In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

在本文中，在存在竞争性失败原因的情况下，在渐进式II型检查中考虑了Chen分布的未知参数的估计。假定失效的潜在原因具有独立的Chen分布，具有相同的形状参数，但比例参数不同。从常客的角度来看，可以通过期望最大化（EM）算法获得参数的最大似然估计。同样，基于缺失信息原理计算期望的费舍尔信息矩阵。通过使用获得的MLE的期望Fisher信息矩阵，构造了参数的渐近95％置信区间。我们还应用引导程序方法（Bootstrap-p和Bootstrap-t）来构建置信区间。从贝叶斯方面来看，通过应用马尔可夫链蒙特卡洛（MCMC）程序计算未知参数的贝叶斯估计值，并进行可信区间的平均长度和覆盖率。贝叶斯推断是基于平方误差，LINEX和一般的熵损失函数。通过仿真研究评估点估计器和置信区间的性能。最后，出于说明目的考虑现实生活中的示例。