Signature theory plays an important part in the field of reliability. In this paper, the ordered multi-state system signature and its related properties are discussed based on a life-test of independent and non-identical coherent or mixed systems with independent and identical binary-state components. Dynamic properties of these systems are considered through a new notion called dynamic multi-state system signature, and then related comparisons are made based on system lifetimes and costs. Finally, the theoretical results established are illustrated with some specific examples to demonstrate the use of dynamic ordered multi-state system signature in evaluating used multi-state coherent or mixed systems.

签名理论在可靠性领域发挥着重要作用。本文基于具有独立和相同二元状态分量的独立和不同相干或混合系统的寿命测试，讨论了有序多状态系统特征及其相关性质。通过动态多状态系统签名的新概念来考虑这些系统的动态特性，然后根据系统寿命和成本进行相关比较。最后，通过一些具体例子来说明所建立的理论结果，以演示动态有序多状态系统签名在评估所使用的多状态相干或混合系统中的使用。