Reliability Analysis Of Ship Based On The Zero Failure Data

With the development of modern technology and the enhancement of product quality,many highly reliable products such as large ships and aircrafts have emerged with Zero Failure Data in experiment and practice.Due to the limited information provided by the Zero Failure case,the results of reliability analysis can't meet the requirements of practice.Therefore,it has been considered as an urgent task to work out an analytic method for the product reliability,which is also under the Zero Failure case.According to the data analysis of reliability,the utilization of prior information has enabled Bayesian theory to become irreplaceable under certain condition.And the wise choice of prior distribution has also become the key to Bayesian method.Based on the theory of Bayesian,a study of the reliability analysis of zero failure data is carried out in terms of the prior distribution of the parameter in the paper.Firstly,as to the ship whose life follows exponential distribution,a hierarchical Bayesian estimation model of the failure rate is presented under the condition that the failure rate follows the Gamma prior distribution and its two hyper-parameters follow three different kinds of prior distribution.The asymptotic property among the three modes of hierarchical Bayesian estimation of failure rate as well as estimation of reliability are both testified.What is more,the model of hierarchical Bayesian estimation is applyed to the study of the zero failure data for certain ship,calculation results indicate that the hierarchical Bayesian estimation of parameter is stable and the second mode is more stable and gets more conservative results.Secondly,as to the ship whose life follows exponential distribution,a expected Bayesian estimation model of the failure rate is presented under the condition that the failure rate follows the Gamma prior distribution and its two hyper-parameters follow three different kinds of prior distribution.The property among the three modes of expected Bayesian estimation of failure rate as well as estimation of reliability are both testified.What is more,the model of expected Bayesian estimation is applied to the study of the zero failure data for certain ships,calculation results show that the expected Bayesian estimation for the parameter is stable.This expression of expected Bayesian estimation model is simple,which does not involve integral computation and convenient for engineering application.Thirdly,in the reliability analysis with Zero Failure Data,the failure data is introduced.A expected Bayesian estimation of the failure rate is presented with the failure data under the condition that the failure rate follows the Gamma prior distribution and its two hyper-parameters follow three different kinds of prior distribution.Combined with the expected Bayesian results of the ship failure rate above and the expected Bayesian results of the ship failure rate with failure data,the compositive expected Bayesian results of the ship failure rate and reliability are also given.What is more,the model of the compositive expected Bayesian estimation is applied to the study of the zero failure data for certain ship,calculation results show that the compositive expected Bayesian estimation of the parameter is stable and and the second mode ie more stable and gets more conservative results.Finally,as to the ship with a life following Weibull distribution,the expected Bayesian estimation of failure probability result pi(i = 1,…,k)will be presented on the condition that ship failure distribution follows Weibull distribution and prior distribution follows Beta distribution.About the point((ti,pi),i = 1,…,k,the estimation results of the distribution parameters m and ? will be also given through the weighted least square method.Based on the Weibull distribution curve,the expected Bayesian results of the ship reliability is given.What is more,the Bayesian estimation is applied to the study of the zero failure data for certain ship,calculation results indicat that the Bayesian estimation of the reliability is stable.