In the construction industry, contingency cost continues to elicit discussions in terms of justification for its estimation. Many research works have offered different methods of estimating contingency cost to a certain level of precision. Yet, some of the methods continue to raise representativeness and subjectivity questions. Accordingly, the unseeming aspects of indeterminacy and subjectivity remain irresolute. This paper identified the inherent risks of cost (c) and time (t) of all work items as indeterminate entities of an entire project cost and postulates that they are vectors of uncertainty in a project that gives rise to contingency cost application. The paper theorizes that contingency cost estimation should representatively be contributed by all items unit rate cost on the basis of the difference in their infimium cost (least upper bound and upper lower bound cost) been the threshold values of contractor’s risk absorption extremium accommodated in markup. This is with the aim of diffusing the risk elements (cost and time) of construction projects cost overruns. This process draws semblance with the vanishing properties of scalar products of orthogonal functions. A parallel construct was deduced towards the vanishing response of cost and time overruns that absorbs contingency cost. A unit cost rate of item idealized geometrically as a length aggregated by several disjointed sub cost and time on the basis of their length, their limiting value were idealized to be their infimiums. A foreword dynamically responding partial summation of cost infimium converges by orthogonal properties as a contingency cost estimation model. A valid application lies in the extrapolation of upper and lower threshold values of unit rate cost of all work items and summing their difference which necessarily, this operation can be performed at the total cost point of the construction project.
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