A new inherent reliability modeling and analysis method based on imprecise Dirichlet model for machine tool spindle

• Published in: Annals of operations research Vol. 311; no. 1; pp. 295 - 310
• Main Authors: Liu, Zheng, Liu, Xin, Huang, Hong-Zhong, Zhu, Pingyu, Liang, Zhongwei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2022; Springer; Springer Nature B.V
• Subjects: Ammonia; Binomial distribution; Business and Management; Combinatorics; Computer simulation; Counting; Data integration; Design and construction; Dirichlet problem; Machine tools; Mathematical analysis; Milling (machining); Multisensor fusion; Numerical controls; Operations research; Operations Research/Decision Theory; Probability theory; Reliability (Engineering); Reliability analysis; Reliability aspects; S.I.: Reliability Modeling with Applications Based on Big Data; Simulation; Spindles; Spindles (Machine-tools); Studies; Theory of Computation; Uncertainty; China; Inherent reliability modeling and analysis; Bayes theory; Gibbs sampling; Machine tool spindle; Imprecise Dirichlet model
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-019-03333-9

The factors that influence the inherent reliability of machine tool spindle are a mixture of various uncertainties and it leads that the reliability modeling and analysis of machine tool spindle can’t be dealt with by one mathematical theory. Meanwhile, the reliability data of the machine tool spindle for reliability modeling and analysis is often insufficient, and data of different types such as accumulated historical data, expert opinions, simulation data, etc. are used to make up for the lack of data. Thus, the unified quantification of mixed uncertainties and the data characterization of different types are the major premises for reliability modeling and analysis of machine tool spindle. By considering this, this paper makes use of the advantage of imprecise probability theory in quantizing the multiple types of data and the advantage of the Bayes theory in data fusion, and proposes a new inherent reliability modeling and analysis method based on imprecise Dirichlet model. In the proposed method, imprecise probability theory is used to quantify mixed uncertainties, imprecise Dirichlet model is built to characterize the different types of reliability data. After analyzing the inherent reliability variation regularity, an inherent reliability model is built, and the proposed method is verified by the inherent reliability calculation of a certain heavy-duty CNC machine tool’s milling spindle. This study can provide new method, theory and reference for reliability modeling and analysis when there are various uncertainties mixed and multiple data existed.