Inverse Gaussian process model with frailty term in reliability analysis

Abstract Traditional reliability analysis techniques focus on the occurrence of failures over time. Nevertheless, in certain cases where the occurrence of failures is tiny or almost null, the estimation of the quantities that describe the failure process is compromised. In this context, we introduce a reliability model for systems adopting the degradation process using frailty. The evolved degradation model has as experimental data, not the failure, but a quality feature attached to it. Degradation analysis can provide information about the lifetime distribution components without actually observing failures. In this paper, we propose an inverse Gaussian process model with frailty as a possible tool to investigate the effect of unobserved covariates. Moreover, a comparative study with the classical inverse Gaussian process based on simulated data was performed, revealing that the asymptotic properties of the maximum likelihood estimators are compromised when the presence of frailty is ignored. The application was based on two real data sets in the literature, showing that the inverse Gaussian process frailty models are propitious to use; however, gamma and inverse Gaussian distributions for frailty present similar results.