A robust bathtub-shaped failure time model for a two-component system with applications to complete and censored reliability data

Abstract

ABSTRACT This article proposes a flexible additive model that adequately describes complex reliability and survival data. The proposed methodology, referred to as the flexible exponential power-Gompertz (FEPG4) distribution, is able to characterize the behavior of a complex system whose failure times have bathtub-shaped, with clear burn-in and wear-out change points and a low, yet lengthy, flat middle segment as its underlying failure rate distribution. We discuss some properties of the model. Parameter inferences are proposed under maximum likelihood and Bayesian techniques. We determine the Bayes estimators of the FEPG4 parameters and used Hamiltonian Monte Carlo for posterior simulations. Extensive simulation experiments are performed to validate the proposed estimators. For assessing the potential of the FEPG4, the model is compared with other recent bathtub distributions constructed via the same approach on devices’ failure and running times (censored and non-censored case) and failure times of some devices, each with the bathtub failure rate. Seven parametric and non-parametric selection criteria and other supporting plots are utilized for comparison purposes. Findings indicate that the FEPG4 model might be the best alternative for representing device failure times, particularly when the bathtub-shaped failure rate of the available data clearly illustrates its three phases.