CHAPTER 9. DATA RESULTS AND DISCUSSION
9.3 Consultancy data
9.3.5 Age of failure
The age of failure for line leaks and tank holes was determined, and the distribution plotted against failures of constant probability. The following section provides further details.
9.3.5.1 Mean age of line and tank failure
Although the number of sites where line leaks and tank holes was recorded as 57 and 35 respectively, the age of failure was not recorded for all these sites. The number of sites where age of failure for line leaks and tank holes was recorded was 40 and 29 respectively. The following graph presents the mean age of failure for line leaks and tank holes.
Figure 9.8 Mean age of equipment failure as a result of line leak and tank holes for biased and non-biased sites (consultancy data). Note high standard deviations.
Figure 9.8 illustrates the mean age of line failure to be 19.5 years. All lines were mild steel or unknown, with the exception of two cases, as described below:
Case 1: The failure of a four year old dual containment non ferrous pipe resulted in the loss of 4 000 L petrol to ground. The incident occurred in 2004 and the cause of line failure was unknown.
Case 2: The loss to ground of 7 000 L petrol was as a result of a failed single containment non ferrous pipe. The site was serviced by submersible pumps and the loss occurred at a buried fusion weld joint not in a junction manhole.
The standard deviation for line leaks was calculated as 9.0 y with a 95% confidence level of 2.9 y.
The mean age of tank failure for the sample population is 23.2 years with a standard deviation of 11.2 y and a 95% confidence level of 4.3 y.
Of the above tank failures, all were mild steel or unknown construction type, with a single key outlier, as follows:
Case 1: Failure of a GRP tank at age 6 years. The exact cause was unknown.
9.3.5.2 Line failure distribution
Cumulative line failures for non-biased sites (n=15) where the age is known have been plotted in Figure 9.9 against cumulative hypothetical / modelled line failure data with the following assumptions and methodology (for the hypothetical data):
The probability of failure was constant.
The population size was calculated based on the total number of sites in the study population that were considered non-biased, where the age was known (n=108).
The probability of failure (failure rate) was determined by calculating the least sum of squares for the actual and hypothetical data. Using Excel Solver, the probability of failure was calculated as 0.004.
Figure 9.9 presents the results:
Figure 9.9 Actual and hypothetical cumulative line failures with age for non-biased sites (consultancy data)
The above data indicates actual line failures to range between ages of 10 years and 32 years. The best fit regression is described by a polynomial distribution and R2 value, as follows:
y = 0.0172x2 - 0.0297x – 0.378 R² = 0.9589
Actual failures are defined by a positive coefficient a (where f(x)=ax2+bx+c) and a concave regression line, while hypothetical line failures with a constant probability have a linear regression line. Results therefore indicate that actual line failures do not occur according to constant probability whereby initial failures are less than the determined constant probability before age 22 years and greater than the determined constant probability after age 22 years.
Line age therefore does influence the likelihood of line failure.
Two likely modes of failure are highlighted, as per the oval shaded areas. Mode 1 indicates few failures before 18 years, while Mode 2 indicates an increasing number of line failures with age. The reason for these two likely modes is unknown. These observations could provide the basis for better modelling.
Distribution of line failures is also presented according to 5 year age categories, as follows:
Figure 9.10 Line failure distribution for all sites (n=40) and non biased sites (n=15) (consultancy data).
Figure 9.10 illustrates the distribution for both data sets, with maximum number of failures between 16 and 30 years. The inclusion of best fit regressions did not provide any meaningful information.
9.3.5.3 Tank failure distribution
Similarly, actual cumulative tank failures (n=14) have been determined for sites where the age is known and for sites with no bias (Figure 9.11). These data are plotted against hypothetical tank failure data (n=108) where, as per the methodology for line leaks, the rate of constant probability has been calculated as 0.003 (according to least sum of squares for the actual and hypothetical data). Figure 9.11 presents the results:
Figure 9.11 Actual and hypothetical cumulative tank failures with age for non-biased sites (consultancy data)
Figure 9.11 indicates that actual tank failures in the sample population occurred between the ages of 5 and 60 years. The best linear regression is polynomial with a negative coefficient a. A relatively good correlation occurs for observed and hypothetical constant probability failures prior to 30 years (Mode 1), however poor correlation thereafter (Mode 2). The actual failure rate is:
less than failures of constant probability prior to age 21 years,
greater than failures of constant probability between ages 21 years and 48 years, and
less than failures of constant probability after age 48 years.
Distribution of tank failures according to 5 year age categories is presented in Figure 9.12.
Figure 9.12 Line failure distribution for all sites (n=29) and non biased sites (n=14) (consultancy data)
Figure 9.12 indicates the distribution of tank failures. The inclusion of best fit regressions did not provide any meaningful information.