Statistical techniques are described for estimating the number of samples required to monitor the quality of drinking water when the dispersion of bacteria in the water can be modeled by the Poisson or the negative binomial distributions. The concept of the operating characteristic (OC) curve of the water distribution system is presented and is used to evaluate the risk of declaring that the bacteriological water quality regulation is met when only a small portion of the water is analyzed. Assuming that the regulation requires that the monthly mean bacterial counts for samples of standard volume are to be less than one per ml, the OC curves are compared for different sample sizes and for different values of the parameters of the negative binomial. The results indicate that the correct specification of the model is very important in evaluating the risk of sampling (i.e. making the wrong decision). Total bacterial counts based on 1-ml samples, from the cities of Nancy and Metz in France, support the use of the negative binomial as a model for the dispersion of bacteria in drinking water. In the few cases where the negative binomial did not fit the data, the lack of fit can be attributed to the greater occurrence of the frequency of finding only one bacterium in the sample than that expected for the negative binomial. The OC curve indicated that the present monitoring strategy for the city of Nancy is adequate for monitoring the water quality if (i) the regulation requires that the monthly mean of total bacterial counts should not exceed one bacterium per ml, and (ii) the probability of accepting that the water quality is meeting the regulation, when the true mean number of bacteria per ml is two, should not be larger than 0.05. On the other hand, the city of Metz data indicated that it is necessary to increase the intensity of sampling both in time and space in order to achieve the same level of adequacy as that of the city of Nancy.

Bacteria↗

PubMed1985

Heterotrophic bacteria in water distribution systems. I. Spatial and temporal variation.

The drinking water distribution system of the city of Metz in France was sampled intensively during six, monthly surveys which were designed to determine the spatial and temporal distribution of total heterotrophic bacteria in the network. A non-hierarchical nearest-centroid clustering method was used for dividing the water distribution system into zones corresponding to different levels of bacterial density. The general pattern of the spatial heterogeneity showed a high degree of reproducibility. Since the frequency distribution of total heterotrophic bacteria within the zones was compatible with the negative binomial distribution, the water distribution system studied may be considered as being composed of several heterogeneous subsystems. The consistency of this structured spatial dispersion pattern of bacteria in light of some physical and chemical characteristics of the system is evident. In consideration of the principal features of flow in the system relevant to the layout of water mains, the location of zones of highest bacterial concentrations have been attributed to lower levels of chlorine residuals and prolonged retention time of the water in the network, especially in the storage units, before reaching the various distribution areas. Although the monthly variation in the bacterial concentration of the entire system showed a marked increase which was concomitant with warmest water temperatures, the zones were subject to noticeable discrepancies in the range of temporal variation.

Bacteria↗

PubMed1985

Heterotrophic bacteria in water distribution systems. II. Sampling design for monitoring.

In this paper, which is a continuation of the work presented in Part I in this issue, previous information on the spatial and temporal variability of bacteriological data from a water distribution system is used to develop a sampling design for use in future water quality monitoring. The water distribution system is considered to be composed of several zones where the variation of bacterial counts in each zone is modelled by the negative binomial distribution. Under the assumption that the objective of monitoring is to determine whether or not the mean bacterial density of the water exceeds a specific standard, a criterion is given which determines the optimal number of sampling stations allocated to each zone. These stations are determined by assuming that either the risk of sampling (i.e. making the wrong decision) is prespecified or that the total number of stations to be sampled is predetermined. Sequential sampling to evaluate the compliance of the water with the standard is also discussed.

Bacteria↗

PubMed1983

Microplate fecal coliform method to monitor stream water pollution.

A study has been carried out on the Moselle River by means of a microtechnique based on the most-probable-number method for fecal coliform enumeration. This microtechnique, in which each serial dilution of a sample is inoculated into all 96 wells of a microplate, was compared with the standard membrane filter method. It showed a marked overestimation of about 14% due, probably, to the lack of absolute specificity of the method. The high precision of the microtechnique (13%, in terms of the coefficient of variation for log most probable number) and its relative independence from the influence of bacterial density allowed the use of analysis of variance to investigate the effects of spatial and temporal bacterial heterogeneity on the estimation of coliforms. Variability among replicate samples, subsamples, handling, and analytical errors were considered as the major sources of variation in bacterial titration. Variances associated with individual components of the sampling procedure were isolated, and optimal replications of each step were determined. Temporal variation was shown to be more influential than the other three components (most probable number, subsample, sample to sample), which were approximately equal in effect. However, the incidence of sample-to-sample variability (16%, in terms of the coefficient of variation for log most probable number) caused by spatial heterogeneity of bacterial populations in the Moselle River is shown and emphasized. Consequently, we recommend that replicate samples be taken on each occasion when conducting a sampling program for a stream pollution survey.

Analysis of Variance↗