Reference no: EM1316322

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 C_i = cost component i, and F_i = cost-influencing factor i. The price is estimated as follows:

P = M₁M₂M₃P_b

Where P_b = base price, and i M = price-influencing multiplier i. These random variables are further defined in Table 1.

The failure probability (P_f ) can be determined as follows:

P_f = 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.