3-1 Learning Theory.pptosp.mans.edu.eg/elbeltagi/R 3-1 Learning Theory.pdf · Learning theory states that whenever the quantity of a product doubles, the unit or cumulative average

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Learning TheoryLearning Theory

12/11/2014 Emad Elbeltagi 2

IntroductionIntroduction

� One of the important issues in repetitive operations is the

effect of learning

� A repetitive operation offers better opportunities to achieve

higher productivity

� That is, the time and effort expended to complete repetitive

activities decrease as the number of repetitions increases

� This phenomenon is usually referred to as learning curve

effect, or learning curve theory

� One of the important issues in repetitive operations is the

effect of learning

� A repetitive operation offers better opportunities to achieve

higher productivity

� That is, the time and effort expended to complete repetitive

activities decrease as the number of repetitions increases

� This phenomenon is usually referred to as learning curve

effect, or learning curve theory

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DefinitionDefinition

� learning is defined as: the improvement that results when

people repeat a process and gain skill or efficiency from

the experience

� There are several reasons for this phenomenon:

� Increased worker familiarization

� Improved equipment and crew coordination

� Improved job organization

� Development of more efficient techniques and methods

� Stabilized design leading to fewer modifications and rework

� learning is defined as: the improvement that results when

people repeat a process and gain skill or efficiency from

the experience

� There are several reasons for this phenomenon:

� Increased worker familiarization

� Improved equipment and crew coordination

� Improved job organization

� Development of more efficient techniques and methods

� Stabilized design leading to fewer modifications and rework



� Learning theory states that whenever the quantity of a product

doubles, the unit or cumulative average cost, man-hour, dollars,

etc. will decline by a certain percentage

� This percentage is called the learning rate which identifies the

learning achieved

� A learning rate of 100% means that no learning takes place

� The lower the learning rate, the greater the learning gain

� Learning theory states that whenever the quantity of a product

doubles, the unit or cumulative average cost, man-hour, dollars,

etc. will decline by a certain percentage

� This percentage is called the learning rate which identifies the

learning achieved

� A learning rate of 100% means that no learning takes place

� The lower the learning rate, the greater the learning gain

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Learning Theory AssumptionsLearning Theory Assumptions

� The time or the cost required for one unit of product to be

completed will be less each time when more units are produced

� The time or the cost will be decreased in a declining distribution

� Learning to take place when:

� There should be repetition in the units being constructed

� Management must create a stable work environment

� The time or the cost required for one unit of product to be

completed will be less each time when more units are produced

� The time or the cost will be decreased in a declining distribution

� Learning to take place when:

� There should be repetition in the units being constructed

� Management must create a stable work environment

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Factors Affecting LearningFactors Affecting Learning

� Characteristics of the Task: Task Complexity, Newness,

Dangerousness, Hazards, and Tediousness

� The Skill of Management on Site: Planning, motivation, safety

precautions, responsibility, level of supervision and inspection and

availability of required materials and tools

� Characteristics of Labor on Site: Morale level, skills and

coherence among crew member

� Characteristics of the Task: Task Complexity, Newness,

Dangerousness, Hazards, and Tediousness

� The Skill of Management on Site: Planning, motivation, safety

precautions, responsibility, level of supervision and inspection and

availability of required materials and tools

� Characteristics of Labor on Site: Morale level, skills and

coherence among crew member


Factors Affecting LearningFactors Affecting Learning

� Project Characteristics: altitude of work, accessibility of work

site, equipment breakdowns, Interruption (e.g., accidents and

holidays), Project size, Noise and Project location

� Among all previous factors, characteristics of the task itself often

have the greatest impact

� Project Characteristics: altitude of work, accessibility of work

site, equipment breakdowns, Interruption (e.g., accidents and

holidays), Project size, Noise and Project location

� Among all previous factors, characteristics of the task itself often

have the greatest impact

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Variability of LearningVariability of Learning

� The learning rate of each

construction task is a function of

various factors

� For Example, interruption or

breakdowns due to either labor

strike, or long holidays can

impact the accumulated learning

skills of laborers

� The learning rate of each

construction task is a function of

various factors

� For Example, interruption or

breakdowns due to either labor

strike, or long holidays can

impact the accumulated learning

skills of laborers


Forgetting PhenomenonForgetting Phenomenon

� The routine-acquiring process is delayed for even a short time,

some of the experience curve effect is lost, although upon

resumption of the activity, the routine-acquiring process resumes

at the same decremented rate

� The routine-acquiring process is delayed for even a short time,

some of the experience curve effect is lost, although upon

resumption of the activity, the routine-acquiring process resumes

at the same decremented rate

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Forgetting PhenomenonForgetting Phenomenon

