Alternate Approach to Civil Interval Factor Estimation (Step 9)

Find below additional details for Step 9 of the Civil RBI Methodology.

The interval factor allows a safety margin between the maintenance or inspection tasks to allow for uncertainty in the prediction of useful or remnant asset life. Overstating the interval factor can incur significant economic consequences as the asset may fail well within the predicted remnant life. Understating the interval factor may result in extensive or unnecessary maintenance and inspection tasks. The proposed method is contingent on the availability of historical data on the condition of an asset or group of similar assets. This approach can have value as asset registers are developed and updated as well as if there is structural health monitoring of civil assets.

For the interval factor, we ask ourselves: “how well can we predict the future, using the presently available information?”. Here we try to relate the degradation rate to the inspection interval as well as our knowledge about the asset to reach a subjective conclusion about the interval factor. Here we try to implement a maintenance/inspection task before the asset transitions to other marginal states. For example, we may wish to perform maintenance/inspection on a critical asset before it transitions from state 2 to 5 in the following table.

Table : Asset States

If there were prior data on the asset or group of assets on the condition or state of the civil asset for a fixed inspection interval, then we would be able to estimate the probability of transitioning from one state to some other state or the interval factor. The description of the process is as follows:

Let N_i,j be the number of observed transitions from state i to state j for a defined inspection interval t (years) for t>0 and n={1,2,3….N} assets according to the grouping in the Definition of the Scope; Let S = {1,2,3,4,5} be the set of state conditions as outlined in the above table; For a sufficient number of observations on transitions from state i to state j for t, we can approximate the transition probability from state i to state j to be:

Now consider the table for Remnant Life (RL) estimation. We may wish for the inspection interval, t, to coincide with the estimated RL:-

Table : Remnant Life estimate.

For each inspection interval, t = {1,2,7,12,17}, we observe a number of transition from state i to state j (N_i,j) such that we can develop the following table:

Number of transitions from state i to j:

We may be able to create tables for remnant lives of 1,2, 12, and 17, respectively. Note that the table also captures the effect of maintenance of the asset.

In applying equation 1, we can now obtain the transition probability from state i to state j (P_i,j) for a remnant life of 13 years under the assumption that the degradation rate remains constant.

Transition probability from state i to j:

The probability or confidence in the remnant life estimation is now based on hard data points represented in the transition from the prior state to the current state and thus reduces the uncertainty in the estimation of the remnant life interval. The confidence or probability value represents how well we can predict the future, given the present measurement. The table also captures the transition to a better condition as a result of a maintenance intervention.