# Certainty Level of Water Delivery of the Required Quality by Water Supply Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}test. Yet, the authors advised being careful while interpreting the results of this probabilistic methodology for the assessment of water quality.

## 2. Methodology

- —set of research points (observation points of the monitoring) (P
_{m}) - $i\in \left\{1,2,\dots ,m\right\}={P}_{m}$—ith research point
- —set of water quality parameters (W
_{n}) - $j=\left\{1,2,\dots ,n\right\}={W}_{n}$—jth water quality parameter

_{ij}is a random (one-dimensional) variable defining the value of the jth water quality parameter at the ith research point of the known distribution function ${F}_{ij}(x):=P({X}_{ij}\le x),\begin{array}{c}\end{array}x\in R$ and X

_{i}= (X

_{i}

_{1}, X

_{i}

_{2}, …, X

_{in}) is an n–dimensional random variable defining the values of water quality parameters at the ith research point of the distribution function given by the formula

_{i}

_{1}, X

_{i}

_{2}, …, X

_{in}, we obtain

_{j}denote a standard (critical, unsurpassable, normative) value of the jth water quality parameter, then the probability of normative water quality at the ith research point is

_{ij}is the empirical probability of non-surpassing the required level of the jth water quality parameter at the ith research point within a given time interval; k

_{ij}is the number of results of water quality tests obtained at the ith research point out of K

_{ij}which do not comply with the required water quality on the basis of the jth quality parameter x; and K

_{ij}is the number of all test results of water quality on the basis of the jth quality parameter taken at the ith research point.

## 3. Results and Discussion

^{3}/day. In this area, water quality indicators are monitored at 12 points. The distribution of the water quality testing points is shown on the city map in Figure 1.

## 4. Conclusions

## Author Contributions

## Research Impact Statement

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distribution of water quality monitoring points in the analyzed area of the distribution system. R1, R2, …, R12—points of water sampling for testing, ◄ P—supplying the zone with water (pumping station).

**Table 1.**(Normative) values of microbiological water quality parameters according to WHO Guidelines [48] used in the calculation example.

Water Quality Parameter | Value of Water Quality Parameter |
---|---|

Number of coliform bacteria in 100 mL of water not higher than (LBC) | 0 |

Number of fecal coliform bacteria in 100 mL of water not higher than (LBCK) | 0 |

**Table 2.**Estimation of empirical probability estimators F

_{ij}of the normative value of the jth microbiological parameter of water quality at the ith research point according to WHO standards.

Research Point “I” | Number of Coliform Bacteria in 100 mL of Water (j = 1) | Number of Fecal Coliform Bacteria in 100 mL of Water (j = 2) | ||||
---|---|---|---|---|---|---|

A | N | F_{ij} | A | N | F_{ij} | |

1 | 25 | 0 | 1 | 25 | 0 | 1 |

2 | 27 | 0 | 1 | 27 | 0 | 1 |

3 | 21 | 0 | 1 | 21 | 0 | 1 |

4 | 44 | 0 | 1 | 44 | 0 | 1 |

5 | 25 | 0 | 1 | 25 | 0 | 1 |

6 | 2 | 0 | 1 | 2 | 0 | 1 |

7 | 23 | 0 | 1 | 23 | 1 | 0.956 |

8 | 25 | 0 | 1 | 25 | 0 | 1 |

9 | 1 | 0 | 1 | 1 | 0 | 1 |

10 | 28 | 0 | 1 | 28 | 0 | 1 |

11 | 1 | 0 | 1 | 1 | 0 | 1 |

12 | 2 | 0 | 1 | 2 | 0 | 1 |

_{ij}—probability estimated from Equation (6).

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**MDPI and ACS Style**

Kwietniewski, M.; Miszta-Kruk, K.; Niewitecka, K.; Sudoł, M.; Gaska, K. Certainty Level of Water Delivery of the Required Quality by Water Supply Networks. *Int. J. Environ. Res. Public Health* **2019**, *16*, 1860.
https://doi.org/10.3390/ijerph16101860

**AMA Style**

Kwietniewski M, Miszta-Kruk K, Niewitecka K, Sudoł M, Gaska K. Certainty Level of Water Delivery of the Required Quality by Water Supply Networks. *International Journal of Environmental Research and Public Health*. 2019; 16(10):1860.
https://doi.org/10.3390/ijerph16101860

**Chicago/Turabian Style**

Kwietniewski, Marian, Katarzyna Miszta-Kruk, Kaja Niewitecka, Mirosław Sudoł, and Krzysztof Gaska. 2019. "Certainty Level of Water Delivery of the Required Quality by Water Supply Networks" *International Journal of Environmental Research and Public Health* 16, no. 10: 1860.
https://doi.org/10.3390/ijerph16101860