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    Learning Curves

    Uploaded by

    ayushc27
    This document discusses learning curves and how the time required to perform a task decreases with increasing repetitions. It provides the following key points: - The degree of improvement is dependent on the complexity of the task, with simple tasks showing quicker improvement than complex ones. - The learning effect can be attributed to factors like worker learning, preproduction preparation, and changes made during production. - The learning effect is predictable, with a constant percentage decrease in time for each doubling of repetitions, typically ranging from 10-20%. - Learning curves can be used to estimate times and costs for future production based on data from initial units, and are useful for planning, budgeting, scheduling, and more.

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    © All Rights Reserved
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    Learning Curves

    Uploaded by

    ayushc27
    139 views33 pages
    This document discusses learning curves and how the time required to perform a task decreases with increasing repetitions. It provides the following key points: - The degree of improvement is dependent on the complexity of the task, with simple tasks showing quicker improvement than complex ones. - The learning effect can be attributed to factors like worker learning, preproduction preparation, and changes made during production. - The learning effect is predictable, with a constant percentage decrease in time for each doubling of repetitions, typically ranging from 10-20%. - Learning curves can be used to estimate times and costs for future production based on data from initial units, and are useful for planning, budgeting, scheduling, and more.

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    This document discusses learning curves and how the time required to perform a task decreases with increasing repetitions. It provides the following key points: - The degree of improvement is dependent on the complexity of the task, with simple tasks showing quicker improvement than complex ones. - The learning effect can be attributed to factors like worker learning, preproduction preparation, and changes made during production. - The learning effect is predictable, with a constant percentage decrease in time for each doubling of repetitions, typically ranging from 10-20%. - Learning curves can be used to estimate times and costs for future production based on data from initial units, and are useful for planning, budgeting, scheduling, and more.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    139 views33 pages

    Learning Curves

    Uploaded by

    ayushc27
    This document discusses learning curves and how the time required to perform a task decreases with increasing repetitions. It provides the following key points: - The degree of improvement is dependent on the complexity of the task, with simple tasks showing quicker improvement than complex ones. - The learning effect can be attributed to factors like worker learning, preproduction preparation, and changes made during production. - The learning effect is predictable, with a constant percentage decrease in time for each doubling of repetitions, typically ranging from 10-20%. - Learning curves can be used to estimate times and costs for future production based on data from initial units, and are useful for planning, budgeting, scheduling, and more.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 33

    Learning Curves

    Learning curve
    The time required to perform a task decreases with
    increasing repetitions
    The degree of improvement is a function of the task being
    done
    Short, routine tasks will show modest improvement relatively
    quickly
    Longer, more complex tasks will show improvement over a longer
    interval
    The learning effect is attributed to a variety of factors:
    Worker learning
    Preproduction factors
    Tooling and equipment selection
    Product design
    Methods analysis
    Effort expended prior to the start of work
    Changes made after production has begun
    Changes in work methods
    Changes in tooling and equipment
    Managerial factors
    Improvements in planning, scheduling, motivation, and control
    Experience Curve
    (http://www.policonomics.com/lear
    ning-curve/)
    The learning effect is predictable
    The learning percentage is constant
    Every doubling of repetitions results in a constant
    percentage decrease in the time per repetition
    Typical decreases range from 10 to 20 percent
    Exl
    The frequency of occurrence of unique words in
    the novel Moby Dick by Herman Melville
    Reference
    Each time cumulative output doubles, the time per unit for that
    amount should be approximately equal to the previous time multiplied
    by the learning percentage.
    If the first unit of a process took 100 hours and the learning rate is 90%:

    Unit Unit Time (hours)


    1 = 100
    2 .90(100) = 90
    4 .90(90) = 81
    8 .90(81) = 72.9
    16 .90(72.9) = 65.61
    32 .90(65.61) = 59.049
    Tn T1 n b

    where
    Tn Time for nth unit
    T1 Time for first unit
    ln r
    b
    ln 2
    r learning rate percentage
    ln stands for the natural logarithm
    If the learning rate is 90, and the first unit took 100
    hours to complete, how long would it take to complete
    the 25th unit?

    ln.90
    T25 100 25 ln 2

    .15200
    100 25
    61.3068 hours
    The learning factor approach uses a table that shows
    two things for selected learning percentages:
    Unit value for the number of repetitions (unit number)

    Tn T1 Unit time factor


    Cumulative value, which enables us to compute the total
    time required to complete a given number of units.

