Further Enhanced Weibayes Method and its Applications

The paper establishes a method, called Further Enhanced Weibayes, or feWeibayes, that extends the Weibayes method [1],[2],[3] and the eWeibayes method [5],[6] by incorporating engineering knowledge-based confidence distribution on β for 2-parameter Weibull distribution applications to derive reliability confidence lower bounds. The paper shows how this additional engineering knowledge on β allows the traditional 2-parameter Weibull analysis to be extend to the applications with no failure or very few failures. The feWeibayes method was illustrated and compared with other existing methods, namely, Fisher Matrix, Likelihood Ratio, and Bayesian methods. The reasonableness and justification of feWeibayes were demonstrated through the method comparison and a Monte Carlo simulation. The ability of feWeibayes in analyzing no-failure or 1-failure data cases is illustrated for 2-parameter Weibull applications which clearly demonstrates the usefulness of feWeibayes methodology as an additional statistical technique that could be applied when other methods are not viable.