Statistical indicators for the optimal prediction of failure times of stochastic reliability systems: A rational expectations-based approach

We introduce a method to estimate the failure time of a class of weighted k-out-of-n systems using the idea of rational expectations, which to the best of our knowledge is a new approach, not found elsewhere in the existing literature. This paper explores the predictive power of several statistical indicators (variance, skewness, kurtosis, Gini coefficient, entropy) and shows how they perform differently as the system approaches global failure. The proposed method is shown to outperform a benchmark prediction model obtained without rational expectations, and our results offer a panoramic view of the predictive power of the statistical indicators under different assumptions about the initial weight distributions.