Cost estimation of software projects: a sub-additive approach
Keywords:
Software cost estimation, Software risk, Project management, Statistical computing.Abstract
Sub-additivity in estimations suggests that the sum of sub-estimates is a good approximation of the overall estimate; alternatively, an overall estimate decomposes into well represented sub-estimates. Traditionally from probability distributions, estimated costs are percentiles of probability distributions; however, such estimates may not be sub-additive. This paper presents a model which produces sub-additive cost estimates from probability distributions. The proposed model relies on expectations as oppose to percentiles of probability distributions. For bottom-up cost estimation scenarios, the proposed model ensures that sub-estimates are sub-additive such that the sum of sub-estimates is a good approximation of the overall cost. For top-down cost estimation scenarios, the model ensure that the overall estimate is sub-additive and decomposing the overall estimate into sub-estimates provides a good representation of sub-estimates. A case-study proves that the proposed model produces sub-additive estimates for bottom-up and top-down cost estimation scenarios while percentile based estimates are susceptible to sub-additivity. Violation of sub-additivity contributes towards under-estimation of sub-estimates for bottom-up scenarios and over-estimation of overall estimates for top-down scenarios. Therefore, sub-additivity consideration is critical in estimation which helps to avoid understated or overstated estimates.
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