How we model failures in the simulations

The O&M simulations include a failure model to trigger failures for the corrective maintenance tasks you input on assets in your case. The inputs to the failure model is the lifetime distribution of the failure, which can be modeled with your input parameters for either an exponential or Weibull distribution.

We're then using inverse transform sampling to generate a time to failure (TTF) for that failure based on your defined distribution. When this TTF is higher than the time since last failure of that task on the specific asset a new failure is triggered, and a new TTF is sampled when its repaired.

Below you can read through this logic step by step, and later how we model lifetime distributions.

How we generate failures in the simulations

Shoresim, our simulation engine, triggers failures durting the simulation by following these steps:

1. Define your failure model per corrective maintenance task
   • Select a distribution to use as your lifetime distribution (exponential or Weibull) and its parameters (annual failure rate, shape) for your corrective maintenance task. For exponential distributions you can also input an annual failure rate time series that will adjust the failure rate yearly based on your inputs, if you want to e.g. model a bathtub curve for your failure rate.
   • Shoresim then uses the lifetime distribution you modeled above to calculate the corresponding cumulative distribution.
2. Generate a randomized time to failure (TTF) for your corrective maintenance task
   • Shoresim applies inverse transform sampling to generate a TTF according to the distribution described in step 1. TTF is the time since the last failure when you will have a new failure of the same type occur.
3. Trigger failure
   • When TTF is larger than the time since last failure a new failure is triggered. If it is critical the asset stops and operational time is not counting until it is fixed. If it is non critical the asset is operational and operational time counts, so new failures can still be triggered on the asset. The failure is triggered when operational time + TTF > operational time of last failure
4. Generate downtime
   • When operational time stops downtime and lost production are counted. Lost production depends on whether the failure is critical (100% production loss) or non-critical (production loss from 0%-100%). From the repair work starts (first visit by techs) to the failure is fixed the asset is non operational, and downtime and 100% production loss are counted.
5. Calculate time-based (TBA) and production-based availability (PBA)
   • Shoreline uses the counted downtime and lost production to calculate TBA and PBA.

Lifetime distributions you can use

You can model lifetime distributions using an exponential or Weibull distribution, with corresponding parameters.

Exponential

The exponential distribution only have one parameter, annual failure rate. The annual failure rate can also be modeled as a time series if the annual failure rate changes year by year.

Weibull

The Weibull distribution provides more flexibility to define a lifetime distribution that is shaped different than the exponential distribution, with some components having e.g. bell shaped lifetime across a population, or few failures early in life but more skewed towards the end of life.

A Weibull distribution has two parameters: the shape parameter (k) and the scale parameter (λ), or annual failure rate in our case:

• The shape parameter (k) determines the shape of the distribution.
  • If <1, this indicates early life failures (decreasing failure rate)
  • If >1, this indicates wear-out failures (increasing failure rate)
  • If =1, then the failure rate is constant. This is equivalent to an exponential distribution.
• The scale parameter (λ) or annual failure rate.