BACKGROUND CORRELATION, COST RISK, AND GEOMETRY

Parametric cost risk is a statistical phenomena. One first assumes that the cost is defined by C = h(p 1,..., p m) where h is a function of the parameters p 1,..., p m. Second, one assumes that each of the parameters is a random variable. This applies to a single cost estimating relationship (CER) which might be in the typical Cobb-Douglas form C = p 1 q 1... pm q m where the q i are the elasticities, or to the sum of n work breakdown structure (WBS) elements p i in the form C = p 1 +... + p n. In a complete cost risk simulation the cost of each WBS element would be a function h i of parameters p 1,..., p m with the form C = h 1 (p) +... + h n (p)- 1-where p is the vector p = p1 ⎤ pm ⎦ with components p i. Third, one must make an assumption about the dependence of the variables within the variable set. One may assume that the variables are statistically independent, that the variables are totally dependent, or that correlation exists between selected pairs of variables. If the assumption of independence is made, then the distribution function F(C ≤ constant) of the WBS elements becomes arbitrarily narrow as more WBS elements are added. If this were the case then we could converge on a point estimate by estimating at the lowest levels of an arbitrarily deep WBS. This is not the case in real life. If the assumption of total dependence is made then the widest distribution function occurs. It has one and only one width no matter how many samples are taken. This also is not the case in real life. In real life, correlation exists between selected pairs of variables. The focus of this paper is to examine key aspects of simulating this case. CORRELATION AND GEOMETRY Correlation is largely perceived to be a statistical phenomena. It is. But it is also a geometric phenomena (Herr, 1980). To see this, we must first view the data in vector form (Halmos, 1974). Let x i be the vector x i