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This study investigates arrivals of sanitary sewer overflows collected from a municipality. The data set consists of recorded overflows from 2011 to 2014 during dry weather. Reliability analysis is conducted upon each data set. The Weibull distribution is adopted to evaluate the data sets. The results show that the arrival of dry weather SSOs cannot be simply modeled with a Poisson process that is featured with a constant arrival rate. For annual data set, 2-parameter Weibull generally has an acceptable fitting (except 2014 data). The shape parameters are close to 1 or a little greater than 1, indicating relatively constant arrival rate or slightly increased rate. For the entire data set, the 3-parameter Weibull distribution is able to fit the data well. The shape parameter is also greater than 1. Therefore, an increased SSO arrival rate is noticed for this data set. There are needs to make more efforts in maintaining the sewer system.

The sanitary sewer overflow (SSO) is a condition in which untreated sewage is discharged from a sanitary sewer into the surroundings before reaching to the treatment facility. The cause of SSOs can be of multiple sources, such as blockage of sewer pipelines, infiltration of storm water into the line during rainfall, pump station failures, and broken or collapsed pipe lines. Therefore, in the sewer pipeline management, the sanitary sewer overflow (SSO) is an important indicator of the system’s performance. Such SSOs are common issues to all municipalities. It is meaningful to study such events to assist decision makers in the facility management.

The arrivals of those events may be assumed to random. Such assumption of independent successive events leads to the Poisson process. In a Poisson process, the inter-arrival times display an exponential distribution [

In real life, the homogenous memory-less assumption may not be justified. The prediction may also be conservative [

In the sewer system management, research has been conducted in several directions. In general, it can be categorized into three major concentrations. The first concentration is the reliability analysis of the system. This method focuses on the failure data and explores the reliability through the data analysis. Atypical example is the research conducted by Jin and Mukherjee [

The second category is the condition prediction. The Markov chains model has been applied extensively in this research concentration. For example, Wirahadikusumah et al. discussed several challenging issues in the sewer pipe condition prediction [

The third category can be the life cycle analysis of the sewer system. Both life cycle cost and life cycle assessment have been conducted upon the system. For example, Najafi and Kim compared the life cycle cost of the trenchless and conventional open-cut pipeline [

This research is similar to the study conducted by Jin and Mukherjee [

In order to evaluate the arrival pattern of SSO events, the time to arrival data are explored. Considering that the data ranges from 2011 to 2014, the yearly data 2011, 2012, 2013 and 2014 are firstly explored individually. The entire dataset is also explored later. The Weibull distribution is adopted to investigate the sequences.

The Weibull distribution has been used to characterize time series data when the arrival rates are not constant. They can be used to model the infant mortality with decreasing failure rate, wear-out situations with increasing failure rate. When the rate is found to be constant, it reduces to an exponential distribution. Specifically, the standard Weibull distribution has the density function

and distribution function

where k is the shape parameter, α is the scale parameter. When k = 1, the Weibull distribution becomes an exponential distribution. The arrival rate is constant, therefore, it is a Poisson process. When k > 1, it indicates that the arrival rate increases with time. When k < 1, it means the arrival rate decreases with time.

The 3-parameter Weibull introduces a location parameter location parameter γ. It is used to describe a shift in the distribution. The density function is given by:

and distribution function is

It should be noted that by applying those reliability models, the following assumptions need to be accepted. Firstly, at time zero, all pipes are of equal condition. Secondly, the external impacts are subject to the same condition as well. Strictly, such assumptions can never be applied in real life. However, the application is able to demonstrate meaningful system behaviors [

Figures 1-5 display results for the individual annual data set. For the 2011data set, the shape parameter is 1.28, indicating the arrival rate increases with time. In terms of 2012 data, the shape parameter is 1.14, the SSOs also arrives in an increased rate over this year. However, the increased trend is gentler than that in 2011. In 2013, the shape parameter drops to 1.1, although it is greater than1, considering it is the life data we are dealing with, the arrival of dry weather SSOs can be reasonably regarded as random. In 2014, the data do not fit the 2-parameters very well. The shape parameter is 2.13, which is not reliable due to the poor fitting. A 3-parameter Weibull fits the data decently as shown in

By considering all available data, both the 2-parameter and 3-parameterWeibull distributions are applied. It can be seen from

Shape parameter | Scale parameter | Location parameter | |
---|---|---|---|

2011 data set | 1.28 | 214 | none |

2012 data set | 1.14 | 214 | none |

2013 data set | 1.10 | 219 | none |

2014 data set | 1.49 | 205 | -7.64 |

Entire data set | 1.62 | 872 | 75.1 |

parameter jumps to 1.62. One major cause could be the inconsistency of the 2014 data. The 2-parameter Weibull has a poor fitting. Such also indicates that it is important to combine and categorize data into short time interval (such as annual data set), the approach would help to find the causes of abnormal data.

The dry weather SSOs can be regarded as an important indicator of the sewer pipeline condition. As a result, the analysis upon such SSO data will assist engineers and managers in the facility management. This paper focuses on the SSOs data that are collected from a municipality. The data are treated as annual data set as well as the entire data set. In terms of analysis results, the shape parameter is able to provide useful information. It shows that in some year, the arrival rate of dry weather SSOs shows relatively constant rate, which is an indication that the general condition of the sewer system stays on the steady condition level. In some other year, an increased SSO arrival rate is noticed. Such findings require attention from the sewer systems manager. There are needs to enhance the system’s performance by investing more maintenance efforts.

Kenneth Tuffour,Chris Samba, (2016) Arrival Analysis of Dry Weather Sanitary Sewer Overflows. Open Journal of Civil Engineering,06,462-468. doi: 10.4236/ojce.2016.63038