Poisson Process and Its Application to the Storm Water Overflows

The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflow data was obtained from the storm water pipeline of a municipality. The aim is to verify the overflow arrival pattern and check whether the Poisson process can be applied. The adopted method is the analysis over the inter-arrival times. The exponential distribution test is conducted on the annual data set as well as the entire data set. The results show that all data sets follow the exponential distribution. With the verification of Poisson process, specific examples are also given to show how the Poisson process properties can be used in the management of storm water pipeline management. For other data that are featured with various heterogeneities, the homogenous Poisson process might not be able to be verified and used. Under such circumstances, non-homogenous survival model can be used to simulate the arrival process.

Analysis of Water Pipeline Breaks

This study explores the arrivals of water pipeline break failures. The aim is to assist the facility manager in the decision making process. Based on characteristics of the data set ranging from 2011 to 2014, two steps of analysis were presented in the paper. This first step is the analysis of partially complete data set (2011 data). The 2-sample KS test is adopted to check the similarity between this data set and the entire data set with no underlying distribution implied. In order to conduct the reliability analysis, the Weibull distribution is adopted to evaluate the data. For annual data set, the 2-parameter Weibull distribution fits data sets pretty well. The shape parameters are a little greater than 1, indicating a slightly increasing arrival rate of such failures. For the entire data set, the 3-parameter Weibull tends to fit the data better than the 2-parameter Weibull. The shape parameter is well above 1, indicating an increasing arrival rate of the failures. To eliminate the impact of missing points for the 2011 data set, data from 2012 to 2014 were also considered as a new set, the Weibull distribution generated a decent fitting. The shape parameter is a little greater than 1. Therefore, there is a slightly increasing arrival rate of those pipeline failures. Results from this study provide decision makers valuable information in terms of whether additional efforts shall be made to enhance the system’s performance in order to reduce the failure rate.

Arrival Analysis of Dry Weather Sanitary Sewer Overflows

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.