Inferential Techniques for Weibull Populations.
Interim rept. 15 Apr 72-15 Apr 74,
SKF INDUSTRIES INC KING OF PRUSSIA PA
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The theoretical basis is developed and tables are supplied for the conduct of multiple comparison hypothesis tests using maximum likelihood estimates, on the Weibull shape parameter and, under the assumption of common shape parameters, on a specific Weibull percentile, given k type II censored samples drawn from independent 2-parameter Weibull populations. A procedure is developed and appropriate tables are given for forming interval estimates for the Weibull shape parameter and a percentile of a 2-parameter Weibull primary failure mode when a competing Weibull failure mode having the same, but unknown shape parameter is operative. Several methods of approximating percentage points of the distribution of certain functions of the maximum likelihood estimates needed for interval estimation of the Weibull parameters are developed and their range of validity discussed. The exact distribution of the largest to smallest ML shape parameter estimates in k samples of size n, type II censored at r 2 failures, is found and its asymptotic behavior for large n is discussed. Tables needed for calculating the OC curve of a one-sided test of the hypothesis that a Weibull percentile assumes a specified value are included.
- Statistics and Probability