Robust Inference for Stress–Strength Reliability of the Garhy Distribution Under Diverse Record Schemes with Engineering and Medical Applications

Source abstract

This paper investigates the stress–strength reliability parameter R=P(Y<X) for the Garhy distribution under upper-, lower-, and mixed-record schemes. The Garhy distribution, a flexible one-parameter lifetime model, is shown to provide an excellent fit to precipitation and medical (kidney dialysis) data, with Kolmogorov–Smirnov p-values of 0.9904 and 0.9072, respectively. Maximum likelihood estimators (MLEs) of R are developed, alongside Bayesian estimators using Jeffreys and extended Jeffreys priors under squared error loss. Markov chain Monte Carlo (MCMC) methods are employed for posterior inference. An extensive Monte Carlo simulation study reveals that: (i) MLEs converge under all record schemes but exhibit larger bias and lower efficiency compared to Bayesian estimators; (ii) Bayesian estimators, in contrast, demonstrate superior stability, lower mean squared error, and better bias control, especially for pure upper and lower records; (iii) mixed records consistently yield the most balanced and reliable estimates, capturing distributional information more effectively than single-type records; and (iv) the extended Jeffreys prior provides effective bias correction, outperforming the standard Jeffreys prior in many scenarios. Analysis of real-world datasets confirms the simulation findings, with Bayesian estimators under mixed records producing stable and accurate reliability estimates, outperforming MLE in terms of precision and stability. The results strongly advocate for Bayesian methodology with non-informative priors when assessing stress–strength reliability from record-breaking data.