International Journal of Advanced Statistics and Probability, 1 (1) (2013) 4-8 ©Science Publishing Corporation www.sciencepubco.com/index.php/IJASP Estimation of stress-strength parameter for two-parameter weibull distribution Narjes Amiri 1 *, Reza Azimi 2 , Farhad Yaghmaei 3 , Manoochehr Babanezhad 4 1 Master Student, Department of Statistics, Faculty of Sciences, Golestan University, Gorgan, Iran 2 Department of Statistics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran 3,4 Department of Statistics, Faculty of Sciences, Golestan University, Gorgan, Iran *Corresponding author E-mail: narjesamiri86@yahoo.com Abstract In this paper, we consider the estimation of R= p(y<x) when x and y are two independent random variables from two- parameter weibull distribution with different scale parameters and the same shape parameter. Assuming that the common shape parameter is known, MLE, UMVUE and Bayes estimators of R are obtained. We also derive a confidence interval and shortest confidence interval for R based on MLE of R. Monte-Carlo simulation are performed to compare the different proposed methods. Keywords: Bayes estimator, Maximum likelihood estimator, shortest confidence interval, stress-strength model, uniformly minimum variance estimator 1 Introduction In this paper, we consider the problem of estimating the stress-strength parameter R=P(Y<X) when X and Y are two independent random variables from two-parameter Weibull distribution. R=P(Y<X) is arised when the random strength X exceeds the random stress Y and we are interested in calculating the probability of it. Because of that R=P(Y<X) is called the stress-strength parameter. Due to practical point of view of reliability stress-strength model many authors represented a lot of papers about the estimation of R=P(Y<X) for different distributions. Kundu and Gupta [4,9], Rezaei et al. [5], Panahi and Asadi [6], Krishnamoorthy et al. [12], Kundu and Raqab [13]. When the common shape parameter α is unknown, Kundu and Gupta [7] considered the estimation of R when     and     are two independent Weibull distributions with different scale parameters. In this paper, we consider estimation of R when the common shape parameter α is known. The layout of this paper is as follow: in section 2, we introduce the Weibull distribution. In section 3, we derive the estimation of R, in this section, the MLE , UMVUE and Bayes estimators of R are obtained. Simulation study for comparison between estimators are given in section 5. 2 Weibull distribution Weibull is one of the most widely used distributions in reliability studies. It is often used as the lifetime distribution, because some failure models are described by their shape parameter. Therefore, the weibull distribution is important and has been studied extensively over the years. A random variable X is said to have weibull distribution, if it´s probability density function (PDF) is given by           (1) The cumulative distribution function of weibull distribution (CDF) is defined by        , where  is a shape parameter and  is a scale parameter.