Weibull distribution-based reliability evaluation of cutting tool via improved Bayesian-Bootstrap method

Abstract

Aiming to address the challenges of accurately assessing product reliability under small sample conditions and the difficulty in obtaining prior distributions in the Bayesian framework, an improved Bayesian-Bootstrap method was proposed. The proposed method replaces the traditional step-type empirical distribution function with a modified version, samples data at different levels of uncertainty, and conducts sensitivity analysis on key parameters to derive the prior distributions of the shape and scale parameters under the Weibull distribution. Subsequently, the posterior distributions required for Bayesian inference are obtained using the MCMC-Gibbs sampling method, from which the product reliability is further derived. Using the life data of a specific type of cutting tool as an example, the interval lengths of the shape and scale parameters obtained by the improved Bootstrap method are reduced by 21.7% and 16.77%, respectively, compared to the traditional method. Moreover, the lengths of the 95% confidence intervals of the shape and scale parameters in the posterior distributions are reduced by 84.1% and 88.2%, respectively. The results demonstrate that the proposed method significantly improves the accuracy of parameter estimation, enhances the reliability of the model, reduces uncertainty in the estimation process, and provides an effective and feasible approach for product reliability assessment under small sample conditions.