Aims
Investigate automated determination of correlation between pairs of cost equations Yi and Yj, where there are N equations (cost components) and i<j.
Transfer the resultant matrix of correlations to the cost risk algorithm to permit calculation of actual cost spreads for lowest level cost components, intermediate cost aggregations and, finally for the LCC aggregation.
Definitions
Correlation between a pair of cost elements ((Rho (i,j)) is the effect that a variation in the value of one has on the value of the other, due to each being a function of common variables and, thus, are dependent to some degree.
Correlation (Rho) is expressed as an index; Rho = {1 or -1} for perfect correlation (total interdependence), for zero correlation (total independence) and somewhere between -1 and 1 for partial correlation.
Objective
The objective is to determine the most likely spread of the Life Cycle Cost (LCC) about the nominal value, given that:
- LCC is an aggregation:
- directly, of cost components at the lowest indenture level, or
- indirectly, of lower level sets of aggregated aCosts;
- an aggregated cost is the correlated sum of subordinate, lowest level cost components (at the lowest indenture level).
- each lowest level cost component may vary about its nominal value according to its individual risk spread; and
- that the risk spread of an aggregated cost will be a function of the correlation between all lowest-level subordinate cost pairs.