Estimation of P[Y<X ] for Weibull Distribution Debasis Kundu 1 Rameshwar D. Gupta 2 Abstract This paper deals with the estimation of R = P [Y<X ] when X and Y are two independent Weibull distributions with different scale parameters but having the same shape parameter. The maximum likelihood estimator and the approximate maximum likelihood estimator of R are proposed. We obtain the asymptotic distribution of the maximum likelihood estimator of R. Based on the asymptotic distribution, the confidence interval of R can be obtained. We also propose two bootstrap confidence intervals. We consider the Bayesian estimate of R and propose the corresponding credible interval for R. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a real data set has also been presented for illustrative purposes. Key Words and Phrases: Approximate maximum likelihood estimator; Bayes estimator; Bootstrap confidence intervals; Credible intervals; Maximum likelihood estimator; Stress- Strength model. Address of correspondence: Debasis Kundu, e-mail: kundu@iitk.ac.in, Phone no. 91- 512-2597141, Fax no. 91-512-2597500. 1 Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Pin 208016, India. 2 Department of Computer Science and Applied Statistics. The University of New Brunswick, Saint John, Canada, E2L 4L5. Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council. 1