Bayesian updating of Copula-based probabilistic project-duration model

This paper presents a generic copula-based method for accurate prediction of probabilistic time performance of projects. The proposed stepwise method first collates all uncertainties of the project activities and propagates them using a Monte Carlo simulation (MCS) in cumulative progress S-curves and commercial project risk analysis software. By fitting the beta distribution function to every normalized simulated progress curve, the corresponding parameters of the so-called Beta-S model can be calculated and the best-fit marginal distribution functions of these parameters, including project completion time, and the correlation matrix can be established. In an innovative approach, a multivariate copula function then is employed to bind the marginal distribution function of these random variables together and produce their prior joint probability distribution as a single closed-form function. The merit of this copula-based function is that it alleviates the incorrect assumption of the independence of random variables in the Beta-S model. The actual progress data of the project are used for efficient Bayesian updating of the model by means of the Metropolis-Hastings (M-H) algorithm. The applicability of the proposed methodology is demonstrated on a project, and it is shown to outperform the existing probabilistic model with independent variables and the earned schedule method as a deterministic method.