A Reliability Evaluation Method for Zero-Failure Products Based on Moment-Entropy Normalization

This paper addresses the challenge of reliability evaluation for small-sample and zero-failure data by introducing a method that integrates Bayesian theory with curve fitting. Initially, we employ the moment-entropy normalization method to determine the hyperparameters of the Beta distribution. This approach incorporates data from similar products, effectively overcoming the limitations posed by small sample sizes. Next, we use a Bayesian method to merge data from similar products with the current product data. By treating the likelihood function as binomial with zero failures, we accurately estimate parameters and improve the precision of reliability assessments. This enables us to obtain point estimates of failure probabilities at different time points and determine the upper confidence limits of failure probabilities at a given confidence level. Furthermore, we introduce the Weibull distribution as a life distribution model and apply curve fitting to estimate the Weibull parameters and their lower confidence limits, further enhancing the robustness of our reliability estimates. Finally, the proposed Bayesian method demonstrates strong practical applicability in case studies, providing valuable insights for the design and testing of reliable products.