Bayesian Analysis Based on Dirichlet Prior Distribution of Dominant Failure Modes for Electromechanical Products

Abstract

Abstract: For complex electromechanical products with several failure modes, the analysis of dominant failure modes is a key process during reliability design and test. But the frequency analysis, which is commonly used for quantitative analysis at present, is not the best method when data is not plenty. For this problem, Bayesian method based on Dirichlet prior distribution is proposed for quantitative analysis of dominant failure modes in the case of small sample size. Monte Carlo simulation is performed to check the proposed methods and an example is provided. The results show that, Bayesian method is more suitable than the frequency analysis method, and is more effective to find out the dominant failure modes when sample size is small.

Key words: mathematical statistics, dominant failure mode, frequency analysis, Bayesian method, Dirichlet distribution, Monte Carlo simulation

CLC Number:

TB114.3

TAN Yuan-yuan， ZHANG Chun-hua， CHEN Xun. Bayesian Analysis Based on Dirichlet Prior Distribution of Dominant Failure Modes for Electromechanical Products[J]. Acta Armamentarii, 2012, 33(2): 209-213.

References

［1］ Peter L, Kosuke I. Global failure modes and effects analysis: a planning tool for global product development[C]∥Proceedings of International Design Engineering Technical Conference. California: FMEA, 2005: 1-10.
［2］李久祥. 整机加速贮存寿命试验研究[J]. 质量与可靠性, 2004,(4): 14-17.
LI Jiu-xiang. Research on accelerated storage life testing of the whole assembly[J]. Quantity and Reliability, 2004,(4): 14-17. (in Chinese)
［3］贺国芳. 可靠性数据的收集与分析[M]. 北京：国防工业出版社, 1995.
HE Guo-fang. Collection and analysis of reliability data[M]. Beijing: National Defense Industry Press, 1995. (in Chinese)
［4］于捷, 贾亚洲. 数控车床故障模式影响与致命性分析[J]. 哈尔滨工业大学学报, 2005, 37(12): 1725-1727.
YU Jie, JIA Ya-zhou. Failure mode effect and criticality analysis on certain serial CNC lathes[J]. Journal of Harbin Institute of Technology, 2005, 37(12): 1725-1727. (in Chinese)
［5］林震, 李宪珊, 姜同敏, 等. 整机产品加速贮存寿命试验研究思路探讨[J]. 环境与可靠性, 2006,(4): 38-41.
LIN Zhen, LI Xian-shan, JIANG Tong-min, et al. Discussion on accelerated storage life testing of assembly-level products[J]. Environment and Reliability, 2006,(4): 38-41. (in Chinese)
［6］ Mazzuchi T A, Soyer R. A bayes attribute reliability growth model[C]∥Proceedings of Annual Reliability and Maintainability Symposium. Orlando: 1991: 322-325.
［7］茆诗松, 王静龙, 濮晓龙. 高等数理统计（第二版）[M]. 北京：高等教育出版社, 2006.
MAO Shi-song, WANG Jing-long, PU Xiao-long. Advanced mathematical statistics (2nd edition)[M]. Beijing: High Education Press, 2006. (in Chinese)
［8］ Smith A F, Gelfand A E. Bayesian statistics without tears: a sampling-resampling perspective[J]. The American Statistician, 1992,(46): 84-88.

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