**COMPARISON OF THE PROPORTION OF COLIFORM POSITIVE DRINKING WATER SAMPLES WITH STATISTICAL PARAMETERS FOR LOGNORMAL DISTRIBUTION DESCRIBING COLIFORM CONCENTRATIONS WITHIN THE SUPPLY
Report No FR0462**

APRIL 1994

SUMMARY

I BENEFITS

Describing coliform concentrations within water supply networks as parametric statistical distributions would provide a more informed assessment of water quality than currently allowed by the proportion of failures;

allow more appropriate comparisons of water qualities in different companies;

define the increased risk of detecting coliforms in 100 ml statutory water monitoring samples after failure of treatment processes.

II OBJECTIVES

The objectives are to compare the statistical parameters (geometric mean and logarithmic standard deviation) for lognormal distributions of coliforms with the proportion of coliform-positive samples. In addition, the reliability of the current statutory water quality sampling scheme would be assessed.

III REASONS

Coliform organisms are intermittently detected in 100 ml volume samples from consumer premises in some water supply zones, although the major proportion of samples register 0 per 100 ml. It is probable that coliforms are present in regions of the water supply network where 100 ml samples register zero coliforms. At present, however, little is known about the coliform concentrations in such regions. Furthermore, the water companies have no information on the probability of detecting coliforms on further sampling from those regions. Currently the microbiological qualities of water supply networks are quantified in terms of the proportion of 100 ml volume water samples registering coliforms. Defining coliform concentrations as parametric statistical distributions would allow water qualities to be assessed in terms of a central tendency (geometric mean) and a dispersion (logarithmic standard deviation). At present it is not known whether some water companies report higher coliform compliances because of differences in the geometric mean coliform concentration or the logarithmic standard deviation. Furthermore, the impact on coliform detections of failures in particular treatment processes which increase overall numbers of coliforms could be predicted on the basis of changes in the statistical distributions of coliform concentrations.

IV CONCLUSIONS

The interpretations of the statistical models in this report are theoretical.

Coliform concentration data from statutory water quality monitoring are used to support the models. The main conclusions are:

- Statistical distributions of coliform concentrations within the drinking water supply appear to be lognormal and hence are defined by two parameters, the logarithm of the geometric mean (µ) and the logarithmic standard deviation (ó). The large proportion of samples registering 0 per 100 ml present a problem for parametric statistical analysis. The parameters µ and ó, however, may be estimated from Normal probability plots.
- Large variations in coliform concentration, ranging 13 log (base
10) orders of magnitude in some water supply networks, are
predicted. Coliforms are predicted to exist in regions where
sampling registers 0 coliforms per 100 ml. Extrapolation of Normal
probability plots predicted coliform concentrations ranging as low
as 10
^{-9}in some parts and up to 10^{-1}per 100 ml in other parts where sampling registered less than 1 coliforms in 100 ml. - Defining the effects of treatment works failure on µ and ó will allow prediction of its impact on the proportion of coliform-positive 100 ml volume samples.
- Data from 10 l sampling would provide useful information about samples registering 0 coliforms per 100 ml. In particular, information on multicomponent coliform concentration statistical distributions will be important for assessing the impact that problems at treatment works will make on numbers of coliform-positive samples.
- Differences in geometric means reflect true differences in overall microbiological water quality between different water supply networks. A change in geometric mean reflects a net gain or loss of coliforms (e.g. through regrowth or ingress).
- In theory, the number of coliform-positive 100 ml volume samples increases with increasing geometric mean (assuming constant logarithmic standard deviation). In this case, water quality assessed on the number of coliform-positive samples is representative of overall water quality.
- Differences in logarithmic standard deviation reflect differences in the dispersion of coliform organisms already within the water supply network and measure the degree of heterogeneity of coliform concentrations within different parts. Water supply networks with the same geometric mean but different logarithmic standard deviations do not differ in overall water quality. In theory they have the same numbers of coliforms which are dispersed differently. Changes in ó could result through accumulation of coliforms in certain design features.
- In theory, the proportion of coliform-positive samples increases with increasing logarithmic standard deviation, when the geometric mean is constant. In this case, the differences in the proportions of coliform-positive samples are not representative of changes in overall water quality.
- Assessing water quality on the proportion of coliform-positive samples does not differentiate between changes in geometric mean and changes in logarithmic standard deviation.
- From 1990-92 statutory water quality monitoring data for coliform concentrations, it was found that in general the proportion of coliform-positive samples was related to the predicted geometric mean but not the logarithmic standard deviation. This would suggest that in general, the statutory water quality monitoring programme, in which zones are judged on the proportion of coliform-positive samples, gives a representative assessment of water quality.
- There were, however, cases where predicted geometric means for two companies were similar, but the proportion of coliform-positive samples, and hence compliance at the 5% level, differed because of differences in logarithmic standard deviations. In another example, a small difference in geometric mean between two companies was amplified into a large change in compliance because of the larger logarithmic standard deviation.

V RECOMMENDATIONS

It is recommended that water companies undertake a limited 10 litre sampling programme to assess the statistical distribution of coliform concentrations at this critical concentration region within their water supply networks.

This would provide companies with better information on the effect of treatment failure on coliform compliance and allow more accurate definition of statistical parameters for coliform concentrations. In addition, 10 l volume sampling data may be sufficient to develop predictive models for coliform concentrations from fluctuations in associated factors. Useful information on the impact of failure of a particular treatment process on the proportion of coliform-positive samples and compliance with The Water Supply Regulations (1989) would also be obtained.

VI RESUME OF CONTENTS

Section 1 outlines the need for investigation of statistical distributions of total coliforms within the water supply network. Two parametric statistical distributions, namely the Poisson and Normal distributions, are introduced. In Section 2, a statistical model is developed for coliform concentrations. Methods for improving the model are discussed. In Section 3, the theoretical implications of the model are described in relation to assessing water quality in terms of the proportion of coliform-positive 100 ml volume samples. The practical realities are then assessed in Section 4- using coliform water quality data from the water companies A to I. Conclusions are made in Section 5.

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