概率统计在矿井通风系统可靠性评估中的应用

构建一个随机非稳定地下矿山通风系统，此通风系统有三个机组，机组的随机运行状态构成了一个完整的“系统的概率结构”。对此通风系统的运行状态进行概率统计分析，探讨了该随机系统的特征。由此推导出了通风系统故障的平均时间是一个显式的概率表达式。同时，假设系统失效时间和更换时间符合指数分布的情况下，得出计算系统故障平均时间的一个五阶多项式公式。通过验证，证明了系统故障平均时间的大小依赖于系统维修和更换的比率，而且是检验系统可靠性的重要指标，有利于提高矿山安全水平。

Application of probability and statistics in assessing the reliability of mine ventilation system

By constructing a stochastic and instability system of ventilation in the underground mines, the stochastic behavior of a three units ventilation system was statistically modeled, and a complete ＂probabilistic structure＂ of the system was presented. A statistical analysis of its characteristics was performed to explore the stochastic features of the ventilation system. So an explicit probabilistic expressions were derived for the mean time to system failure （MTSF） of the ventilation system. Also, a fifth order polynomial formula for the MTSF was provided under the ex- ponential assumption for the failure time and replacement time distribution. A numerical example was presented to demonstrate the dependence of MTSF on repair and replacement rate, as well as its importance, as a measure of system reliability, in elevating the safety levels in mines.