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Learning TheoryLearning Theory
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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
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DefinitionDefinition
� 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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DefinitionDefinition
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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
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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
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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
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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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Learning Curve ModelsLearning Curve Models
� 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
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Learning Curve ModelsLearning Curve Models
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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Learning Curve ModelsLearning Curve Models
There are five different modelsThere are five different models
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Learning Curve ModelsLearning Curve 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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Learning Curve ModelsLearning Curve Models
� 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.
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Learning Curve ModelsLearning Curve Models
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.
� 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.
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Learning Curve ModelsLearning Curve Models
Straight line ModelStraight line Model
� The straight-line learning curve model is the most commonly
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
� The straight-line learning curve model is the most commonly
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
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Learning Curve ModelsLearning Curve Models
� 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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Learning Curve ModelsLearning Curve Models
� 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
Straight line Model: ExampleStraight line Model: Example
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Learning Curve ModelsLearning Curve Models
Straight line Model: ExampleStraight line Model: Example
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Learning Curve ModelsLearning Curve Models
� 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
Straight line Model: ExampleStraight line Model: Example
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ExampleExample
Straight line Model: ExampleStraight line Model: Example
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Learning Curve ModelsLearning Curve Models
� 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.
� 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.
Stanford B ModelStanford B Model
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Data Representation in Learning ModelsData Representation in Learning Models
� It is a modified straight line power model where it includes a
B-factor for better modification
� Learning curve data is usually represented using either:
� unit data
� cumulative-average data
� the moving average and
� the exponentially weighted average
� It is a modified straight line power model where it includes a
B-factor for better modification
� 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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Data Representation in Learning ModelsData Representation in Learning Models
� 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
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Data Representation in Learning ModelsData Representation in Learning Models
Unit DataUnit Data
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Data Representation in Learning ModelsData Representation in Learning Models
� 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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Data Representation in Learning ModelsData Representation in Learning Models
Cumulative Average DataCumulative Average Data
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Data Representation in Learning ModelsData Representation in Learning Models
� 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
Cumulative Average DataCumulative Average Data
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Data Representation in Learning ModelsData Representation in Learning Models
� 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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Data Representation in Learning ModelsData Representation in Learning Models
� 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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Data Representation in Learning ModelsData Representation in Learning Models
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Data Representation in Learning ModelsData Representation in Learning Models
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Data Representation in Learning ModelsData Representation in Learning Models
ExampleExample
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Data Representation in Learning ModelsData Representation in Learning Models
ExampleExample
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Data Representation in Learning ModelsData Representation in Learning Models
ExampleExample
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Data Representation in Learning ModelsData Representation in Learning Models
ExampleExample
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