ABSTRACT
When cost uncertainty analyses are presented to decision-makers, questions often asked are “What is the chance the system can be delivered within cost and schedule?” “How likely might the point estimate cost be exceeded for a given schedule?” “How are cost reserve recommendations affected by schedule risk?” During the past 30 years, techniques from univariate probability theory have been widely applied to provide insight into P(Cost≤ x1) and P(Schedule≤ x2). Although it has long been recognized that a system’s cost and schedule are correlated, little has been applied from multivariate probability theory to study joint cost-schedule distributions. A multivariate probabilitymodelwould provide analysts anddecision-makers visibility into joint and conditional cost-schedule probabilities, such as
P(Cost ≤ x1 and Schedule ≤ x2)
and
P(Cost ≤ x1 | Schedule = x2)
This chapter introduces modeling cost and schedule uncertainties by joint probability distributions. A family of joint distributions (Garvey 1996) has been developed for this purpose. This family consists of the classical bivariate normal and two lesser known joint distributions, the bivariate normallognormal and the bivariate lognormal. Experiences with Monte Carlo simulations suggest these distributions are plausible models for computing joint and conditional cost-schedule probabilities. Appendixes B and C summarize key statistical formulas associated with the bivariate normal-lognormal and bivariate lognormal distributions. Formulas for the bivariate normal distribution are well known and are summarized in this chapter.
