Inference on the Weibull Location Parameter

Abstract

A simple method is proposed for testing the 2-parameter Weibull distribution against the 3-parameter alternative. It is based on the ratio of the maximum likelihood estimate of the shape parameter calculated with the observations censored at the r₁^th ordered value and the corresponding estimate, using all r > r₁ observed values in the Type II censored sample of size n ≥ r. Critical values for conducting the test are given for 10 ≤ n ≤ 100 and various r and n₁. The choice of ni in the range 5–9 is found to give nearly maximum power over the range of sample sizes explored. The acceptance region for the test can be translated into a lower confidence interval estimate for the location parameter. Two numerical examples illustrate the calculations.

• Interval Estimation
• 3-Parameter Weibull
• Threshold Parameter

Additional information

Notes on contributors

John I. McCool

Dr. McCool is an Associate Professor in the Industrial and Manufacturing Engineering Department. He is a member of ASQ.