Developing and using a new family of project S-curves using early and late shape parameters

Different types of functional relationships have been proposed by many authors to model the cumulative progress curve or the S-curve of a project. They have mostly tried to develop equations which generate a curve having the shape of an S and then tried to mold that into the project of choice. A completely different approach has been used based on a hypothesized behavior of the progress rate of the project. This leads to the development of beta S-curves based on the beta distribution having two parameters. Although beta S-curves have been used earlier for probabilistic forecasting of estimated duration at completion, the early and the late shape parameters of the beta S-curves are explored and ways to estimate these are presented-both before and after the detailed planning have been done. When applied to data from real projects taken from published literature, it was found that the beta S-curves uniformly reported better fit compared to the logistic S-curves.