A Bayesian Product Reliability Assessment Approach with Varying Sample Sizes

In new product development (NPD) process, reliability analysis and predictive modeling are crucial for ensuring product performance. However, the accuracy of these models can be affected by inaccurate estimation of distribution parameters, particularly when dealing with small or varying sample sizes. For instance, while Maximum Likelihood Estimation (MLE) is efficient for large datasets, its reliability diminishes with smaller samples. Bayesian random effects modeling, though widely studied, has been underexplored for Weibull parameter estimation with varying sample sizes. This paper investigates the effectiveness of Bayesian methods integrated with MLE for such tasks. Through a series of simulations, we generate various sample lifetime data sets under different estimation scenarios and fit multiple Bayesian random effects models. Model performance is assessed using metrics such as the Bayesian Information Criterion (BIC), Akaike Information Criterion (AIC), and residual plots. Results show the usability and applicability of Bayesian approaches for predictive modeling in estimating Weibull parameters estimation, given varying sample sizes.