Generalized progressive hybrid censoring schemes have become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T. Otherwise, due to the necessity of more realistic stress strength models, this article considers to estimate the reliability of an s-out-of-k system with non-identical component strengths when component strengths and stress follow Weibull distributions under generalized progressive hybrid censoring scheme. The maximum likelihood estimation of the reliability of such a system is obtained with corresponding asymptotic and bootstrap confidence intervals. Further, Bayesian estimations are derived by using the Lindley's approximation and Markov Chain Monte Carlo method with the Metropolis-Hasting algorithm. The corresponding highest posterior density confidence intervals of the Bayes estimates are obtained. In Bayesian estimations symmetric and asymmetric loss functions are evaluated. Comparisons for the performances of the estimators are made with simulation studies and a real data example.

This article considers the estimation of the stress–strength reliability with non-identical and also jointly censored component strengths. Both stress and strength variables are assumed to follow two-parameter Weibull distribution. In this reliability model, we assume type-II censoring scheme for common stress variable and jointly type-II censoring scheme for strength variables. Inferences for the reliability of this system are obtained with maximum likelihood estimation (MLE) and Bayesian estimation methods. In the Bayesian section, point estimations are obtained with Lindley's approximation and Markov Chain Monte Carlo method with the Metropolis-Hasting algorithm. Also, asymptotic confidence intervals for the MLEs and the highest posterior density credible intervals for Bayesian estimations are obtained. Theoretical outcomes are illustrated with simulation studies and a real data example.

In this study, inference for the power Lindley distribution under a step-stress partially accelerated life test based on progressive Type-II censoring scheme is studied. The maximum likelihood estimates of the parameters and acceleration factor is investigated with their corresponding approximate confidence intervals by using asymptotic theory. The performances of the estimators and their corresponding approximate confidence intervals are evaluated with simulation studies. A real data set is used to illustrate the estimation procedure.

The generalized progressive hybrid censoring schemes (GPHCS) have become quite popular in the case when there are very few failures before pre-determined time T in progressive hybrid censoring schemes. Whereas the GPHCS always ensures a fixed number of failures, which makes this scheme very popular. In this paper, we introduce a new joint generalized progressive hybrid censoring scheme (J-GPHCS) for two independent samples from different populations. We place both the samples simultaneously on the life testing experiment. Further, we assume the lifetime of the experimental units, under both samples, to follow exponential distribution with mean ${\theta }_1$ and ${\theta }_2$, respectively. The maximum likelihood estimators, of the unknown parameters and their exact distributions, are derived. Asymptotic and bootstrap confidence intervals are also constructed. Further, the Bayesian inference of some unknown parametric functions is considered under a very flexible Inverse-Gamma priors. We also obtain the Bayes estimators, and associated credible intervals of the unknown parameters. Extensive simulation studies are performed to investigate the proposed estimators. Finally, the methods are illustrated with the analysis of a real data set.

This article deals with the estimation of the stress–strength reliability model in the event of its strength variable is subjected to the step-stress partially accelerated life test. Inferences for the reliability of such a system are obtained under the assumption that the strength and stress components have one-parameter exponential distributions. Maximum likelihood estimations with their asymptotic and bootstrap confidence intervals are first obtained. Alternatively, the Bayesian estimations with their highest posterior density credible intervals are provided. The performances of the estimators and their corresponding approximate confidence intervals are evaluated using simulation studies. A numerical engineering example is used to illustrate the handled reliability problem.