The classic E-Bayesian estimation methods can only derive point estimation of the reliability parameters. In this paper, an improved E-Bayesian estimation method is proposed to evaluate product reliability under heavily censored data, which can achieve both point and confidence interval estimation for the reliability parameters. Firstly, by analyzing the concavity & convexity and function characteristics of the Weibull distribution, the value of product failure probability is limited to a certain range. Secondly, an improved weighted least squares method is utilized to construct the confidence interval estimation model of reliability parameters. Simulation results show that the proposed approach can significantly improve the calculation speed and estimation accuracy with just very few robustness reductions. Finally, a real-world case study of the sun gear transmission mechanism is used to validate the effectiveness of the presented method.

Multitask emergency logistics planning is a complex optimization problem in practice. When a disaster occurs, relief materials or rescue teams should be dispatched to destinations as soon as possible. In a nutshell, the problem can be described as an optimization of multipoint-to-multipoint transportation delivery problem in a given multimodal traffic network. In this study, a multimodal traffic network is considered for emergency logistics transportation planning, and a mixed-integer programming (MIP) formulation is proposed to model the problem. In order to solve this model, we propose a two-layer solution method. The inner layer is to manage the single-task route recommendation, for which we develop a shortest-path algorithm with the multimodal traffic network. Here, the optimal substructure of the algorithm and its time complexity are presented. With the route of each task calculated by the single-task solver, a general optimization algorithm based on improved particle swarm optimization (PSO) is proposed at the outer layer to coordinate the execution of each task constrained by the limited transportation capacity, so as to derive solutions for multi-commodity emergency logistics planning. Extensive computational results show that the proposed method can find solutions of good quality in reasonable time. Meanwhile, through the sensitivity analysis of the algorithm, we find the appropriate parameters for general optimization algorithm to solve the problem proposed in this paper. The proposed approach is effective and practical for solving multitask emergency logistics planning problem under multimodal transportation, which can find a satisfactory solution in an acceptable time.