A single alternative formula for department of health and social security S-curves

The formula most commonly used in the United Kingdom for prediction of cash flows during construction of a building is that published by the Department of Health and Social Security (DHSS). The one empirical formula for the S-curve requires a series of parameters to be used for different contract costs. From a reliability theory approach, an alternative mathematical form, which includes the Weibull function, has been proposed as the basis for the S-curves. This paper demonstrates that not only can the Weibull function be used as an excellent altnerative to the DHSS formula but also that the Weibull function overcomes some of the limitations of the original formula. Relationships between the Weibull parameter values for each of the fits to the set of DHSS curves are derived empirically so that one single formula with a total of seven parameters replaces the DHSS formula and its associated tables for different project costs.