Estimation of Weibull Shape Parameter for Samples of Size 2

Maximum likelihood (ML) estimation of the Weibull shape parameter in samples of size 2 is considered in the context of life testing. For single samples the shape parameter is estimable even when one of the two items in the sample is censored at life L. The ML shape-parameter estimate is the same as if the suspended test had failed at life L1.88. For k uncensored samples of size 2, with possibly different scale parameters, the ML estimate of a common shape-parameter is a function of the ratios of the second to first failure times within each of the k samples. Applying the ML method directly to the joint distribution of these k order-statistic ratios results in a shape-parameter estimate that is a different function of these same ratios. The s-normal distribution behaves similarly.