多重加速寿命试验下多部件系统的参数估计

Parameter Estimation of aMulticomponent System underMultiple Accelerated Life Tests

摘要: 多部件系统的可靠性推断是可靠性理论研究中的重要问题。本文首先基于多重恒应力加速寿命试 验研究了部件具有 kumaraswamy 寿命分布的 s-out-of-k 系统，建立了系统可靠性的似然函数， 还给出了模型参数极大似然估计的存在性和唯一性。基于极大似然估计的渐进正态性得到了模型 参数的渐进置信区间。同时，在给定参数共轭伽马先验的假设下，基于不同的损失函数，得到了 参数和系统可靠性的不同贝叶斯估计。其次，构造了参数的 Bootstrap 区间作为渐进置信区间和 贝叶斯区间的对比。最后，分析了一组真实数据来说明本文方法的可行性。

Abstract: Reliability inference for multicomponent systems is an important issue in reliability theory research. In this paper, the reliability of s-out-of-k systems with kumaraswamy life distributions of components is firstly investigated based on multiple constant stress accelerated life tests, the likelihood function of system reliability is established, and the existence and uniqueness of the maximum likelihood estimation for model parameters are also given. Asymptotic confidence intervals for the model parameters are obtained based on the asymptotic normality of the maximum likelihood estimates. Meanwhile, different Bayesian estimates of the parameters and system reliability are obtained based on different loss functions under the assumption of a conjugate gamma prior for the given parameters. Next, Bootstrap intervals for the parameters are constructed as a comparison between asymptotic confidence intervals and Bayesian intervals. Finally, a set of real data is analysed to illustrate the feasibility of the methodology of this paper.