    T n T1 Total time factor


    If the learning rate is 90, and the first unit took 100
    hours to complete, how long would it take to complete
    the 25th unit?
    T25 100 .613
    61.3 hours
    How long would it take to complete the first 25 units?

    T 25 100 17.713
    1,771.3 hours
    Useful application areas:
    1. Manpower planning and scheduling
    2. Negotiated purchasing
    3. Pricing new products
    4. Budgeting, purchasing, and inventory planning
    5. Capacity planning
    1. Learning rates may differ from organization to
    organization and by type of work
    Base learning rates on empirical studies rather than assumptions
    where possible
    2. Projections based on learning curves should be regarded
    as approximations of actual times
    3. Because time estimates are based on the first unit, care
    should be taken to ensure that the time is valid
    4. It is possible that at some point the curve might level off
    or even tip upward
    5. Some of the improvements may be more apparent than
    real: improvements in times may be caused by increases
    in indirect labor costs
    6. In mass production situations, learning curves may be of
    initial use in predicting how long it will take before the
    process stabilizes
    The concept does not usually apply because improvement in time
    per unit is almost imperceptible
    7. Users of learning curves fail to include carryover effects
    from previous experiences
    8. Shorter product life cycles, flexible manufacturing, and
    cross-functional workers can affect the ways in which
    learning curves may be applied
    A manager wants to determine an appropriate learning rate for a new
    type of work his firm will undertake. He has obtained completion times
    for the initial six repetitions of a job of this type. What learning rate is
    appropriate?

    Completion According to theory, the time per unit decreases at a


    Unit Time (hours) constant rate each time the output doubles (e.g., 1 to
    2, 2 to 4, and 3 to 6). The ratios of these observed
    1 15.9 times will give us an approximate rate.
    2 12.0 Unit 2 12.0 Unit 4 9.1 Unit 6 7.5
    .755 .758 .743
    3 10.1 Unit 1 15.9 Unit 2 12.0 Unit 3 10.1
    4 9.1 Not surprisingly, there is some variability; the rate is
    usually a smoothed approximation. Even so, the
    5 8.4 ratios are fairly close a rate of 75 percent in this
    6 7.5 case.
    An aircraft company has an order to refurbish the
    interiors of 18 jet aircraft. The work has a learning
    curve of 80%. On the basis of experience with
    similar jobs, the IED estimates that the first plane
    will require 300 hours to refurbish. Estimate the
    amount of time needed to complete:
    The 5th plane
    The first 5 planes
    All 18 planes.
    Given: An aircraft company has an order to refurbish 18 aircraft. Learning curve percentage =
    80%. IE estimates that the first plane will take 300 hours.

    T1 = 300 hr. P = 80%.

    a. Time for the fifth unit:

    Unit time factor = .596 (from Table 7S.1))


    Tn = T1 x Unit time factor
    T5 = 300 x .596 = 178.80 hours (round to 2 decimals)

    b. Time for the first five units:

    Total time factor = 3.738 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-5 = 300 x 3.738 = 1,121.40 hours (round to 2 decimals)

    c. Time for all 18 units:

    Total time factor = 9.716 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-18 = 300 x 9.716 = 2,914.80 hours (round to 2 decimals)
    A contractor intends to bid on a job installing 30
    airport security systems. Because this will be a new
    line of work for the contractor, he believes there
    will be a learning effect for the job. After reviewing
    time records from a similar type of activity, the
    contractor is convinced that an 85% LC is
    appropriate. He estimates that the first job will
    take his crew 8 days to install. How many days
    should the contractor budget for:
    The first 10 installations
    The second 10 installations
    The final 10 installations
    Given: Job calls for installing 30 security systems. Learning curve percentage = 85%. Estimate
    for first job = 8 days.

    a. Time for first 10 installations:

    Total time factor = 7.116 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-10 = 8 x 7.116 = 56.93 days (round to 2 decimals)

    b. Time for the second 10 installations (11-20):

    Step 1: Find the time for the first 20 installations.

    Total time factor = 12.402 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-20 = 8 x 12.402 = 99.22 days (round to 2 decimals)

    Step 2: Determine the time for installations 11-20.

    Time for installations 11-20 = Time for the first 20 installations Time for the first
    10 installations.

