Keywords: loglogistic distribution, water consumption, water distribution systems, stochastic modelling, risk-based design.

Water distribution systems are normally designed based on the consumption that would occur during the peak day of the year together with fire-fighting flows. Obviously, demands should also be satisfied during the peak hour. The conventional design approach does not make explicit use of safety factors or the more comprehensive methods of risk-based design. However, there is general recognition of the inherent uncertainty about the levels of water consumption and the need to allow for the possible unavailability of the components of water distribution systems due to electromechanical failures or because of maintenance. Consequently, water distribution systems (WDS) are generally over designed, with the margin of safety being unknown.

Also, while design optimization methods can yield more economical designs, the demands upon which the designs are based do not have any explicit factors of safety or estimates of exceedance probabilities in general. Risk-based assessments are being used increasingly in the design of major water resources projects [1]. As such, the traditional approach of unquantified overdesign of WDS would appear to be questionable. Therefore, studies of short-term and random variations in water consumption are needed so that suitable statistical distribution models can be found. The models, in turn, would assist in the estimation of exceedance probabilities and the assessment and management of risks.

It is often assumed that variations in water demands in drinking water distribution systems follow the normal or other distributions, usually with little justification. Bao and Mays [2] were concerned with the reliability of water distribution systems. Due to the uncertainty associated with the choice of distribution model, they carried out sensitivity analyses using 10 distributions. Khomsi et al. [3] were interested in the performance of WDS and analysed daily water consumption in the South West of England. They concluded that the normal provided the best fit to the data. Xu and Goulter [4] assumed that demands were normally distributed in order to develop a stochastic reliability model for WDS. Lansey et al. [5] used a similar assumption in an attempt to include uncertainties in their WDS design model.

There is insufficient reliable data regarding the suitability of various distributions for the modelling of water demands. In this study, a new distribution, the loglogistic distribution, for modelling short term fluctuations in water consumption was assessed and the results compared to the normal and lognormal distributions. Daily water consumption data for two areas in the UK were analysed. The results show that the three distributions used might give acceptable results under certain circumstances. However, the main conclusion based on the data and distributions used is that the loglogistic distribution is the most suitable for modelling short-term variations in water consumption. Indeed, the loglogistic distribution provided a far better fit than the normal and/or lognormal. Finally, it seems on the basis of the results that further research on the proposed new application of the loglogistic distribution would be desirable.

1

McCuen, R.H., "Do Water Resources Engineers Need Factors of Safety for Design?", Journal of Water Resources Planning and Management, ASCE, 127(1), 4-5, 2001. doi:10.1061/(ASCE)0733-9496(2001)127:1(4)

2

Bao, Y. and Mays, L.W., "Model for Water Distribution System Reliability", Journal of Hydraulic Engineering, 116(9), 1119-1137, 1990. doi:10.1061/(ASCE)0733-9429(1990)116:9(1119)

3

Khomsi, D., Walters, G.A., Thorly A.R.D. and Ouazar, D., "Reliability Tester for Water Distribution Networks", Journal of Computing in Civil Engineering, ASCE, 10(1), 11-19, 1996. doi:10.1061/(ASCE)0887-3801(1996)10:1(10)

4

Xu, C. and Goulter, I.C., "Probabilistic Model for Distribution Reliability", J. Water Resources Planning and Management, ASCE, 124(4), 218-228, 1998. doi:10.1061/(ASCE)0733-9496(1998)124:4(218)

5

Lansey, K., Duan, N., Mays, L. and Tung, Y.-K., "Water Distribution System Design under Uncertainties", Journal of Water Resources Planning and Management, ASCE, 115(5), 630-645, 1989. doi:10.1061/(ASCE)0733-9496(1989)115:5(630)

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