The use of historical data for estimating the number of samples required for monitoring drinking water.
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.
D001419:Bacteria / Q000302:isolation & purification*; D008954:Models, Biological; D013223:Statistics as Topic; D014871:Water Microbiology; D014881:Water Supply / Q000592:standards*