Based on progressively Type-II censored samples, this paper deals with the estimation of multicomponent stress-strength reliability by assuming the Kumaraswamy distribution. Both stress and strength are assumed to have a Kumaraswamy distribution with different the first shape parameters, but having the same second shape parameter. Different methods are applied for estimating the reliability. The maximum likelihood estimate of reliability is derived. Also its asymptotic distribution is used to construct an asymptotic confidence interval. The Bayes estimates of reliability have been developed by using Lindley's approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The uniformly minimum variance unbiased and Bayes estimates of reliability are obtained when the common second shape parameter is known. The highest posterior density credible intervals are constructed for reliability. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.

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Based on independent progressively Type-II censored samples from two-parameter Rayleigh distributions with the same location parameter but different scale parameters, the UMVUE and maximum likelihood estimator of R = P (Y < X) are obtained. Also the exact, asymptotic and bootstrap confidence intervals for R are evaluated. Using Gibbs sampling, the Bayes estimator and corresponding credible interval for R are obtained too. Applying Monte Carlo simulations, we compare the performances of the different estimation methods. Finally we make use of simulated data and two real data sets to show the competitive performance of our method. 1 further details on progressive censoring schemes and relevant references, the reader is referred to the book by Balakrishnan and Aggarwala [4].In reliability analysis, a general problem of interest is inference of the stress-strength parameter R = P (Y < X). The stress Y and the strength X are treated as independent random variables. The system fails when the applied stress is greater than the strength. Estimation of the stress-strength parameter has received considerable attention in the statistical literature. These studies started with the pioneering work of Birnbaum [5]. Since then many studies have been accomplished on the estimation and inference of the stress-strength parameter, from the frequentist and Bayesian point of view, by imposing different classes of distributions. The monograph by Kotz et al. [15] provided a comprehensive review of the development of this model till 2003. Further recent work on the stress-strength model can be fined in Kundu and Gupta [17, 18], Raqab and Kundu [23], Krishnamoorthy et al. [16], Raqab et al. [24], Kundu and Raqab [19], Panahi and Asadi [22], Lio and Tsai [21] and Babayi et al. [2].Based on progressively Type-II censored samples, this paper deals with inference for the stress-strength reliability R = P (Y < X) when X and Y are two independent two-parameter Rayleigh distributions with different scale parameters but having the same location parameter. This distribution was originally proposed by Khan et al. [14]. Statistical inference about this distribution was studied by Dey et al. [9]. In the rest of the paper, a two-parameter Rayleigh distribution with the pdf (1) is denoted by tR(µ, λ).In this paper, we study the estimation of the stress-strength parameter R = P (Y < X) when X and Y are independent two-parameter Rayleigh random variables, with common location parameter µ and scale parameters λ > 0 and α > 0, respectively. The probability density functions (pdfs) of X and Y for x > µ and y > µ are;

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