Inferential Techniques for Weibull Populations. II.
Final rept. 15 Apr 74-15 Jun 75,
SKF INDUSTRIES INC KING OF PRUSSIA PA
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Two test statistics are examined and shown to have the required properties to serve as a test of the null hypothesis that k 2-parameter Weibull populations, having a common but unknown shape parameter, have a common scale parameter. The test statistics are the ratios of the maximum likelihood ML shape-parameter estimate derived on the assumption that the scale parameters differ to 1 the ML shape-parameter estimate calculated using the earliest failure in each sample and to 2 the ML shape-parameter estimate calculated after combining the k data samples. The theory for drawing inferences on Weibull parameters in the presence of a single competing Weibull failure mode having the same but unknown shape parameter as the primary mode is generalized to the case of k competing modes. An illustration is given of the construction of a joint confidence region for the proportion of failures due to mode j and a percentile of the distribution of failure due to mode j when only that mode operates.
- Statistics and Probability