### Abstract

In this research, the model of hierarchical structure from universe theory is imported into the general probability system which helps logically and subordinately describing, measuring, and evaluating the hierarchical probabilistic system. To clearly classify the hierarchy, “fayer” is proposed as the unit of hierarchy. Then, discussions on the relationship between hierarchy and system-of-systems and the risks caused by the hierarchy are proposed. This paper divides the problems of hierarchical probability mainly into two classes: the problems of surviving ratio and problems of passing ratio, and also, mixed problems of surviving ratio and passing ratio. Simultaneously, the surviving ratio is called as reliability. System reliability is one marked kind of hierarchical probability for the risk assessment of the hierarchical system. This paper introduces a new reliability system, P-out-of-1 system, which is derived from the K-out-of-N systems in hierarchy. The hierarchical reliability calculation of every fayer of the P-out-of-1 system is different from other fayers. Furthermore, the risk assessment of the hierarchical system for decision making of one maintenance manifests many differences by different descriptions in different fayers, even these descriptions concentrate on the same system.

Original language | English |
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Pages (from-to) | 242-260 |

Number of pages | 19 |

Journal | Reliability Engineering and System Safety |

Volume | 189 |

DOIs | |

Publication status | Published - 2019 Sep 1 |

### Keywords

- Hierarchical probability
- Hierarchical reliability
- K-out-of-N
- P-out-of-1
- Risk assessment

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality
- Industrial and Manufacturing Engineering

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## Cite this

*Reliability Engineering and System Safety*,

*189*, 242-260. https://doi.org/10.1016/j.ress.2019.04.026