Bayesian Inference For General Half-normally Distributed Lifetime Products

The generalized half-normal(GHN)distribution was first proposed by Cooray and Ananda in 2008.It is mainly used to describe the life model of component failure caused by wear.It is widely used in engineering to simulate the life distribution with wear properties.At present,there is little research on the theory and application.In this paper,DE(differential evolution),GA(genetic algorithms)and MH-MCMC(metropolis Hastings Markov chain Monte Carlo)are used to solve the parameters of generalized semi normal distribution model.And the conclusion is applied to the life prediction and reliability analysis of oil field equipment sucker rod,which has certain theoretical significance and practical application value.The main contents of this paper are as follows:Firstly,the basic principles of Gibbs sampling method and MH-MCMC algorithm are given.Secondly,the commonly used limiting methods are described in detail,and the general form of the generalized half-normal distribution model and the related characteristic functions are given under the mixed limiting conditions.Differential evolution(DE),genetic algorithm(GA)and MH-MCMC algorithm are used to solve the two parameters in the generalized half-normal distribution model.By comparing the performance of Monte Carlo simulation,the relative deviation(RB)and mean square error(RMSE)of the parameters obtained by the three methods are calculated.The results show that the MH-MCMC algorithm has small relative deviation and mean square error,and can obtain more stable MLE estimation.Finally,the model is applied to the oilfield equipment,and the sucker rod life distribution function,failure rate function and quantile function are obtained,and the equipment life distribution law is obtained,so as to realize the reliability analysis of sucker rod,and then the theoretical equipment maintenance time can be obtained.It provides a reference for the maintenance and repair in oilfield work,and has a certain engineering application value.