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In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher's information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

The joint censoring scheme is of great importance when the motive of study is to compare the relative merits of products in relation of their service times. In last few years, progressive censoring received considerable attention in order to save cost and time of the experiment. This paper deals with inferences for Lindley populations, when joint progressive type-II censoring scheme is applied on two samples in a joint manner. Here, the maximum likelihood estimators of parameters are derived along with their associated confidence intervals which are dependent on the Fisher's information matrix. The boot-p and boot-t confidence intervals are also obtained. Bayes estimators of the unknown parameters assuming gamma priors are calculated. The concept of importance sampling technique and Gibbs sampling technique are used as the Bayes estimators cannot be calculated in closed form. HPD credible intervals are also constructed. A Monte Carlo simulation study is performed to measure the efficiency of the estimates. A real data set is given for illustrative purpose. Finally some criteria for an optimum censoring scheme are discussed. [ABSTRACT FROM AUTHOR]

This paper develops the Bayesian estimation for the Birnbaum–Saunders distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration. [ABSTRACT FROM AUTHOR]

In lifetime experiments, sometimes censoring is inevitable to save experimental cost and to accelerate execution of the test. For conducting a comparative lifetime experiment of the products, which are from different production lines under the same environmental conditions, the joint type-II censoring scheme is practically much significant. The present article deals with inferences, when jointly type-II censored sample is taken from k Lindley populations. The maximum likelihood estimators of the model parameters are derived with their asymptotic confidence intervals and log-transformed asymptotic confidence intervals. The boot-p and boot-t confidence intervals are also calculated. In order to evaluate the impact of prior information, the parameters are estimated in Bayesian framework based on balanced loss function assuming the informative and non-informative priors. Since the expressions for Bayes estimates cannot be obtained in closed form so the importance sampling and the Gibbs sampling techniques are used. Finally, a Monte Carlo simulation study and a real dataset are given to exemplify all the methods of estimation developed here. [ABSTRACT FROM AUTHOR]