A Comparative Study of Fitting Methods for the 2‐Parameter Weibull Distribution: An Engineering Application Perspective

ABSTRACT The 2‐parameter Weibull distribution is widely used in the analysis of the reliability of materials and devices, and several methods have been proposed for estimating the 2‐paramether Weibull distribution, such as the maximum likelihood estimation (MLE) method, the least squares regression (LSR) method, the moments estimation (ME) method, etc., and several methods have been proposed for estimating the confidence intervals of the 2‐parameter Weibull distribution, such as the pivotal quantity (PQ) method, the Wald‐approximation (WA) method, the Bayesian analysis (BA) method, the method of approximate combined limits (ACL), etc. This paper summarizes the theoretical basis of different methods, and compares their performances in engineering applications through Monte Carlo sampling simulation. The confidence interval analyzed by MLE with ACL can fully cover that analyzed by MLE with PQ. MLE provides a slightly narrower confidence interval of shape parameter than ME does. Increasing the specimen number only has a minor effect on reducing the probability of misjudgment when comparing the shape parameters of different materials. When BA and WA, especially WA is used to estimate A‐basis or B‐basis, there is a greater probability of getting a value larger than the true value, and this is detrimental to engineering design. MLE with ACL or PQ is the best choice for the design concept of increasing material efficiency.