Alomani Ghadah A, Hassan Amal S, Al-Omari Amer I, Almetwally Ehab M
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia.
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt.
Sci Rep. 2024 Sep 6;14(1):20865. doi: 10.1038/s41598-024-71498-w.
Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson-Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.
当加速寿命试验的结果无法推广到使用环境时，可采用部分加速寿命试验（PALT）。本文讨论了在具有完整数据的恒定PALT中不同估计策略面临的挑战。假设试验项目的寿命分布服从幂半逻辑分布。提出了几种经典和贝叶斯估计技术来估计幂半逻辑分布的分布参数和加速因子。这些技术包括安德森-达林检验、最大似然估计、克拉默-冯米塞斯检验、普通最小二乘法、加权最小二乘法、最大间距乘积法和贝叶斯估计法。此外，还构建了贝叶斯可信区间和近似置信区间。提供了一项模拟研究，以比较基于均方误差、绝对平均偏差、区间长度和覆盖概率的各种估计方法的结果。该研究表明，在采用均方误差和平均偏差的最小值时，最大间距乘积估计在大多数情况下是最有效的策略。在大多数情况下，考虑到均方误差和平均偏差值时，贝叶斯方法优于其他方法。在比较近似置信区间和贝叶斯可信区间时，后者具有更高的覆盖概率和更小的平均长度。为说明起见，研究了两个真实数据集。对这两个真实数据集的研究表明，所采用的方法可行且适用于某些与工程相关的问题。
