Page 294 - Industrial Process Plant Construction Estimating and Man Hour Analysis
P. 294
274 Appendix B
Chapter 12 Analysis of risk probability in construction
Expected value method
If X denotes a discrete random variable that can assume the values X1, X2, …,
X i with respective probabilities p1, p2, …,p i where p1+p2 + ⋯ p i ¼1, the math-
ematical expectation of X or simply the expectation of X denoted by E(X) is
defined as
P P
E(X)¼p1X1+p2X2+⋯+p i X i ¼ pjXj¼ pX
where
E(X)¼expected value of the estimate for event i
pj¼probability that X takes on value Xj, 0<¼Pj (Xj)<¼1
Xj¼event
Range method
The mean and variance for each of the three single cost elements are calculated as
ðÞ
EC i ¼ L+4M +Hð Þ=6
^
ðÞ
var C i ¼ H Lðð Þ=6Þ 2
where
E(C i )¼expected cost of distribution i, i¼1, 2, …,n
L¼lowest cost or best-case estimate of cost distribution
M¼modal value or most likely estimate of cost distribution
H¼highest cost or worst-case estimate of cost distribution
var(C i )¼variance of cost distribution i, I ¼ 1, 2, …, n, dollars 2
The mean of the sum is the sum of the individual means, and the variance is the
sum of the variances:
ð
ð
ð
ECrÞ ¼ EC1Þ +E C2Þ + ⋯ +E CnÞ
ð
ð
ð
var CrÞ ¼ var C1Þ + var C2Þ + ⋯ + var CnÞ
ð
ð
where
E(Cr)¼expected total cost of independent subdistributions i
var (Cr)¼variance of total cost of independent subdistributions i
The probability is calculated using
1
ð
ð
½
Z ¼ UL ECrÞ= var CrÞ ⁄2
where
Z¼value of the standard normal distribution, Appendix A
UL¼upper limit of cost, arbitrarily selected