� The rate and amount of forgetting decrease as the number of units

completed before an interruption occurs increases

� When the interruption is sufficiently long, there is nothing more to

forget, since everything has already been forgotten

� The typical learning-forgetting-learning model

� The rate and amount of forgetting decrease as the number of units

completed before an interruption occurs increases

� When the interruption is sufficiently long, there is nothing more to

forget, since everything has already been forgotten

� The typical learning-forgetting-learning model


Learning Curve ModelsLearning Curve Models

� The learning curve relationship is commonly modeled with a power

function described as the log-linear or constant percentage model

� This model below recognizes that labor hours decrease

systematically by a constant percentage each time the volume of

production increases (usually a doubling of units)

� The learning curve relationship is commonly modeled with a power

function described as the log-linear or constant percentage model

� This model below recognizes that labor hours decrease

systematically by a constant percentage each time the volume of

production increases (usually a doubling of units)

Y= aNx

� Y = the number of labor hours required to produce the nth unit

� a = the number of labor hours required to produce the first unit

� N = cumulative number of units produced

� x = learning exponent

� Y = the number of labor hours required to produce the nth unit

� a = the number of labor hours required to produce the first unit

� N = cumulative number of units produced

� x = learning exponent

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� x = learning exponent, which is always negative

� k = Y2 / Y1 = K = (a × 2x) l (a × 1x) = 2x

� log K = x log 2

� X = log k / log 2

� The negative learning exponent x is (log k)/(log 2)

� where k is the learning rate represented by the constant

percentage decrease in hours as per increase in output (doubling

the number of units)

� For example, an 80% learning rate with a doubling of units has a

learning exponent b equal to –0.3219

� x = learning exponent, which is always negative

� k = Y2 / Y1 = K = (a × 2x) l (a × 1x) = 2x

� log K = x log 2

� X = log k / log 2

� The negative learning exponent x is (log k)/(log 2)

� where k is the learning rate represented by the constant

percentage decrease in hours as per increase in output (doubling

the number of units)

� For example, an 80% learning rate with a doubling of units has a

learning exponent b equal to –0.3219



There are five different models

� The straight-line model

� The Stanford "B" model

� The cubic power model

� The piecewise (or stepwise) model

� The exponential model

There are five different models

� The straight-line model

� The Stanford "B" model

� The cubic power model

� The piecewise (or stepwise) model

� The exponential model

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There are five different modelsThere are five different models



� The straight-line model assumes learning rate is a constant

� However, several researchers have shown that the learning rate

is not constant throughout the progress of an activity

� When the acquired experience and the productivity leveling off

effect are both present, the learning is not constant

� High learning rates are usually due to acquired experience with

similar products

� The straight-line model assumes learning rate is a constant

� However, several researchers have shown that the learning rate

is not constant throughout the progress of an activity

� When the acquired experience and the productivity leveling off

effect are both present, the learning is not constant

� High learning rates are usually due to acquired experience with

similar products

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� After the effect of the experience factor diminishes, the learning

rate decreases

� Once production has reached the so-called standard production

point, which marks the end of the learning effect, the cumulative

man-hours per unit stabilize

� Thereafter, the learning rate is 100%, and no further

productivity improvement is realized.

� After the effect of the experience factor diminishes, the learning

rate decreases

� Once production has reached the so-called standard production

point, which marks the end of the learning effect, the cumulative

man-hours per unit stabilize

� Thereafter, the learning rate is 100%, and no further

productivity improvement is realized.



Straight line ModelStraight line Model

� The straight-line learning curve model is the most commonly

used model for construction activities

� It forms a straight line when plotted on a Log-Log scale

� The underlying assumption of the straight-line model is that

the learning rate remains constant throughout the duration of

the activity

� It mainly assumes that each time the number of cycles

doubles, the time taken to finish a cycle is decreased by a

constant percentage called the learning rate.


used model for construction activities

� It forms a straight line when plotted on a Log-Log scale

� The underlying assumption of the straight-line model is that

the learning rate remains constant throughout the duration of

the activity

� It mainly assumes that each time the number of cycles

doubles, the time taken to finish a cycle is decreased by a

constant percentage called the learning rate.

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Straight line ModelStraight line Model


used model for

� Y = A Xn

� Y is cumulative average time to finish the nth unit

� A is time required for the first unit

� X is the cumulative unit number (number repetitions)

� n learning index


used model for

� Y = A Xn

� Y is cumulative average time to finish the nth unit

� A is time required for the first unit

� X is the cumulative unit number (number repetitions)

� n learning index



� Assume the surfacing of a wearing course layer in a road

construction project has an initial duration of 10 days. It is

repeated 10 consecutive times without any interruptions using

only one crew.

� This activity has a learning rate of 90%.

� Assume the surfacing of a wearing course layer in a road

construction project has an initial duration of 10 days. It is

repeated 10 consecutive times without any interruptions using

only one crew.

� This activity has a learning rate of 90%.

