Bayesian Estimations of Reliability on One Type of Missile with Zero-Failure Data

For zero-failure datas which were in accord with exponential distribution, the prior distribution of the failure rate was set as Gamma distribution. The hierarchical Bayesian estimation method and E-Bayes estimation(Expected Bayesian) method of the failure rate were proposed. As the hyper parameters were in accord with uniform distribution, the hierarchical Bayesian estimation and E-Bayes estimation of the failure rate were derived. Based on the datas of a unique type of missile engine, the two estimations of both the failure rate and reliability were calculated. All the estimations were robust while the latter reliability estimation was less than the former and the range was dramatically less than the former. The results indicated the E-Bayes estimation was more robust and accurate. On the other hand, there was an integral operation in the hierarchical Bayesian estimation. In general, the E-Bayes estimation method was more practical in use and the calculation was easier and more accurate.