For a given symmetric random variable \(Z\) on \(\mathbb{R}\), a random variable \(T\) with the corresponding generalised Birnbaum-Saunders distribution (with parameters \(\alpha\) and \(\beta\)) is defined by \[ T=\beta\left(\frac{\alpha Z}{2}+\sqrt{\left(\frac{\alpha Z}{2}\right)^2+1}\right)^2\,. \] The authors investigate the properties and estimation of the failure rate of this random variable \(T\) in the cases where \(Z\) has either a standard normal, logistic or Student’s-\(t\) distribution. This includes a simulation study and application to real-world data.