V is for… variability

Consultant James Finley considers approaches that help deliver understanding of variability in relation to assets.

Consultant James Finley considers approaches that help deliver understanding of variability in relation to assets.

We are living in variable times, whether it be variability in the cost of our future energy bills or variability in the weather.

Variability also persists in the context of asset integrity. For example, a nuclear reactor may be operated under a variety of different conditions, or reactors may feature subtle differences across different sites. In addition, there may be inherent variability in the reactor materials which cannot be changed.

In most cases, the effects of variability are captured by simply considering the most onerous design conditions, and by applying reserve factors to a design. However, this approach can often lead to overly conservative solutions which feature significant weight, cost, or performance penalties. Furthermore, can we really be sure that our designs remain conservative under every combination of design conditions?

The first step to better understanding the influence of variability is to quantify the variability in the input variables. For example, a client may want to understand whether a nuclear reactor component will operate for ten years without failure. When calculating the life of a reactor component, the component life will be strongly influenced by the operating temperature, operational loads, and the material properties; each of these conditions will likely feature variability, which can be expressed using a probability distribution.

Once we have quantified the variability in the input variables, we can use probabilistic methods to approximate the probability distribution of the required output(s) (which in this example may be the component life). The simplest means to achieve this is via a Monte-Carlo analysis. This approach samples the probability distribution of each input, and calculates the output using a conventional lifing analysis method. The analysis is then repeated many times and the results are aggregated to approximate a probability distribution of the output.

Calculating the probability distribution of an output has many benefits. In the context of structural integrity analysis, the probability distribution of the component life can be directly linked to the risk of failure. For example, if a client requires 99% of components to have a life greater than ten years, a probabilistic approach can directly inform the client whether their components will meet this requirement. On the other hand, a deterministic analysis with a reserve factor applied will reveal very little detail to the client about the integrity risk of the component.

Further value can be added to a probabilistic analysis by considering historic data. For example, if several reactor components are known to have operated for a significant time, the failure of these components is conditional on any defects observed during inspections. Bayesian statistics can then be used to modify the probability distribution of the component lives, conditional on the inspection findings. This approach can then provide further value to clients by quantifying the integrity risk of life extension.

There are many ways in which probabilistic analysis methods can help you get to grips with variability in this world. I would be very interested to hear how tackling variability could help you in your role.

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