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Work Systems and the Methods, Measurement, and Management of Work

by Mikell P. Groover, ISBN 0-13-140650-7.

©2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

Learning Curves

Sections:

1. Learning Curve Theory

2. Crawford Model

3. Total Cumulative Time

4. Determining the Learning Rate

Chapter 19




Learning Curve Phenomenon

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




Learning Curve Phenomenon

Learning Curve analysis has been applied for different

areas rather than cycle unit time:

1- It can estimates the product cost.

2- Product quality

3- Occupational safety

Learning Curve phenomenon is easiest to envision for individual worker,

the same kind of improvement occurs in the repetitive operations of workers

team.

Learning Curve is also called experience curve




Learning Curve Theory

According to theory, there is a constant learning rate that

applies to a given repetitive task

Learning rate (LR) is the proportion by which the

dependent variable (e.g., task time) is multiplied every time

the number of task cycles doubles

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




Learning Curve for LR = 80%




Learning Curve Theory (Cont.)

There is one important term related to the learning rate

which is called improvement rate.

Improvement rate is the percentage of improvement in

cycle time of the unit (dependent variable) as the number

of unit doubles.

Improvement Rate (IR) = 1- LR

IR = improvement rate expressed as a decimal fraction

LR = Learning rate expressed as a decimal fraction

Learning Curve Theory (Cont.)

The studies have been presented that the in industrial sector that

the learning rate range from 60% to less than 100%.

Learning rate of 60% indicates a very reduction in task time

while the number of cycles are doubled.

The means higher value of LR (value of LR closer to one)

slower learning in the task or operation. In contrast, the lower

value means faster learning.

Learning rate of 60% very reduction in task time while the

number of cycles are doubled.

Learning rate of 100% Meaning no learning

Higher than of 100% Meaning loss of learning

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 (time of the task), 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

2ln

LRln

LR = Learning rate expressed as a decimal fraction

(e.g., 80% = 0.80)

m = learning curve slope




Same Learning Curve in Log-Log Plot

Example: for learning rate less than 1.0 (100%), m is negative value so, the

slope is negative as presented in the Figure (m= -0.322 for 80% LR)




Crawford Model

Crawford Model: is the most widely used learning

curve model in industry today to determine the

expected time to perform the Nth work cycle:

m

N NTT 1

TN = unit time for the Nth work cycle, T1 = time for the first unit cycle, N = number of the

work cycle in the repetitive sequence. and m = learning curve slope (see the equation

in slide 8)




Crawford Model (Cont.)

Example: T1 = 10 hr, LR = 80%, how long will it take

to complete the 20th work unit?

m = ln(0.80)/ln 2 = -0.32193

T20 = 10(20)-0.32193 = 3.81 hr

mN NTT 1

Solution:




Total Cumulative Time

Total cumulative time of the N work units. This time is

important and useful in bidding on a batch of N work units

for a prospective customer.

Total cumulative time is also necessary to estimate the

cost of the production as well as it helps to identify the

extra time of work (additional work shift) if needed.

Total Cumulative Time (TCT)

Total cumulative time for number of work

units cycles:

TTN = Total cumulative time for N work units, T1 = time for the first cycle, i = an

intermediate variable for the summing procedure

The

se b

oth

equa

tions

use

d to

det

erm

ine

TC

T (

Cra

wfo

rd

Mo

del

)

N = number of the work cycles units

Total Cumulative Time

Example: Determine the cumulative total time of the 20

work units of a task for learning rate of 80%, given that the time

of first unit is 10 hr?

Solution:

First way: summing the unit times for unit 1 through 20

using equation:

TT20 = 10 [(1)m + (2)m +(3)m + (4)m + (5)m + ……. (20)m ]

TT20 = 10 [(1)-0.32193 + (2) -0.32193 +(3) -0.32193 + ……. +(20) -0.32193 ]

m = ln(0.80)/ln 2 = -0.32193

TT20 = 10 [1+ 0.80+ 0.7021+ ……. +0.3812] = 104.85 hr

Total Cumulative Time (Cont.)

Solution:

Second way: using the approximation equation:

E(TT20) = 10

(20 + 0.5)1-0.32193 – (0.5) 1-0.32193

1 - 032193 = 105.12 hr

Note: The differences between to results is due to the error of correct value of TT20 of only 0.258% and

this percentage good for application and is not consider as a significant difference in the time.

Total Cumulative Time (Cont.)

Other equation to determine Total cumulative Time is the Wright

model equation:

TTN = T1 * Nm+1

Cumulative average time

N

TTT N

N

TTN = Total cumulative time for N work units, T1 = time for the first cycle

OR TN E(TTN)

= N




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




Why the Learning Curve Occurs (Cont.)

Contributions of the larger organization

Methods improvements by the IE Department

Technological improvements

Better scheduling

Improved logistical support

Better motivation of workers

Determining the Learning Rate (LR)

There are two ways to obtain learning rate (LR):

(1) Industry average: Some typical values of learning rate for the Crawford

model are listed below:

Type of work LR, %

Assembly 84-85

Prototype assembly 65

Clerical operations 75-85

Inspection 86

Machining 90

Welding 85-90

Industry LR, %

Aerospace 85

Complex machines 75-85

Construction 70-90

Electronics mfg 90-95

Machine shop 90-95

Shipbuilding 80-85

Determining the Learning Rate (LR) Cont.

There are two ways to obtain learning rate (LR):

(2) Using the data from application: Some typical values of learning rate for

the Crawford model are listed below:

The learning rate can be estimated by determine the ratio of every time the

number of units doubles:

LR =

T2N

TN

Where N is any unit number and 2N is double that number

Determining the Learning Rate (LR) Cont.

Finding the slope from any two observations: if the data are not available or

missing for the doubling effect in unit time values. The LR can be determine by

calculate the slope learning for any two values

m =

lnTN2 – lnTN1

Where; m = learning curve slope and TN2 and TN1

are the unit times for units N2 and N1

ln(N2) – ln(N1)

Upper unit value

lower unit value

After determine the slope (m), then can find the LR by the below equation:

LR = 2m

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