Straight line Model: ExampleStraight line Model: Example

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� Y2 = 10 x 2 (log 0.9 / log 2) = 9

� So, the duration at unit 2 = n x Yn – Yn-1 = 2x9 – 10 = 8 days

� Note that Y is the cumulative average duration

� Y2 = 10 x 2 (log 0.9 / log 2) = 9

� So, the duration at unit 2 = n x Yn – Yn-1 = 2x9 – 10 = 8 days

� Note that Y is the cumulative average duration





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� It is noticed that the effect of learning on activities’ duration is

applied each time the number of repetitions is doubled

� This is clear at repetitions number 1, 2, 4 and 8 where the

duration decreased by 90% to be 10, 9, 8.1 and 7.3

� It is noticed that the effect of learning on activities’ duration is

applied each time the number of repetitions is doubled

� This is clear at repetitions number 1, 2, 4 and 8 where the

duration decreased by 90% to be 10, 9, 8.1 and 7.3



ExampleExample


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� It is a modified straight line power model where it includes a

B-factor for better modification

� Y = A (X + B) n

� The B-factor is added to account for the crew's acquired

experience

� A crew with no prior experience will have a B factor of zero

� The B factor is defined as the equivalent number of units'

worth of experience describing.



� Y = A (X + B) n

� The B-factor is added to account for the crew's acquired

experience

� A crew with no prior experience will have a B factor of zero

� The B factor is defined as the equivalent number of units'

worth of experience describing.

Stanford B ModelStanford B Model


Data Representation in Learning ModelsData Representation in Learning Models



� Learning curve data is usually represented using either:

� unit data

� cumulative-average data

� the moving average and

� the exponentially weighted average



� Learning curve data is usually represented using either:

� unit data

� cumulative-average data

� the moving average and

� the exponentially weighted average

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� Unit data is the time to complete a given cycle versus the cycle

number

� It shows the actual performance of the repetitive activity

exactly as it happened

� This is the raw data in its simplest form

� It always shows highly variable unit data

� It is apparent that no clear relation exists

� There may be a great deal of noise or scatter in the data

� When learning curve is plotted, trends may not be readily

apparent to forecast future performance

� Unit data is the time to complete a given cycle versus the cycle

number

� It shows the actual performance of the repetitive activity

exactly as it happened

� This is the raw data in its simplest form

� It always shows highly variable unit data

� It is apparent that no clear relation exists

� There may be a great deal of noise or scatter in the data

� When learning curve is plotted, trends may not be readily

apparent to forecast future performance

Unit DataUnit Data



Unit DataUnit Data

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� It is the average time to complete all cycles up to and

including the given cycle versus the cycle number

� It helps smooth out the noisy in the data by averaging many

cycles together

� Long-term trends become much more obvious

� As more and more cycles are incorporated into the data set,

the most recent cycle or cycles are discounted and contribute

relatively little to the overall cumulative average

� The predictive capabilities are obviously enhanced using the

cumulative average data.

� It is the average time to complete all cycles up to and

including the given cycle versus the cycle number

� It helps smooth out the noisy in the data by averaging many

cycles together

� Long-term trends become much more obvious

� As more and more cycles are incorporated into the data set,

the most recent cycle or cycles are discounted and contribute

relatively little to the overall cumulative average

� The predictive capabilities are obviously enhanced using the

cumulative average data.

Cumulative Average DataCumulative Average Data




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� CAi = (X1 + X2 + x3 + ….. + Xi)/i , where i is the cycle no.

� CAi is the cumulative average at cycle no. I

� X1 , X2 , x3 , ….. , Xi are the corresponding (unit data)

� When all of the data points arrive (i = K(total number of

cycles)), the cumulative average will equal the final average

� CAi = (X1 + X2 + x3 + ….. + Xi)/i , where i is the cycle no.

� CAi is the cumulative average at cycle no. I

� X1 , X2 , x3 , ….. , Xi are the corresponding (unit data)

� When all of the data points arrive (i = K(total number of

cycles)), the cumulative average will equal the final average




� Moving average uses only the most recent data in calculating

the average.

� The analyst must decide how far back in time the data are still

significant when choosing how many cycles to incorporate in

the moving average

� This help not hiding the short term trends

� The moving average is, then, a compromise of sorts between

the unit data and the cumulative-average data.

� Moving average uses only the most recent data in calculating

the average.

� The analyst must decide how far back in time the data are still

significant when choosing how many cycles to incorporate in

the moving average

� This help not hiding the short term trends

� The moving average is, then, a compromise of sorts between

the unit data and the cumulative-average data.

Moving Average DataMoving Average Data

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� where N is the number of cycles which used in the calculation

� MAt is the moving average production rate of order N at cycle t

� Yt-N+1+ … + Yt-1 + Yt are the corresponding production rate

(unit data)

� t is cycle number

� where N is the number of cycles which used in the calculation

� MAt is the moving average production rate of order N at cycle t

� Yt-N+1+ … + Yt-1 + Yt are the corresponding production rate

(unit data)

� t is cycle number

Moving Average DataMoving Average Data



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ExampleExample

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ExampleExample



ExampleExample

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ExampleExample

Thank youThank you

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3-1 Learning Theory.pptosp.mans.edu.eg/elbeltagi/R 3-1 Learning Theory.pdf · Learning theory states that whenever the quantity of a product doubles, the unit or cumulative average