We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov process such that the level of performance of one component can change only for one level lower than the observed one, and the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such systems.

中文翻译：

---

具有毕业失败和相等转变强度的多状态系统

我们考虑具有分级故障的不可恢复的同质多状态系统，其中每个组件都可以在M +1个线性排序的性能级别上工作。每个组件的潜在故障过程是同质的马尔可夫过程，因此一个组件的性能水平只能在比所观察到的水平低一个级别的范围内变化，并且故障对于不同的组件是独立的。我们推导随机向量X的概率分布，表示发生故障时的系统状态，并将其用于测试均等跃迁强度的假设。在这些强度相等的假设下，我们推导了矩估计器的方法，用于确定给定状态向量中的故障概率和强度。最后，我们计算了此类系统的可靠性函数。