Tracking Function for Earned Value in Construction

PDCA analysis is extremely simplified for homogeneous works, if measurement of work can be simplified in generic instances of time. It has been shown that for homogeneous works, measurement of work during ith segment of time Vi = ti Vb {for ti<1}. This can also be extended to show the validity of superposition in work measurement as : Vi+j = ti Vb + tj Vb = Vi + Vj. Hence, measurement functions are linear and due to the absence of intercept, should also be scalable.

This is possible if and only if measurement function Vb = g (x1, x2, x3,… xm) is homogeneous in at least one variable x1, so that g (zj x1, x2, x3,…xm) = zj g (x1, x2, x3,…xm). Thus, the measurement function can be rewritten as Vb = x1. x2…xq j (xq+1,…xm) and is homogeneous in the product function x1. x2…xq. This product function can serve as a quick measure of work at generic instants of time, since it does not involve measurement of all Lebesgue integrals. We shall call this function as a tracking function, q = x1. x2…xq. Therefore, measurement function is Vb = q j (xq+1,…xm) such that zj Vb = zj q j (xq+1,…xm).

For instance, a common measurement function is Vb = NLBDR (N=numbers, L=length, B=breadth, D=depth and R=cost of unit volume). For homogeneous works, there always exist tracking functions in the set of functions {N, NL, NLB, NLBD} which can be used as a quick measure for work during generic intervals of time. Thus for footing concrete, no. of footings may be a tracking function. Similarly, total length of road may be used as tracking function for pavement carpet, total area for plastering and percentage of total volume itself in mass concrete works.

There is a tendency to assume the measurement function itself or percentage thereof as the tracking function. Although, there is no technical error in this assumption, it warrants complete measurement of works in all short intervals of time. It is necessary to keep the tracking function simple in measure albeit under the expense of a complex definition of work package. For instance, conventional measurement of brick masonry in walls by short wall-long wall survey minus deductions is not viable to simple tracking. Length of wall can be used as a tracking function instead of total volume, if wall masonry is defined at instances – below-sill, sill-lintel and above-lintel units with respective deductions applied. The difference is basically that all site quantities are pre-measured and correlated to a unique tracking measure.

Not all measurement functions fall in the category of NLBD measurement. For volume of truncated pyramids in footings, the measurement function is not a product function, which is why the non-tracking component is generalized above as j.

Trivially, the measurement function may also be defined as Vb = S qj j (xq+1,…xm), such that measurement during ith segment of time is the sum of measurements in j works of similar nature. The measurement function here is indeed a summation function. Similarity of works is such that other functional components except tracking function remains constant for all terms of summation. When a work is defined as Vb = q j (xq,…xm), we call the work as a simple work. When the work is a summation of simple works Vb = S qj j (xq,…xm) we call it compound work. In NLBD measurement function for brick masonry in walls, the function may be (N1L1BD + N2L2BD + N3L3BD) for instance, in which case this will be a compound work.