Department of Mathematics, Faculty of Science, New Valley University, El-Khargah 72511, Egypt.
Department of Mathematical Science, Faculty of Applied Science, Umm AL-Qura University, Makkah 24382, Saudi Arabia.
Math Biosci Eng. 2023 Jan;20(2):1674-1694. doi: 10.3934/mbe.2023076. Epub 2022 Nov 4.
This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.
本文讨论了使用 II 型逐步截尾样本的阶跃应力部分加速寿命试验中的估计问题。使用条件下的项目寿命遵循双参数倒 Kumaraswamy 分布。通过最大似然估计的渐近分布特性，我们计算了未知参数的渐近区间估计。贝叶斯程序用于从对称和非对称损失函数计算未知参数的估计值。贝叶斯估计值不能显式获得，因此使用林德利近似和马尔可夫链蒙特卡罗技术来获得贝叶斯估计值。此外，还计算了未知参数的最高后验密度可信区间。通过一个实例说明了推断方法。最后，提供了一个明尼阿波利斯失败时间的三月降水量（英寸）的实际例子，说明了这些方法在实践中的表现。
