Percentiles of Pooled Estimates of Weibull Parameters

In fatigue testing of metals or composite materials under different levels of stress, the underlying distributions are often assumed to be Weibull with a common shape parameter. The problems of estimation and hypothesis tests of the common shape parameter and scale parameters in the Weibull distributions are considered in this paper. The results are: 1) the maximum likelihood equation for estimating the shape parameter, 2) a s-confidence interval and hypothesis test for the shape parameter, 3) s-bias factors and variances of the pooled estimator of shape parameter, and 4) s-confidence interval and hypothesis test for the scale parameters. Examples are given for composite material applications. Results are based on Monte Carlo simulation methods.