Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied.

中文翻译：

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基于渐进式首次失败截尾数据的对数Logistic分布的生命周期性能指标的统计推断

估算对产品寿命性能的准确评价一直是制造业的热门话题。本文以寿命性能指标为基础，重点评价给定规格下限时的性能指标。我们讨论的渐进式首次失败删失数据具有共同的对数逻辑分布。贝叶斯和非贝叶斯方法都被研究。在对称和非对称损失函数下，使用 Lindley 近似和 Monte Carlo Markov Chain 方法获得对数逻辑分布参数和寿命性能指数的贝叶斯估计量。至于区间估计，我们应用最大似然估计量来构建渐近置信区间和 Metropolis-Hastings 算法来建立最高后验密度可信区间。而且，为了演示目的，我们分析了一个真实的数据集。此外，还研究了决定最佳审查方案的不同标准。