After processing the existing programme cost data and running a regression model on the preview, projects, the
Question:
After processing the existing programme cost data and running a regression model on the preview, projects, the cost of product development and manufacturing (CDM) has been estimated to follow the equation: CDM = $0.8 million + $3.83 million x R2 (R is the achieved product reliability at service life and is expected to be above 90%). The cost of failure (CF) has been estimated as the sum of fixed cost of $40 000 plus variable cost of $150 per failure. The total number of the expected failures is n x (1 - R), where n is the total number of produced units. Considering that the production volume is expected to be 50 000 units, estimate the optimal target reliability and the total cost of the programme.
Total Cost = 800 000 + 3 830 000R^2 + 40 000 + 150n (1 - R)
n = 50 000
To minimize the cost function we need to find its first derivative with respect to the reliability and set it equal to zero (feel free to recap on your differentiation rules HERE):
d(Total Cost) / dR = 2 * 3 830 000R - 150 * 50 000 = 0
Solving R, produces R = 0.979
The associated total cost is:cost = $4 668 329.03
Explain steps and differentiation.
Project Management in Practice
ISBN: 978-0470533017
4th edition
Authors: Samuel J. Mantel Jr., Jack R. Meredith, Sco