Question

Give a brief discussion, comparing and contrasting unit theory learning curves and cumulative average theory learning curves.  Include a discussion of what the impact might be if you incorrectly used a unit theory curve in lieu of a cumulative average theory curve, and vice versa.

Answer 1

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Learning curve analysis is developed as a tool to estimate the recurring costs in production process .

Recurring costs are considered to be those costs incurred on each unit of production.The learning curves doesnot take into acoount the overhead costs . It only considered manufacturing costs.

The theory of the learning curve is  based on the idea that the time required to perform a task decreases as a worker gains experience. The basic concept is that the time, or cost, of performing a task decreases at a constant rate as cumulative output doubles.

Learning curves are useful for preparing cost estimates, bidding on special orders, setting labor standards, scheduling labor requirements, evaluating labor performance etc.

There are two different learning curve models.

The original model was developed by T. P. Wright in 1936 and is referred to as the Cumulative Average Model or Wright's Model. A second model was developed later by a team of researchers at Stanford. Their approach is referred to as the Incremental Unit Time Model or Crawford's Model.

Simple learning curve problems are more easily introduced with Wright's model, but it is the Unit Theory Model that is widely practiced

Wright's Cumulative Average Model

In Wright's Model, the learning curve function is defined as follows:

Y = aX^b

where:
Y = the cumulative average time (or cost) per unit.
X = the cumulative number of units produced.
a = time (or cost) required to produce the first unit.
b = slope of the function when plotted on log-log paper.
   = log of the learning rate/log of 2.

The equation for cumulative total hours (or cost) is found by multiplying both sides of the cumulative average equation by X.

Since X times X^b = X^1+b, the equation is:

XY = aX^1+b

Crawford's Incremental Unit Time (or Cost) Model

The equation used in Crawford's model is as follows:

Y = aK^b

where: Y = the incremental unit time (or cost) of the lot midpoint unit.
           K = the algebraic midpoint of a specific production batch or lot.

Xcan be used in the equation instead of K to find the unit cost of any particular unit, but determining the unit cost of the last unit produced is not useful in determining the cost of a batch of units. The unit cost of each unit in the batch would have to be determined separately. This is obviously not a practical way to solve for the cost of a batch that may involve hundreds, or even thousands of units. A practical approach involves calculating the midpoint of the lot. The unit cost of the midpoint unit is the average unit cost for the lot. Thus, the cost of the lot is found by calculating the cost of the midpoint unit and then multiplying by the number of units in the lot.

Since the relationships are non linear, the algebraic midpoint requires solving the following equation:

K = [L(1+b)/(N2^1+b - N1^1+b)]^-1/b

where: K = the algebraic midpoint of the lot.
             L = the number of units in the lot.
             b = log of learning rate / log of 2
            N1 = the first unit in the lot minus 1/2.
            N2 = the last unit in the lot plus 1/2.

Once Y_c is determined for the algebraic midpoint of a lot, then the cost of the entire lot is found by multiplying Y_c by the number of units in the lot as indicated above.

Learning curves range from around 70% to 100%. A learning curve below 70% is rare. A 100% learning curve indicates no learning at all. On the other hand, a 50% learning curve would indicate that no additional time or cost would be required for additional units beyond the first unit, since the cumulative average time, or the incremental unit time would decrease by 50% each time output doubled. This means that the cumulative total time would not increase because it would equal 100% of the previous cumulative total time.

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