Page 110 - Water Loss Control

92 Cha pte r Se v e n

An infrastructure leakage index close to 1.0 demonstrates that all aspects of a suc-
cessful leakage management policy are being implemented by a water utility. However,
typically it will only be economic to achieve an ILI close to 1.0 if water is very expen-
sive, scarce, or both. Economic values of ILI depend upon the system-specific marginal
cost of real losses, and typically lie in the range 1.5 to 2.5 for most systems.

7.8 The Use of 95% Confidence Limits and Variance
Analysis for Water Audits
The use of 95% confidence limits to validate the degree of uncertainty in individual
components of the water balance is nowadays best practice among qualified water loss
management professionals.
In order to understand the concept of 95% confidence limits, it is first necessary to
understand normal distributions which are an important class of statistical distribu-
tions. All normal distributions are symmetric and have bell-shaped density curves with
a single peak. To speak specifically of any normal distribution, two quantities have to
be specified: the mean μ where the peak of the density occurs, and the standard devia-
tion s, which indicates the spread or girth of the bell curve. Different values of μ and s
yield different normal density curves and hence different normal distributions.
The normal density can be actually specified by means of an equation. The height
of the density at any value x is given by

1 1 −
/
e − (x μσ )
2
σ 2π
Although there are many normal curves, they all share an important property which
is often referred to as the empirical rule:
• 68% of the observations fall within one standard deviation of the mean, that is,
between μ − s and μ + s.
• 95% of the observations fall within two standard deviations of the mean, that is,
between μ − 2s and μ + 2s.
• 99.7% of the observations fall within three standard deviations of the mean, that
is, between μ − 3s and μ + 3s.
Thus, for a normal distribution, almost all values lie within three standard devia-
tions of the mean as can be seen in Fig. 7.6.
Using 95% confidence intervals allows generating a lower and upper limit for the
water balance component. The interval estimate or lower and upper limit gives an indication
of how much uncertainty there is in the volume used for each water balance compo-
nent. The narrower the interval, the more precise is the value used.
The 95% confidence limits also allow for the calculation of the variance related to each
water balance component. Variance is a measure of dispersion around the mean. Compo-
nents with a large variance will have the biggest impact on 95% confidence limit related to
the final result of the water balance. The final derived result of the water balance is the vol-
ume of real losses. This component will have a 95% confidence limit that is an accumulated
value based on the variance related to each component of the water balance. The variance
analysis is based on standard statistical principles of normal distribution and uses the root-
mean-square (RMS) method for accumulation of error on derived values (see Table 7.5).