    Time for installations 11-20 = 99.22 56.93 = 42.29 days

    c. Time for the final 10 installations (21-30):

    Step 1: Find the time for the first 30 installations.

    Total time factor = 17.091 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-30 = 8 x 17.091 = 136.73 days (round to 2 decimals)

    Step 2: Determine the time for installations 21-30.

    Time for installations 21-30 = Time for the first 30 installations Time for the first
    20 installations.

    Time for installations 21-30 = 136.73 99.22 = 37.51 days (round to 2 decimals)
    The 5th unit of a 25-unit job took 14.5 hours to
    complete. If a 90% LC is appropriate:
    How long should it take to complete the last unit?
    How long should it take to complete the 10th unit?
    Estimate the average time per unit for the 25 units.
    Given: Unit 5 of a 25-unit job took 14.5 hours. Learning curve percentage = 90%.

    a. Time for the last unit (Unit 25):

    Step 1: Find the time for the first unit.

    Unit time factor = .783 (Table 7S.1)

    Tn = T1 x Unit time factor


    T5 = T1 x .783
    14.5 = T1 x .783
    T1 = 14.5 / .783 = 18.52 (round to 2 decimals)

    Step 2: Find the time for Unit 25.

    Unit time factor = .613


    Tn = T1 x Unit time factor
    T25 = 18.52 x .613 = 11.35 hours (round to 2 decimals)
    a. Time for the 10th unit:

    Unit time factor = .705


    Tn = T1 x Unit time factor
    T10 = 18.52 x .705 = 13.06 hours (round to 2 decimals)

    b. Average time per unit for the 25 units:

    Average time for the 25 units = Total time for 25 units / 25

    Total time factor = 17.713 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-25 = 18.52 x 17.713 = 328.04 hours (round to 2 decimals)

    Average time = 328.04 / 25 = 13.12 hours (round to 2 decimals)


    The labor cost to produce a certain item is 8.50
    per hour. Job setup costs 50 and material costs
    are 20 per unit. The item can be purchased for
    88.50 per unit. The learning rate is 90%.
    Overhead is charged at a rate of 50% of labor,
    materials, and setup costs.
    Determine the unit cost for 20 units, given that
    the first unit took 5 hours to complete.
    Given: Labor cost to produce an item = $8.50 per hour. Setup cost = $50.00. Material cost = $20.00
    per unit. Learning curve percentage = 90%. Overhead is charged at 50% of labor, materials,
    and setup costs. Time for first unit = 5 hours. Possible purchase cost per unit = $88.50.

    a. Unit cost for 20 units:

    Step 1: Determine labor time and costs.

    Total time factor = 14.608 (from Table 7S.1)


    Tn = T1 x Total time factor
    T1-20 = 5 x 14.608 = 73.04 hours (round to 2 decimals)
    Labor cost = 73.04 hours x $8.50 per hour = $620.84 (round to 2 decimals)

    Step 2: Determine material cost.

    Material cost = 20 units x $20 per unit = $400.00

    Step 3: Determine overhead cost.

    Overhead cost = 0.50 x ($620.84 + $400.00 + $50.00) = $535.42 (round to 2 decimals)

    Step 4: Determine total cost.

    Total cost = Setup cost + Labor Cost + Overhead cost + Material Cost

    Total cost = $50.00 + $620.84 + $535.42 + $400.00 = $1,606.26

    Step 5: Determine average cost.

    Average cost per unit = $1,606.26 / 20 units = $80.31


    Estimate the number of repetitions that new
    service worker Irene will require to achieve
    standard if the standard is 18 minutes per
    repetition. She took 30 minutes to do the initial
    repetition and 25 minutes to do the next
    repetition.
    Given: Standard = 18 minutes per repetition. Irene took 30 minutes for first repetition and 25 minutes
    for the second.

    Number of repetitions needed for her to achieve standard of 18 minutes:

    Step 1: Estimate the learning curve percentage for Irene.

    T2 / T1 = 25 / 30 = .8333 (round to 4 decimals)


    This value does not fall in Table 7S.1; therefore, we must use the formula.

    Step 2: Solve for the unit number needed to achieve the standard time.

    Tn = T1 x nb where b = ln (Learning %) / ln (2)

    = 30 (ln .8333/ ln 2)
    18 = 30 .26309
    18/30 = .26309
    . 60 = .26309
    .26309
    = . 60
    n = 6.97 (round up to 7) repetitions.
    System Archetypes

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