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    Estimation of the stress-strength parameter under two-sample balanced progressive censoring scheme
    (Taylor & Francis Ltd, 2024) Sultana, Farha; Cetinkaya, Cagatay; Kundu, Debasis
    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 beta and different scale parameters alpha, lambda, 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.
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    Öğe
    Step-stress life-testing under tampered random variable modeling for Weibull distribution in presence of competing risk data
    (Wiley, 2024) Sultana, Farha; Cetinkaya, Cagatay; Kundu, Debasis
    In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step-stress life-testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step-stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co-efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type-II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also.