On the Stochastic Analysis of a Three-Units Ventilation Sytstem for Promoting the Safety of Mines

by: Mohammad El-Moniem Soleha(1), Ghada E. El-Shanshoury(2).

Abstract: This paper aims at constructing a stochastic system of ventilation in the underground mines. Thus, a complete “probabilistic structure” of the system has been presented, upon which the stochastic behavior of a three-similar units (fans) ventilation system is statistically modeled. Having established the model, a statistical analysis of its characteristics is performed to explore the stochastic features of the proposed system. In this context, an explicit probabilistic expressions are derived for the mean time to system failure (MTSF) of the ventilation system. Also, a fifth order polynomial formula for the (MTSF) is provided under the exponential assumption for the failure time and replacement time distribution. A numerical example is presented to demonstrate the dependence of the (MTSF) on repair and replacement rate, as well as its importance, as a measure of system reliability, in elevating the safety levels in mines.

Key Words: Stochastic system, stochastic behavior, probabilistic structure, system reliability, exponential assumptions, mean time to system failure

Authors:
Mohammad El-Moniem Soleha, drsoleha@Yahoo.com
hada E. El-Shanshoury,

Editor: Weiming Ke, Weiming.ke@sdstate-edu

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