ABSTRACT

Generalized progressive hybrid censoring schemes have become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre-determined time T. Otherwise, due to the necessity of more realistic stress strength models, this article considers to estimate the reliability of an s-out-of-k system with non-identical component strengths when component strengths and stress follow Weibull distributions under generalized progressive hybrid censoring scheme. The maximum likelihood estimation of the reliability of such a system is obtained with corresponding asymptotic and bootstrap confidence intervals. Further, Bayesian estimations are derived by using the Lindley's approximation and Markov Chain Monte Carlo method with the Metropolis-Hasting algorithm. The corresponding highest posterior density confidence intervals of the Bayes estimates are obtained. In Bayesian estimations symmetric and asymmetric loss functions are evaluated. Comparisons for the performances of the estimators are made with simulation studies and a real data example.

摘要

广义渐进式混合删失方案已经变得非常流行，这取决于在预定时间 T 之前很少发生故障时不能应用渐进式混合删失方案。否则，由于需要更现实的应力强度模型，本文考虑估计一个在广义渐进混合删失方案下，当分量强度和应力遵循 Weibull 分布时，具有不同分量强度的 s-out-of-k 系统。这种系统的可靠性的最大似然估计是通过相应的渐近和自举置信区间获得的。此外，贝叶斯估计是通过使用林德利近似和马尔可夫链蒙特卡罗方法与 Metropolis-Hasting 算法得出的。获得贝叶斯估计的相应最高后验密度置信区间。在贝叶斯估计中，评估对称和非对称损失函数。通过模拟研究和真实数据示例对估计器的性能进行了比较。