论文标题
更新过程和扩展的叠加的下限和上限
Lower and upper bounds of the superposition of renewal processes and extensions
论文作者
论文摘要
考虑一个由多个插座组成的系统，每个插座都插入了一个组件。如果组件失败，则立即更换并恢复系统操作。然后，系统的故障过程是更新过程的叠加（或叠加的更新过程，SRP）。如果导致系统失败的组件的标签尚不清楚，但已知失败之间的时间，我们将此类数据称为{\ it掩盖故障数据}。基于蒙版故障数据估算SRP是具有挑战性的。 本文仅可用时，获得了SRP速率的下限和上限。如果在失败的组件上进行维修（而不是替换），则系统的故障过程是广义续订过程（SGRP）的叠加。然后，纸是SGRP速率的下部和上限，并提议使用边界的加权线性组合来近似SGRP。提供了与其他结构（例如并行系统）的系统的可能扩展的讨论。然后提出用于模拟SGRP的算法。数值示例用于说明所提出的近似方法。
Consider a system consisting of multiple sockets into each of which a component is inserted. If a component fails, it is replaced immediately and system operation resumes. Then the failure process of the system is the superposition of renewal processes (or superimposed renewal process, SRP). If the label of the components that cause the system to fail are unknown but the times between failures are known, we refer to such data as {\it masked failure data}. To estimate the SRP based on masked failure data is challenging. This paper obtains the lower and upper bounds of the rate of the SRP when only masked failure data are available. If repair (rather than replacement) is conducted on failed components, the failure process of the system is the superposition of generalized renewal processes (SGRPs). The paper then derives the lower and upper bounds of the rate of SGRPs and proposes to use a weighted linear combination of the bounds to approximate the SGRP. Discussions are provided for possible extensions of the bounds for systems with other structures such as parallel systems. An algorithm for simulating the SGRP is then proposed. Numerical examples are used to illustrate the proposed approximation method.
