Reliability Parameter Estimation Method Of Weibull Distribution In Small Samples

Among various types of failure life distribution,Weibull distribution has been commonly used in reliability data analyses for its qualified properties.The accurate estimation of distribution parameters counts most in Weibull distribution.Most of methods are established on the statistical theory,the essence of which is a large amount of life data.With the flying upgrades in modern industrial devices,the reliability of products has been more guaranteed.Nevertheless,when it comes to practical use,for those most valuable and large-tonnage mechanical equipment,it is quite hard to collect massive failure data,considering both the experimenting conditions and financial feasibility.In this case,due to the fact that the classical statistical method can be concluded as the asymptotic statistical theory based on large samples,the pool performance in evaluation of estimation based on small samples leaves an unfinished problem,thus making the results in reliability evaluation of small samples less convincing,which hardly satisfies the actual demand.Based on this,combined with relevant research projects,this thesis aims at the problems and difficulties that the condition of small samples brought to traditional methods of parameter estimation methods.This dissertation takes the Weibull distribution as the research object,and studies the parameter estimation methods in the case of small samples.The specifics are as follows.Given that the prior distribution is usually difficult to determine in Bayesian method,and the lack of accuracy in bootstrap method,a confirmation method for Bayesian prior distribution based on bootstrap method is proposed.Meanwhile,the Bayesian posterior function is solved by MCMC method.According to an engineering example,the results using the method in this dissertation and others are illustrated to verify the feasibility of the proposed method.Considering that in practices of engineering,except failure data,there are data which can reflect the degradating performance of products.Thus the degradation trajectory model is used for analysing the degradation data by in this dissertation.On account of the needs in engineering practice,accelerated degradation data is collected through the accelerated test,which are more frequently used,and the data are processed by degradation trajectory model and then converted to the normal level of working stress.For the next,we use the bootstrap method to transform it into the prior distribution and furtherly propose a method,which successfully combines accelerated degradation data and history failure data.In an engineering example of a certain type of rubber rings,the validity and advantages of this method are well verified.In consideration of the multiple failure mode in complex systems,the limitations of Weibull distribution in fitting such failure data are explained,and mixed Weibull distribution is considered as a replacement.According to the characteristics of failure data in the multiple failure mode,a data processing method based on fuzzy clustering analysis is proposed.Specifically,experts scoring is used to establish the fuzzy relation matrix between failure mode and failure mechanism,and its similarity matrix is calculated.Furthermore,the fuzzy similarity matrix is transformed into equivalent matrix on the basis of transitive closure method,and the results are classified in terms of fuzzy clustering threshold.According to the results of classification,the Bayesian method is used to estimate the parameters of Weibull distribution.Finally,an engineering example is given to illustrate the necessity of mixed Weibull distribution in dealing with data in multiple failure mode.The effectiveness of parameter estimation method gets proved.