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Table 2

The results of trend analysis of the failure rate indexes λ of the tested water pipelines in the multi-year period of 2007–2017

ZonepVar(S)Z p*Var*(S)Z*
For months 
0.126 180,086 − 1.53 1.00 0.126 180,086 −1.53 
0.387 241,998 −0.87 1.39 0.462 335,928 −0.74 
0.000 241,338 −5.09 1.00 0.000 241,338 −5.09 
0.965 230,483 0.04 0.54 0.952 124,118 0.06 
0.018 233,086 −2.37 2.80 0.157 652,573 −1.42 
0.008 251,174 −2.67 1.25 0.017 314,979 −2.38 
0.000 240,929 −3.57 1.82 0.008 438,742 −2.65 
For seasons 
0.385 9,111 −0.87 1.00 0.385 9,111 −0.87 
0.596 9,614 −0.53 1.00 0.596 9,614 −0.53 
0.000 9,660 −4.02 1.00 0.000 9,660 −4.02 
0.774 9,514 −2.87 1.16 0.789 11,053 −2.66 
0.066 9,552 −1.84 0.41 0.004 3,903 −2.88 
0.019 9,681 −2.34 1.00 0.019 9,681 −2.34 
0.016 9,607 −2.42 1.00 0.016 9,607 −2.42 
ZonepVar(S)Z p*Var*(S)Z*
For months 
0.126 180,086 − 1.53 1.00 0.126 180,086 −1.53 
0.387 241,998 −0.87 1.39 0.462 335,928 −0.74 
0.000 241,338 −5.09 1.00 0.000 241,338 −5.09 
0.965 230,483 0.04 0.54 0.952 124,118 0.06 
0.018 233,086 −2.37 2.80 0.157 652,573 −1.42 
0.008 251,174 −2.67 1.25 0.017 314,979 −2.38 
0.000 240,929 −3.57 1.82 0.008 438,742 −2.65 
For seasons 
0.385 9,111 −0.87 1.00 0.385 9,111 −0.87 
0.596 9,614 −0.53 1.00 0.596 9,614 −0.53 
0.000 9,660 −4.02 1.00 0.000 9,660 −4.02 
0.774 9,514 −2.87 1.16 0.789 11,053 −2.66 
0.066 9,552 −1.84 0.41 0.004 3,903 −2.88 
0.019 9,681 −2.34 1.00 0.019 9,681 −2.34 
0.016 9,607 −2.42 1.00 0.016 9,607 −2.42 

p is test probability, Var(S) is variance, Z is standardized test statistic, represents a correction due to the autocorrelation, p* is correction of the test probability, Var*(S) is correction of the variance, Z* is correction of the standardized test statistic.

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