基于Kumaraswamy分布多部件应力-强度模型统计推断

Statistical Inference of Multi-component Stress-strength Model Based on Kumaraswamy Distribution

为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法给出参数及应力-强度模型可靠度的贝叶斯估计;最后,利用逆矩估计方法给出参数及应力-强度模型可靠度的逆矩估计(inverse moment estimation,IME)。数值模拟结果表明,在不同系统可靠度及不同样本量条件下,通过对3种估计方法的数值进行比较发现贝叶斯估计效果最好,IME优于MLE。该研究为探讨串联系统多部件应力-强度模型可靠性提供了一定的理论基础。

In order to study the reliability of multi-component stress-strength model in series system,based on Kumaraswamy distribution,the maximum likelihood estimation(MLE)of parameters and stress-strength model reliability was given by maximum likelihood method.The Jeffreys criterion was used to construct the uninformative prior distribution,and the Markov chain Monte Carlo(MCMC)method was used to give the Bayesian estimation of the parameters and the stress-strength model reliability.Finally,the inverse moment estimation(IME)of the parameters and the stress-strength model reliability was given by the inverse moment method.The numerical simulation results showed that under different system reliability and different sample sizes,by comparing the values of the three estimation methods,the Bayesian estimation was the best,and IME was better than MLE.This study provided a certain degree of theoretical basis for exploring the reliability analysis of multi-component stress-strength model under series system.