to produce.
- The other is a cumulative value, which enables us to compute the total number of hours needed to
complete any given number of units.
The computation for both is a relatively simple operation: Multiply the table value by the time required for the
Example: C.W. Crow has just received an order for 200 special customized tote bags for a professional football
team. It has been established that the first tote will take 20 minutes to produce and a 90% learning curve is
a. How many labor minutes should the 200th unit require?
b. How many labor hours should the whole order of 200 tote bags take?
Using the Learning-Curve Coefficients table in text:
a. 20 minutes x .447 = 8.94 minutes
b. 20 minutes x 105.0 = 2, 100 minutes = 35 hours
Critically Important in Industrial Cost Analysis
The learning effect can lead to very large reductions in cost as production progresses
Finding ways to make learning faster can result in a huge competitive advantage
- Starting production ahead of your competitors
- Finding better processes and being faster to implement them
- But…any proposal to improve the learning rate usually involves an investment - The cost of the investment should be traded off against the savings caused by faster
Some Industrial Uses
- Manufacturing labor of a repeated product
- Construction (repeated structures like spans of a bridge or tract houses)
- Creation of documents (e.g., engineering specs and drawings, manuals)
- Boring of tunnels
- Drilling of wells
- Upgrades of existing products
- Purchase or raw materials (improved yield, decreased scrap)
- Component procurement (suppliers have learning, too)
Not Useful when…
- production is sporadic
Small lot job shops
- work is fully automated a