This paper is concerned with the small sample size estimation of the location and scale parameters when both are unknown, or only the scale parameter is known, from the Rayleigh distribution. Best linear unbiased estimates (BLUE) for sample size in =5(1)45 are derived. The coefficients to be used in computing the estimates and their variances and covariances are given. Examples are given to show how to use the tables in this paper to estimate the three fundamental characteristics of reliability function (probability of failure free operation), the intensity failure, and mean time to failure MIF (mean time to free operation).