Inference for two Weibull populations under joint generalized progressive type-I hybrid censoring with a simulation study and applications

Year 2025, Early Access, 1 - 28

Farha Sultana , Çağatay Çetinkaya , Debasis Kundu

https://doi.org/10.15672/hujms.1501168

Abstract

The generalized progressive censoring scheme has been considered one of the most general
cases of censoring schemes. In this study, we consider two Weibull populations under a
jointly generalized progressive hybrid censoring scheme as a more flexible extension of the
exponential distribution. The methods presented in this paper let experimenters evaluate
life testing studies in the case of the most generalized censoring scheme based on a flexible
distribution that has increasing, constant, and decreasing failure rates. The maximum
likelihood method is used to obtain point estimates of the unknown parameters and the
corresponding approximate confidence intervals by using asymptotic theory and bootstrap
sampling. The Bayesian inferences are handled under informative and non-informative
priors. The highest posterior density credible intervals are also obtained for the Bayesian
estimations. We further obtained results with a challenging task an optimal censoring
scheme using the A-optimality, D-optimality, and F-optimality criterion to let researchers
determine the optimal censoring plan before conducting experiments or collecting data.
Following the numerical results within this paper, A-optimality and D-optimality proposed
the same scheme, while F-optimality proposed a scheme similar to them. In the last part
of the study, we provide simulation studies under different censoring plans and use a
numerical example to exemplify the theoretical outcomes. It is observed that the best
estimation performances are obtained by informative Bayesian methods.

Keywords

Joint censoring scheme, bayes estimation, generalized progressive censoring, type-I hybrid censoring, maximum likelihood estimation, optimal censoring

References

• O. Abo-Kasem and A. Elshahhat, A new two sample generalized type-II hybrid censoring scheme, Am. J. Math. Manag. Sci. 41 (2), 170184, 2022.