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• A novel W-DATA method for mechanical degradation performance description and reliability estimation. • ApEn and P-EMD are introduced for degradation feature extraction and quantification. • An ApEn -based Wiener degradation model with a pseudo failure threshold is employed to estimate the reliability. • W-DATA can be effectively used for lubricating oil pump reducer reliability estimation. The Wiener-process-based Degradation Approach with Two-phase Algorithm (W-DATA) is introduced as a multi-dimensional framework explicitly designed for modeling mechanical system reliability. This approach leverages an enhanced Empirical Mode Decomposition, known as P-EMD, for degradation feature extraction, and utilizes Approximate Entropy (ApEn) for quantifying feature complexities. W-DATA seamlessly integrates these components into a time-resolved degradation model. To enhance its robustness, the proposed reliability model synergizes with a Box-Cox transformed Wiener model, allowing for improved adaptability to non-Gaussian data landscapes. The paper outlines a strategy for establishing a reliable threshold for this data-driven degradation model based on non-Gaussian data, a critical aspect for reliability modeling using the Wiener process. This strategy addresses the challenge of Wiener process verification through normality and independent testing of data increments. The integrative methodology is recommended for application in machinery reliability analytics and has undergone rigorous validation through a 770 h real-world test on a marine lubricating oil pump reducer. The results affirm its efficacy and feasibility in accurately estimating mechanical system reliability. [ABSTRACT FROM AUTHOR]

• Propose a new reliability model by determining the optimal redundant number. • Incorporate satellite operating environment into the reliability model. • Model the satellite communication system using a Markov Bayesian network. • Give a new importance measure to identify the critical satellite communication. • Use MOPSO algorithm to solve the redundancy design of satellite propulsion system. Satellite communication system holds a crucial role in modern society, so it is significant to improve its reliability and stability. Optimizing reliability and designing redundancy become imperative methods to ensure continuous and efficient operation of the system in the intricate space environment. In this paper, we initially model the satellite communication system using a Markov Bayesian Network in conjunction with a non-working reserve system, facilitating a systematic analysis of its reliability. Secondly, we propose a novel Bayesian environmental importance measure by considering the unique attributes of the space environment. This importance measure verifies the contributions and significance of the individual subsystems within the satellite communication system. Subsequently, we formulate a redundancy design strategy for critical subsystems to maximize reliability while minimizing costs. To solve the optimal number of redundancies of components in the subsystem, we employ the multi-objective particle swarm optimization algorithm. Finally, the effectiveness of the proposed method is demonstrated by a satellite communication system. [ABSTRACT FROM AUTHOR]