Interval Estimation of the Weibull Location Parameter

The versatility of the Weibull distribution greatly contributes to its wide use in reliability and life data analysis. The 3-parameter Weibull distribution introduces a location parameter into the more commonly used two-parameter Weibull distribution which includes the shape and scale parameter. Although very flexible and useful in modeling life length, the three-parameter model is much less common in applications due to the uncertainty in accurately determining the value of the location parameter. Although the value of the location parameter can be hard to determine, a confidence interval for the location parameter can be determined using various mathematical computations and techniques, including the bisection method. A method for determining the lower confidence interval of the three-parameter Weibull distribution using equations and algorithms written in Mathcad is discussed. Numerical examples illustrate the calculations used to find the confidence levels and the median unbiased estimate of the location parameter, and an analysis of the results is given