A construction company assesses the uncertainty in the return, i.e., gross margins (G), of a project as follows:
G = P - C
Where P = price and C = cost. The cost is estimated as follows:
C =F1C1 + F2 C2 + F1 F2 C3
Where Ci = cost component i, and Fi = cost-influencing factor i. The price is estimated as follows:
P = M1M2M3Pb
Where Pb = base price, and i M = price-influencing multiplier i. These random variables are further defined in Table 1.
The failure probability (Pf ) can be determined as follows:
Pf = P (G≤0) = P (P≤C)
Table: Random Variables and their Probabilistic Characteristics ($ in millions)
|
Parameter
|
Description
|
Mean
|
CoefficientofVariation
|
DistributionType
|
|
C1
|
Materials cost component
|
$10
|
0.10
|
Lognormal
|
|
C2
|
Labor cost component
|
$8
|
0.12
|
Lognormal
|
|
C3
|
Subcontracting cost component
|
$4
|
0.05
|
Normal
|
|
F1
|
Materials cost-influencing factor
|
1
|
0.10
|
Lognormal
|
|
F2
|
Labor cost-influencing factor
|
1.1
|
0.15
|
Normal
|
|
Pb
|
Base price
|
$30
|
N/A
|
Deterministic
|
|
M1
|
Competition price-influencing multiplier
|
0.95
|
N/A
|
Deterministic
|
|
M2
|
Customer-history price-influencing multiplier
|
0.98
|
N/A
|
Deterministic
|
|
M3
|
Change-order price-influencing multiplier
|
1.05
|
0.10
|
Lognormal
|
Perform a parametric analysis by assessing the fractional change in the probability of failure with respect to a small change in the mean and standard deviation of selected variable.