Application of Time-Dependent Fault Tree Models for the Analysis of Project Schedule Failure Conditions

This paper examines calculations of the earliest and the latest possible starting times for various tasks in a project. It considers classical precedence relationships with additional complications involving lead and lag times between tasks. Since the problem of analyzing large network diagrams with complicated relationships can become computationally intractable, there is a need for a mathematical formulation for the solution of this problem that would be transparent and easy to implement. Such a solution is proposed in this paper. It involves an introduction of the fault tree models with time dependencies. Such models were recently introduced in the context of equipment safety analysis and this paper adapts these concepts in the project management field of interest. With this approach it is possible to model by means of special gates not only logical dependencies (e.g. event A and event B must happen so that failure occurs) but also to answer a question 'when A and B should happen for the failure to occur'. Introduction of each new gate is accompanied by a numerical example from a sample project.