Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt.
Sci Rep. 2024 Mar 8;14(1):5694. doi: 10.1038/s41598-024-55511-w.
Besides achieving high quality products, statistical techniques are applied in many fields associated with health such as medicine, biology and etc. Adhering to the quality performance of an item to the desired level is a very important issue in various fields. Process capability indices play a vital role in evaluating the performance of an item. In this paper, the larger-the-better process capability index for the three-parameter Omega model based on progressive type-II censoring sample is calculated. On the basis of progressive type-II censoring the statistical inference about process capability index is carried out through the maximum likelihood. Also, the confidence interval is proposed and the hypothesis test for estimating the lifetime performance of products. Gibbs within Metropolis-Hasting samplers procedure is used for performing Markov Chain Monte Carlo (MCMC) technique to achieve Bayes estimation for unknown parameters. Simulation study is calculated to show that Omega distribution's performance is more effective. At the end of this paper, there are two real-life applications, one of them is about high-performance liquid chromatography (HPLC) data of blood samples from organ transplant recipients. The other application is about real-life data of ball bearing data. These applications are used to illustrate the importance of Omega distribution in lifetime data analysis.
除了实现高质量的产品外，统计技术还广泛应用于与健康相关的许多领域，如医学、生物学等。坚持将物品的质量性能保持在期望的水平是各个领域非常重要的问题。过程能力指数在评估物品的性能方面起着至关重要的作用。在本文中，基于逐次型 II 截尾样本计算了基于三参数 Omega 模型的大即好过程能力指数。在逐次型 II 截尾的基础上，通过最大似然法对过程能力指数进行了统计推断。此外，还提出了置信区间，并进行了寿命性能的假设检验。吉布斯在马尔可夫链蒙特卡罗（MCMC）技术中使用 metropolis-hasting 采样器程序，以实现未知参数的贝叶斯估计。模拟研究表明，Omega 分布的性能更有效。本文最后有两个实际应用，一个是器官移植受者血液样本的高效液相色谱（HPLC）数据，另一个是实际的球轴承数据。这些应用旨在说明 Omega 分布在寿命数据分析中的重要性。
