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

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.

KEYWORDS:

• Bayesian inference
• maximum likelihood method
• reliability data applications
• statistical model
• simulations

Disclosure statement

No potential conflict of interest was reported by the authors.

CRediT author statement

Badamasi Abba: Conceptualization, Methodology, Software, Data curation, Formal analysis, Writing—Original draft preparation. Hong Wang: Conceptualization, Software, Supervision, Validation, Reviewing and Editing, Funding Acquisition. Mustapha Muhammad: Conceptualization, Methodology, Software Validation, Writing-Reviewing and Editing. Hassan S. Bakouch: Conceptualization, Validation, Writing—Reviewing and Editing.

Supplementary data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/16843703.2023.2193771.

Additional information

Funding

The work was supported by the National Statistical Scientific Research Project of China [2022LZ28]; Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong, Shenzhen [B10120210117-OF04]; Changsha Municipal Natural Science Foundation [kq2202080].