New statistical inference for the Weibull distribution

Abstract

Weibull distribution has become a popular tool for modeling life data and improving growth in the field of reliability. The successful application of Weibull distribution to real data depends on the statistical power of hypotheses tests to a large extent. Here we propose two methods to test the shape parameter of a two-parameterWeibull distribution, and its confidence interval is considered. Simulation studies show that coverage of the confidence intervals is close to its desired confidence level, and the two proposed methods exhibited satisfactory performance. A real example employing a Boeing air-conditioning system development study is presented to illustrate the proposed methods.

Keywords

• Weibull distribution
• Gamma distribution
• Dirichlet distribution
• Rejection region
• Power