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Optimal replacement of water pipes
Author(s) -
Mailhot Alain,
Poulin Annie,
Villeneuve JeanPierre
Publication year - 2003
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2002wr001904
Subject(s) - hazard , constant (computer programming) , minification , exponential function , function (biology) , probability density function , basis (linear algebra) , mathematics , mathematical optimization , statistics , computer science , mathematical analysis , geometry , chemistry , organic chemistry , evolutionary biology , biology , programming language
Pipe breaks are used as indicators of the structural state of pipe network. The approach used considers times to failure between pipe breaks as random variables. Pipe lifespan is divided into two periods, the first one characterized by time‐dependent hazard functions (nonexponential period) and the second one characterized by constant hazard functions (exponential period). Closed‐form expressions have been derived for probability density functions of occurrence of breaks for all break orders as well as expressions for the time evolution of the average number of pipe breaks per unit time. An optimal replacement criterion is defined on a pipe‐to‐pipe basis based on a cost function using conditional probabilities to estimate the expected future costs. Minimization of this cost function leads to a replacement criterion involving hazard functions. When applied to models with constant hazard functions, this criterion identifies a critical pipe break order at which replacement should be made.