# Decision Support Models for Operations and Maintenance for Offshore Wind Farms: A Review
## 2 Operation and Maintenance: Influential Factors
### Degradation and Failure Modeling
}\mathrm{e}^{-\lambda t}\)), where the time intervals between failures are exponentially distributed, according to a given failure rate \(\lambda\). In some models, the failure rate can be updated, leading to an inhomogeneous Poisson process, with a failure rate function \(\lambda(t)\). Other distributions that are being used to sample the time between failures are the Weibull distribution (the Weibull distribution is a continuous probability distribution with density function \(f(x)=\frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}\mathrm{e}^{-(x/ \lambda)^{k}}\)), Gamma process (A Gamma process is a stochastic process, comprised of increments that are independently Gamma distributed, with density functions: \(f(x)=\frac{\lambda^{3t}}{\Gamma(\gamma t)}\mathrm{\Sigma}^{\gamma t-1}\mathrm{ e}^{-\lambda x}\), where \(\Gamma(\cdot)\) is the Gamma function.) and Bernoulli process (A Bernoulli process is a discrete stochastic process taking two different values and is comprised of a sequence of binary random variables). A summary of the different methods used to model degradation and failures in the literature is presented in Table 2. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Publication** & **Failure Modeling** & **Degradation Modeling** & **Number of Components** \\ \hline [PERSON] et al. [28] & operational data & & \\ \hline [PERSON] et al. [29] & & updated failure rates & \\ \hline [PERSON] and [PERSON] [10] & & damage growth function & \\ \hline [PERSON] et al. [11] & Markov chain, Poisson distributed failures & Weibull distributed failure rate & 4 \\ \hline [PERSON] et al. [30] & Poisson distributed failures & Weibull distributed failure rate & \\ \hline [PERSON] et al. [12] & Poisson process & & 12 \\ \hline [PERSON] et al. [14] & Weibull distributed failures & & \\ \hline [PERSON] et al. [15] & & & 4 \\ \hline [PERSON] and [PERSON] [16] & Bernoulli process & & 3 \\ \hline [PERSON] and [PERSON] [31] & component specific failure rate & updated based on data & \\ \hline [PERSON] et al. [17] & non-homogeneous Poisson process & Weibull distributed failure rate & 19 \\ \hline [PERSON] and [PERSON] [32] & Poisson process & Gamma process & bearings only \\ \hline [PERSON] et al. [19] & Bernoulli process & & 3 \\ \hline [PERSON] et al. [20] & component specific failure rate & & \\ \hline [PERSON] and [PERSON] [21] & non-homogeneous Poisson process & Weibull distributed failure rate & 19 \\ \hline [PERSON] et al. [33] & occurrence probability & & including errors \\ \hline [PERSON] et al. [22] & Poisson process & time-based and random & \\ \hline [PERSON] et al. [34] & Weibull distributions & & 4 \\ \hline  & discrete deterioration: Markov process & & \\ [PERSON] and [PERSON] [35] & & continuous deterioration: Wiener process, Gamma process and Inverse Gaussian process & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: This table summarizes the methods used for degradation and failure modeling presented in the literature.