The Research Of Reliability With Three-parameter Weibull Distribution

With the development of science and technology, the reliability of aerospacesystems, major equipments and products are more demanding than ever before. Hence,it has becom very important to evaluate the reliability of systems and productsaccuracy and quickly. Because three-parameter Weibull distribution widely used inmodeling failure data, the assessment of reliability with three-parameter Weibulldistribution has become a hot issue in recent years. The assessment of reliabilitymainly includes parameter estimation, optimal confidence interval evaluation andhypothesis testing. How to assess the reliability of three-parameter Weibulldistribution effectively and accuracy would be a focus in this paper.The minimum weighted-relative-entropy norm and bootstrap has been proposedin this paper for the assessment of reliability of three-parameter Weibull distribution.Firstly, let the test lifetime data vector substitute into three-parameter Weibulldistribution reliability function, the theoretical value vector of reliability has beenobtained. Then through non-parametric estmation for the lifetime data by Johnson orNelson method, the experience value vector of reliability has been obtained. Based onthe relative difference information of the experimental value vector to the theoreticalvalue vector of reliability, with the help of relative entropy theory and norm, sixcriterions of the minimum weighted-relative-entropy norm are established to extractthe optimal information vector of the Weibull parameters in the reliability experimentof product lifetime. By bootstrap resampling the information vector of the Weibulloptimum parameters, a generated information vector was obtained to simulate theprobability density function of the parameters. Through solving the parameterprobability density function, the parameter estimated truth-value and confidenceinterval have been worked out. The estimated truth-value function and its optimumconfidence interval function of the reliability have been established accordingly. At last, the rejection region used in the hypothesis testing has been decided via the area ofintersection set of the estimated truth-value function and its confidence intervalfunction of three-parameter Weibull distribution. The simulation case, helicoptercomponent case and ceramic material case have showed that the assessment ofreliability is able to reflect the practical situation of the reliability experiment by theproposed minimum weighted-relative-entropy norm and bootstrap in this paper. Andcompared the minimum weighted-relative-entropy norm and bootstrap, maximum-likelihood method, moment method and probability weighted-moment method, theBayesian method in parameter estimated, the results have showed that the proposedminimum weighted-relative-entropy norm and bootstrap is optimal for the reliabilityassessment.Using three-parameter Weibull distribution to model the failure data whichcollected in reiability test in this paper. And the minimum weighted-relative-entropynorm and bootstrap also be used to assess the reliability of the model. The research ofthe reliability has showed that the relative difference of experience value vector totheoretical value vector is obvious and the failure data collected in the test has a largererror and deviate from three-parameter Weibull distribution.