1

Miriam is interested in estimating the annual labor and material costs for a new production facility.
She was able to obtain the following labor and material cost data:
Material cost index value was at 544 three years ago and is 715 today.
Annual material costs for a similar facility were $2,455,000 three years ago.
Example 2.6 (Continued)
Power-Sizing Model

X = Power-sizing exponent

Equipment/Facility X
Blower, centrifugal 0.59
Compressor 0.32
Crystallizer, vacuum 0.37
Dryer, drum 0.40
Fan, centrifugal 1.17
Equipment/Facility X
Filter, vacuum 0.48
Lagoon, aerated 1.13
Motor 0.69
Reactor 0.56
Tank, horizontal 0.57

(Eq. 2-3)
Example Power Sizing Exponent Values
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Example 2.7

A. Considering Power-Sizing Index Change
Miriam has been asked to estimate the cost today of a 2500 ft2
heat exchange system for the new plant being analyzed. She has the following data.
Her company paid $50.000 for a 1000 ft2 heat exchanger 5 years ago.
Heat exchangers within this range of capacity have a power sizing exponent (x) of 0.55
69

B. Considering Cost Index Change

Example 2.7 (Continued)
Miriam has been asked to estimate the cost today of a 2500 ft2
heat exchange system for the new plant being analyzed. She has the following data.
Five years ago the Heat Exchanger Cost Index (HECI) was 1306; it is 1487 today.
Learning Phenomenon: As the number of repetitions increase, performance of people becomes faster and more accurate.
Learning curve captures the relationship between task performance and task repetition.
In general, as output doubles the unit production time will be reduced to some fixed percentage, the learning curve percentage or learning curve rate
Improvement and Learning Curve
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70
Let T1 = Time to perform the 1st unit
TN = Time to perform the Nth unit
b = Constant based on learning curve LC%
N = Number of completed units

(Eq. 2-4)
(Eq. 2-5)
Learning Curve
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Example 2.8
Calculate the time required to produce the hundredth unit of a production run if the first unit took
32.0 minutes to produce and the learning curve rate for production is 80%.
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Estimate the overall labor cost portion due to a task that has a learning-curve rate of 85% and reaches a steady state value of 5.0 minutes per unit after 16 units.
Labor and benefits are $22 per hour, and the task requires two skilled workers.
The overall production run is 20 units.

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