**3.2 Bayesian estimation of survival function for Weibull distribution**

From Eq. (6), according to the squared loss function, the Bayesian estimator for the survival function is [8]:

$$
\hat{\mathbf{S}}(\mathbf{t}) = \int\_0^\infty \mathbf{S}(\mathbf{t}) \, \mathbf{f}(\theta/\mathbf{t}) \, d\theta
$$

$$
\hat{\mathbf{S}}(\mathbf{t}) = \left(\frac{\mathbf{b} + \boldsymbol{\tau}(\mathbf{t})}{\mathbf{b} + \boldsymbol{\tau}(\mathbf{t}) + \mathbf{t}\_i^\emptyset}\right)^{\mathbf{a} + \mathbf{n}} \tag{8}
$$
