In reliability theory, there are many measures for describing the characteristics of repairable systems, such as reliability, point availability and interval availability. However, these reliability measures do not cover some situations that one may be interested in. In this work, two new reliability measures, multi-point bounded-covering availability and multi-interval bounded-covering availability, are introduced, and derived in matrix form for aggregated Markovian repairable systems. The formulas for single-point, single-interval, binary-point and binary-interval bounded-covering availabilities are all obtained by an enumeration method. The formulas for multi-point and multi-interval bounded-covering availabilities are given in a recursive computational form. Some properties of these two new measures are then discussed briefly, and a few numerical examples are provided to illustrate the results presented here. Finally, some conclusions and discussions are given.

在可靠性理论中，描述可修系统特性的度量有很多，如可靠性、点可用性和区间可用性。然而，这些可靠性度量并没有涵盖人们可能感兴趣的某些情况。在这项工作中，引入了两个新的可靠性度量，多点有界覆盖可用性和多区间有界覆盖可用性，并以矩阵形式导出用于聚合马尔可夫可修复系统。单点、单区间、二元点和二元区间有界覆盖可用性的公式都是通过枚举的方法得到的。多点和多区间有界覆盖可用性的公式以递归计算形式给出。然后简要讨论这两个新措施的一些性质，并提供了一些数值示例来说明此处提供的结果。最后，给出了一些结论和讨论。