Based on some real backgrounds, a new balanced system structure, a consecutive k-out-of-m: F system with a symmetry line, is proposed in this paper. Considering different state numbers of a subsector, the new balanced system is analyzed under two situations respectively: the subsector with binary-state and the subsector with multi-state, while the multi-state balanced systems have not been studied in the previous research. Besides, two models are developed in terms of assumptions for the two situations, respectively. For this system, several methods, such as the finite Markov chain imbedding approach, the order statistics technique and the phase-type distributions, are used on the models. In addition to system reliability formulas, the means and variances of the system lifetimes under two models for different situations are given. Finally, numerical examples are presented to illustrate the results obtained in this paper.

基于一些真实的背景，一个新的平衡系统结构，一个连续的k -out-of- m：F 系统具有对称线，在本文中被提出。考虑到子扇区的不同状态数，分别在二元子扇区和多状态子扇区两种情况下对新的平衡系统进行分析，而多状态平衡系统在以往的研究中尚未进行研究。此外，分别根据两种情况的假设开发了两个模型。对于该系统，模型上使用了多种方法，例如有限马尔可夫链嵌入方法、阶次统计技术和相型分布。除了系统可靠性公式外，还给出了两种模型下不同情况下系统寿命的均值和方差。最后，给出了数值例子来说明本文获得的结果。