Planning and executing a successful capital project is one of the main objectives of every public agency. A successful capital project is defined as a project completed in accordance with a given scope, within budget, and on time. Due to risks associated with complex projects, an owner agency usually adds an amount known as contingency to the estimated project cost to absorb the monetary impact of the risks and to prevent cost overrun. However, studies show that large capital infrastructure projects, especially transit projects all around the globe have been mostly experiencing cost and schedule overruns. Despite all efforts and evolving new probabilistic methods to establish sufficient and optimum contingency budget, many agencies have not been able to provide adequate contingency for their large capital projects. For instance, nearly 50% of the large active transportation projects in the United States overran their initial budgets. Some agencies have reacted to this issue by employing approaches that result in too large a contingency budget. Having too much contingency can be just as undesirable as insufficient contingency, especially where the agency is dealing with a portfolio of projects rather than a single project. Assigning large contingencies will use up the agency's budget and will reduce the number of projects that may receive funding.

In this research, a new probabilistic model is proposed for calculation of contingency in a portfolio of construction projects. A Bayesian approach is used to update historical contingency values based on new project data that becomes available as construction projects are completed. Most agencies dealing with a portfolio of infrastructure projects should define the level of confidence γ for the portfolio budget based on available funding and the agency's policy goals. An important question is what level of confidence η is needed at the individual project level to insure that the portfolio budget will not overrun with a probability of more than 1–γ. This information is indispensable for the conduct of probabilistic risk assessment for individual projects.

The mathematical model developed in this research provides an analytical tool for calculating contingency levels in such a way to meet agency goals with respect to individual projects and the project portfolio. The model assumes a hybrid normal distribution for the cost of individual projects and uses the historical data to calculate the primary parameters of the model. The model defines the required confidence level for the risk assessment of individual project with respect to the desired confidence level for sufficiency of the portfolio budget. The required increase in the portfolio budget is calculated based on the desired confidence level. The correlation between costs of projects is recognized and a structured guideline along with a mathematical method is suggested for estimating correlation coefficients between costs of projects in the portfolio. To consider the recent performance of projects and to update model characteristics based on new project data that becomes available, a Bayesian approach is employed to update the model on regular intervals, such as once every two years. As more information becomes available, the required adjustment in portfolio budget will be reduced, because the accuracy of estimating the contingency is improved. The proposed model is an effective tool for the agencies to develop contingency budgets based on all the performance data historically available and the new data that becomes available in the future. Even though the proposed model is a generic model that can be used on any type of infrastructure projects, our emphasis in this research is mostly on transit projects. Because of this, the funding process for the Federal Transit Administration (FTA) is analyzed and the practical application of the model is based on transit projects' characteristics and costs.