Kayid Mohamed, Alshehri Mashael A
Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia.
Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh 11362, Saudi Arabia.
Entropy (Basel). 2023 Jul 9;25(7):1033. doi: 10.3390/e25071033.
Recently, there has been growing interest in alternative measures of uncertainty, including cumulative residual entropy. In this paper, we consider a mixed system consisting of components, assuming that all components are operational at time . By utilizing the system signature, we are able to compute the cumulative residual entropy of a mixed system's remaining lifetime. This metric serves as a valuable tool for evaluating the predictability of a system's lifetime. We study several results related to the cumulative residual entropy of mixed systems, including expressions, limits, and order properties. These results shed light on the behavior of the measure and provide insights into the predictability of mixed systems. In addition, we propose a criterion for selecting a preferred system based on the relative residual cumulative entropy. This criterion is closely related to the parallel system and provides a practical way to choose the best system configuration. Overall, the present study of cumulative residual entropy and the proposed selection criterion provide valuable insights into the predictability of mixed systems and can be applied in various fields.
最近，人们对不确定性的替代度量，包括累积剩余熵，越来越感兴趣。在本文中，我们考虑一个由组件组成的混合系统，假设所有组件在时刻都是可运行的。通过利用系统特征，我们能够计算混合系统剩余寿命的累积剩余熵。这个度量是评估系统寿命可预测性的一个有价值的工具。我们研究了几个与混合系统累积剩余熵相关的结果，包括表达式、极限和序性质。这些结果揭示了该度量的行为，并为混合系统的可预测性提供了见解。此外，我们提出了一个基于相对剩余累积熵选择首选系统的准则。这个准则与并联系统密切相关，并提供了一种选择最佳系统配置的实用方法。总体而言，目前对累积剩余熵的研究以及提出的选择准则为混合系统的可预测性提供了有价值的见解，并可应用于各个领域。
