Describing a beta probability distribution function for construction simulation

A typical proposed application for a construction simulation model is to assess the productivity of a future operation. This type of application inherently presents the modeler with a situation where there is only a limited amount of data available for choosing an underlying probability distribution function (PDF). This paper presents a formulation for developing a Beta PDF for use in construction simulation modeling. The hypothesis of this paper is that there is a ratio that relates the 75th percentile to the mode of the activity duration. The research demonstrates that using such ratios, along with the minimum, mode, and maximum activity durations, results in estimates of a beta PDF that accurately describes the underlying duration distribution of construction activities. In the methodology proposed here the minimum and maximum activity durations are predicted using deterministic methods based on the physical characteristics of the job and equipment employed. The beta-shaped parameters a and b are estimated using a procedure for fitting beta distributions to activity times when sample data are not available.