Worked Example

A 50 years old Welded Steel (WS) water trunk main in an open country area is assessed in regard to the probability of failure and the optimal timing for replacement. Based on past experience the nominal economical life of the Steel Main is about 80 years, and various profiles of the probability of failure (resulting in catastrophic consequence and requiring the existing water main to be out of service) had been derived from previous failure histories of other similar WS mains.

However, there has not been previous failure records for the particular water main and the operator believes that the water main is generally in good condition relative to other similar pipelines of the same age.

There is a 20% chance that the main will exhibit a late failure profile and 80% chance that it will exhibit the nominal (average) failure profile).

The replacement cost for the water main is estimated to be $400,000 and the consequential cost of failure is $2 million. A new main will improve its reliability and hence lower the probability of failure in the ensuing years.

The opportunity cost of capital is 10%. It is necessary to determine whether it is more economical and the optimal timing to replace the main relative to the expected risk cost before the end of its effective life. The impact of the new main on the future maintenance costs and improved hydraulic condition are not considered.

As illustrated in the table below, six different scenarios were examined:

• Scenario 1: No Replacement
• Scenario 2: Replace in year 6
• Scenario 3: Replace in year 8
• Scenario 4: Replace in year 10
• Scenario 5: Replace in year 13
• Scenario 6: Replace in year 15.

The weighted average probabilities of failure reflecting the level of confidence for each year were first calculated. These are multiplied by the consequential cost of failure to arrive at the expected risk costs for each year. The true expected risk cost for the period is represented by the present value of the incremental risk costs for each year.

The present values under different scenarios are summarized below.

The mains would be replaced if the present value cost of replacement plus the reduced expected risk costs over the remaining life of pipe is less than the present value cost of the expected risk cost without any replacement (Do nothing).

The above table and the graph illustrates that it is more economical to replace the mains provided it is completed within year 9 to year 11 and the optimal timing would be around year 10 (PV minimum).

In addition to replacing the mains other treatment options such as rehabilitation or additional maintenance can be considered by performing similar evaluations. A series of curves representing other options can be plotted and the option with the lowest present value cost adopted.