Appendix B 383
SE S SE C^1
(^2) + C 22 + C 32 +... + Cp^2
Eq. 10
If the savings (S) estimate is a product of several independently esti-
mated components (C), then
S = Cl × C 2 × C 3 × ... × Cp Eq. 11
the relative standard error of the estimate is given approximately by
SE S
S ≈
SE C 12
C 1 +
SE C 22
C 2 +
SE C 32
C 3 +...+
SE Cp^2
Cp Eq. 12
The requirement that the components be independently estimated
is critical to the validity of these formulas. Independence means that
whatever random errors affect one of the components are unrelated to
errors affecting the other components. In particular, different compo-
nents would not be estimated by the same regression fit, or from the
same sample of observations.
The above formulae for combining error estimates from different
components can serve as the basis for a Propagation of Error analysis.
This type of analysis is used to estimate how errors in one component
will affect the accuracy of the overall estimate. Monitoring resources
can then be designed cost-effectively to reduce error in the final savings
estimate. This assessment takes into account:
- the effect on savings estimate accuracy of an improvement in the
accuracy of each component. - the cost of improving the accuracy of each component.
This procedure is described in general terms in ASHRAE 1991 and
EPRI 1993. Applications of this method have indicated that, in many
cases, the greatest contribution to savings estimate uncertainty is the
uncertainty in baseyear conditions. The second greatest source of error
tends to be the level of use, typically measured by hours (Violette et
al. 1993). Goldberg (1996a) describes how to balance sampling errors
against errors in estimates for individual units in this type of analysis.