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With the advances in modern technology and sophisticated technology, high-precision, high-reliability bearings are also increasingly been widely promoted , especially in the aerospace field has been widely used , however, when the bearing life test , there will be small sample data without failure and, therefore, difficult to determine the bearing life prediction . To be able to accurately predict bearing life and reliability , the use of Weibull distribution theory and fuzzy theory respectively bearing life and reliability analysis of budget methodology . Describes the origin and development of Bayesian statistics , the test data, statistical inference methods of analysis, and focused on Bayesian methods prior distribution , likelihood function and the posterior distribution OK. Bayesian statistics theory, a mathematical model of the cumulative failure probability , based on least squares method for solving the two -parameter Weibull distribution of two unknown parameters , get the bearing reliability mathematical model . Three-parameter Weibull distribution based on the theory , a detailed three-parameter Weibull distribution for the geometric and physical significance of the analysis, Weibull likelihood equations, based on Newton iteration method to obtain three-parameter Weibull distribution model bearing reliability . By analyzing the factors that affect the bearing life , were established factor set , the alternative set and weight set , based on the weighted average method theory, the life of the bearing fuzzy mathematical model, through the application of analysis, the conventional method of calculating bearing life is rough, and fuzzy methods calculation results are more realistic , more valuable , fuzzy theory calculations illustrate the feasibility of bearing life . Respectively, using the two -parameter Weibull distribution statistics and three -parameter Weibull statistical method for the same group bearing life data processing, by analyzing the comparison, when the bearing reliability in [ 0.9 , 1 ] interval , the use of two -parameter Weibull three-parameter Weibull distribution and bearing reliability of distributed computing with large differences , but bearing reliability is less than 0.9, compared with similar results .
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