8 Indexes Provides a means to account for fluctuations in cost over time. Dimensionless numbers that can be used to estimate future or past cost relative to an arbitrarily defined reference year ??= ??(𝐼?𝐼𝑘); kis the reference year, nis the year of estimation, Cis cost, Iis the index value. Maintained and published for a wide variety of industries. Ex. Consumer Price Index (measure of inflation). For a composite of items a weighted average can be used to determine the index for a given year provided that we know the cost 𝐼?=∑?𝑖(??,𝑖?𝑘,𝑖)?𝑖=1∑?𝑖?𝑖=1× 𝐼?For now it is not important how the index value is derived without knowing the costs. Unit Technique Applicable if there is a reliable average for cost (revenue) per unit. To estimate cost multiply per unit cost by number of units. ? = ∑?????Ex. cost of housing per square foot, or digging a ditch per meter for a given soil type. Factor Technique (no included in video) Extension of unit method, where the estimated cost is the sum of directly estimated components and components estimated on a per unit basis. ? = ∑???+ ∑?????; Cis cost, Cdis the cost of any component that can be estimated directly of component m; fmis cost be unit of component m, Umis the number of units of component m. Parametric Cost Estimatingis the use of historical cost data and statistical techniques to predict future costs. Statistical techniques are used to develop cost estimating relationships (CERs) that tie the cost of an item to one or more independent variables. Power-sizing Technique Estimation using the cost of a similar project that takes into account economy of scale. Economy of Scalerefers to reduction in per-unit cost as the number of units increase. As the number of units increase, fixed costs are spreads over more units, lowering the per-unit cost. ??= ??(????)?; Crefers to the cost, Arefers to estimated project, Brefers to known project, Srefers to size of the project, Xis the cost-capacity factor that reflects economy of scale. Cost-Capacity Factor oVaries with each project, and takes complex analysis to calculate the known value. o? < 1implies decreasing economy of scale o? > 1implies increasing economy of scale o? = 1implies a linear relationship of cost with size.