Reliability Analysis Based on Evidential Likelihood for Uncertain Mixed Weibull Distribution

In reliability analysis, mixed Weibull distributions have gained considerable attention due to its exceptional flexibility in modeling complex failure mechanisms. In the practical analysis of mixed distribution life data, obtaining complete failure information presents significant challenges, leading to various forms of uncertainty. In this paper, we propose a novel framework based on evidence theory to address uncertainty in the reliability analysis of progressively censored data following a mixed Weibull distribution. This approach can simultaneously handle the uncertainty arising from unobserved censored data and prior knowledge in the dataset. The maximum likelihood estimation is derived by optimizing the introduced evidential likelihood. Moreover, we prove the asymptotic normality and invariance property of the estimators. Furthermore, leveraging these properties, we provide both point and interval estimates for the reliability function. Numerical experiments are conducted to demonstrate the effectiveness of the proposed method.