Failure modelling is a way to simulate corrective maintenance procedures by calculating the chance of a component working at a given point in time.

Using exponential or Weibull distributions, you can model failures based on real-world data. If you lack real world data, you can use a time series to mimic a Weibull distribution.

Shoreline's failure modelling consists of 5 main steps:

- Define a failure function.
- Define a failure distribution (exponential or Weibull) and parameters (shape, scale, time series).
- Shoresim calculates the probability and cumulative density functions.

- Generate a randomized time to failure (TTF).
- Shoresim applies inverse transform sampling to generate a random number to calculate a TTF according to the distribution described in the failure function.

- Release a work order.
- A TTF countdown begins. The countdown only runs during turbine operational hours. Once the TTF is exhausted, a simulated failure occurs and a corrective maintenance work order is released.

- Generate downtime.
- Vessel and personnel scheduling takes place to resolve the failure. During this period, downtime occurs. Downtime is calculated according to the severity setting you have selected for the maintenance.

- Calculate time-based (TBA) and production-based availability (PBA).
- Shoreline uses the aggregated downtime to calculate the TBA and PBA metrics.
- PBA accounts for critical and scheduled failures.
- TBA accounts for critical, non-critical, and scheduled failures.

# Failure distribution

Shoreline models failures—and hence corrective maintenance tasks—using a Weibull distribution, and by extension exponential distribution.

There are some key differences between Weibull and exponential distributions.

In short, an exponential distribution assumes a fixed rate of failure within the timeframe described. A Weibull distribution offers more flexibility: adjust the shape parameter to model early or late-life failures. A Weibull distribution includes an exponential distribution as a possibility by setting the shape parameter to `=1`

.

## Exponential

An exponential distribution models random events where the time between events follows a constant failure intensity. In the context of wind turbines, this can be the time between failures of a particular component, such as the gearbox or a blade.

### Gearbox example.

If the failure of a gearbox follows an exponential distribution, the probability of failure within a specific time interval is constant. An exponential distribution is characterized by a single parameter corresponding to the average failures per year.

In this case, if the average time between gearbox failures is 5 years (1/5 = 0.2 failures per year), then the exponential distribution assumes that the probability of a gearbox failing within any given year is the same, and it doesn't depend on how long the gearbox has been in operation. The time since the last failure doesn't affect the probability of the next failure.

## Weibull

A Weibull distribution is commonly used in reliability analysis when the failure rate is not constant over time. This distribution provides more flexibility than an exponential distribution by allowing you to model various types of failure patterns, including both early life and wear-out failures.

A Weibull distribution has two parameters: the shape parameter (k) and the scale parameter (η or λ):

- The shape parameter (k) determines the shape of the distribution curve.
- 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) influences the rate of failures.
- This is set using the
`Annual failure rate`

parameter in the Shoreline Design web app.

- This is set using the

Calimo, Weibull PDF, CC BY-SA 3.0

## Failure-rate time series

In addition to exponential and Weibull distributions, you can define variable failure rates using a time series, in which case you set the updates failure rates for each year of operation.

When using a time series, once a failure is corrected and a new time to failure is defined, the system will refer to the failure distribution input for the year the turbine is fixed.

A failure-rate time series is a useful option for when you lack real-world data on component failure rates. Manually defining failure-rate time series values can mimic a Weibull distribution.