Inference on p{Y<X} in the weibull case

The probability that a Weibull random variable Y is less than another independent Weibull random variable X is considered for the case where both X and Y have the same, but unknown, shape parameter. Tables, developed by Monte Carlo sampling, are presented whereby 90% confidence limits for this probability may be found in terms of its maximum likelihood estimate for 21 combinations of the size of the sample taken from each of the two populations and the ordered observation number at which the samples are type II censored. A normal approximation is also discussed and its accuracy vis-a-vis the exact values is examined as a function of sample size for a particular case.