Risk Assessment in Drinking Water Production Using Belief Functions

This paper presents an original method for risk assessment in water treatment, based on belief functions. The risk of producing non-compliant drinking water (i.e., such that one of the quality parameter exceeds the regulation standards), is estimated taking into account the quality parameters of raw water and the process line of the treatment plant (technology, different failure modes and corresponding failure rates). Uncertainty on available data (treatment steps efficiency, failure rates, times to repair and raw water quality) is modeled using belief functions that are combined to compute a degree of confidence that the produced water will meet quality standards. The methodology recovers the classical results (obtained by fault tree analysis) as a limit case when uncertainties on input data are modeled by probabilities, and still provides informative results when only weaker forms of knowledge are available. 1 Problem Description The production and distribution of good quality water to consumers is a fundamental issue, given the medical and financial consequences that could result from the delivery of insufficient quality water. It is therefore necessary to set up a treatment process adapted to the raw water to be treated, and to estimate the residual risk of producing water that does not comply with the regulation (in most cases the problem is detected by real time monitoring and the production is stopped, but this induces heavy financial penalties). In the classical approach, this risk assessment process is performed by determining the probability of the undesirable event “production of non-compliant water”, taking into account the quality of the resource to be treated (i.e., the estimated probability to find a given concentration of an undesirable component), characteristics of the treatment unit (efficiency of the treatment steps), as well as different failure modes that can occur in the process line (failure rates and repair times of each mode). Such a process was developed and described in detail in previous papers [5, 1]. One major difficulty in applying risk assessment methods in the environmental engineering domain is that basic data are not perfectly known and are often determined by expert judgement with a high level of uncertainty. In this paper, it is proposed to model the uncertainty on raw water quality, process line efficiency and state of the treatment plant (nominal or failure mode) in the belief function framework. Each source of information will be modeled by a belief function and combined to obtain an assessment of the plausibility to produce non compliant water. In the limit case where the basic belief functions are probabilities, the proposed methodology recovers the results obtained by the classical approach: in that case, the belief function obtained for the variable representing the non compliance of produced water is also a probability measure. In the general case, however, the belief function obtained is no more a probability and it is possible to compute the belief, the plausibility and the pignistic probability to produce non compliant water. These results can be used to estimate a level of confidence to meet contractual requirements with a given treatment plant technology, and therefore to help treatment plant designers to choose the optimal architecture, given an objective level of residual risk. The rest of the paper is organized as follows. The classical methodology is first recalled in Section 2. Our approach is then described in Section 3, and compared to the classical approach in Section 4. Simulations are presented in Section 5, and Section 6 concludes the paper. 2 Classical Approach The following is just a brief reminder of the major concepts described in [5, 1]. The current regulation on potable water takes into accont 62 quality parameters of various types (turbidity, colour, concentration of mineral or organic components, physicochemical properties...). To meet these requirements, the treatment process must be adapted, on the one hand, to the general quality of water, and on the other hand to exceptional pollution peaks. To take into account this resource variability, a treatment plant is composed of the succession of various treatment processes (preoxydation, clarification, polishing, disinfection...). For each quality parameter, the efficiency of each treatment step is represented by a transfer function, giving the output concentration Cout as a function of the input concentration Cin for the considered parameter. In most cases, this transfer function is linear and can be expressed using a single parameter α, called the abatement rate or reduction factor: Cout = (1 − α)Cin. It is also possible to account for nonlinear transfer functions by defining different abatement rates according to the input concentration, but we will not consider that case in this paper. By combining these local transfer functions (established for each treatment step), it is possible to define a global transfer function, which represents the global efficiency of the treatment line for a given parameter. This global transfer function must be determined for the nominal mode of the treatment plant (abatement rate α0) and also for all possible failure modes. The “Failure Modes Effects and Criticality Analysis” (FMECA) methodology allows to determine, for each of the n possible failure modes, the corresponding degraded abatement rate αi, the failure rate λi and the repair time Ti. The probability to be in failure mode i is then pi = λiTi, (1) and the probability of being in the nominal state is given by