(1) Find the minimum path set
Because there are many OR gates in the fault tree, it is easier to find the minimum path set than the minimum cut set, so we use the method of finding the minimum path set to judge the danger of the system. The method of finding the minimum path set is the same as the method of finding the minimum cut set, except that the AND gate of the fault tree is replaced by OR gate, and the operation is the same after the OR gate of the fault tree is replaced by AND gate. The definition of the minimum path set shows that if the basic event in the minimum path set does not occur, the top event will not occur. The more minimum path sets in the fault tree, the safer the system.
T=A 1A2
=B 1B2B3(B4+B5)
= x 1x 2 x3 x4 x 5 x 6(X7+X8+X9)(x 10+x 10+x 12+x 13+x 14+x 15+x 16)
= x 1x 2 x3 x4 x 5 x 6 x 7x 10+x 1x 2 x3 x4 x 5 x 7 x 10+x 1x 2 x3 x4 x 5 x 6 x 12+x 1 x 2 x3 x4 x 5 x 6 x 13+x 1x 2 x3 x4 x 5 x 6 x 14+x 65438
x 1 x2 x3 x4 x 5 x 6 x 7 x 16+x 1 x2 x3 x4 x 5 x 6 x8x 10+x 1 x2 x3 x4 x 5 x 6 x8x 1 1
+x 1 x2 x3 x4 x 6 x 8 x 12+x 1 x2 x3 x4 x 5 x 6 x 8x 13+x 1 x2 x3 x4 x 5 x 14+x 1 x2 x3 x4 x 5 x 15+x 1 x2 x3 x4 x 5 x 6 x 16+x 1 x2 x3 x4 x 5 x 6 x 6
+x 1 x2 x3 x4 x 5 x6x 9 x 1 1+x 1 x2 x3 x4 x 5 x 6 x 9x 12+x 1 x2 x3 x4 x 5 x 6 x 9x 13
+x 1 x2 x3 x4 x 5 x 6 x 9x 14+x 1 x2 x3 x4 x 5 x 6 x 9x 15+x 1 x2 x3 x4 x 5 x 6 x 9x 16
From the above solution, 2 1 minimum cut sets are obtained:
P 1={ X 1，X2，X3，X4，X5，X6，X7，X 10}
P2={ X 1，X2，X3，X4，X5，X6，X7，X 1 1}
P3={ X 1，X2，X3，X4，X5，X6，X7，X 12}
P4={ X 1，X2，X3，X4，X5，X6，X7，X 13}
P5={ X 1，X2，X3，X4，X5，X6，X7，X 14}
P6={ X 1，X2，X3，X4，X5，X6，X7，X 15}
P7={ X 1，X2，X3，X4，X5，X6，X7，X 16}
P8={ X 1，X2，X3，X4，X5，X6，X8，X 10}
P9={ X 1，X2，X3，X4，X5，X6，X8，X 1 1}
P 10={ X 1，X2，X3，X4，X5，X6，X8，X 12}
P 1 1={ X 1，X2，X3，X4，X5，X6，X8，X 13}
P 12={ X 1，X2，X3，X4，X5，X6，X8，X 14}
P 13={ X 1，X2，X3，X4，X5，X6，X8，X 15}
P 14={ X 1，X2，X3，X4，X5，X6，X8，X 16}
P 15={ X 1，X2，X3，X4，X5，X6，X9，X 10}
P 16={ X 1，X2，X3，X4，X5，X6，X9，X 1 1}
P 17={ X 1，X2，X3，X4，X5，X6，X9，X 12}
P 18={ X 1，X2，X3，X4，X5，X6，X9，X 13}
P 19={ X 1，X2，X3，X4，X5，X6，X9，X 14}
P20={ X 1，X2，X3，X4，X5，X6，X9，X 15}
P2 1={ X 1，X2，X3，X4，X5，X6，X9，X 16}
Structural importance analysis
As can be seen from the minimum cut set above, X 1x2x4x5x6 appears in each minimum cut set, so I φ (1) = I φ (2) = I φ (3) = I φ (4) = I φ (5).
= I φ (6) is the largest, I φ (7) = I φ (8) = I φ (9) is second only to the first six factors, I φ (10) = I φ (1) = I φ (1).
(3) Suggestions
1. Strengthen the gas detection, keep the monitoring system intact, and strictly implement the gas inspection systems such as "one gun, three inspections" and "three-person chain".
2, tunneling faces should keep enough air volume, so as to avoid the tunneling faces gas overrun and accumulation.
3, put an end to electrical fire and open flame, put an end to illegal shooting, underground smoking is strictly prohibited, in strict accordance with the operating procedures.
In the second quarter, the fault tree analysis of coal dust explosion in coal mining face (see next page for the fault tree)
Thirdly, qualitative analysis of fault tree.
The minimum cut set of fault tree is 80 groups, and the minimum path set is only 2 groups, so it is more convenient to analyze with the minimum path set.
Solution of minimum path set
Make a success tree according to the construction rules of success tree.
The structural functions of the success tree are:
t′= a 1′+A2′
=(b 1′×B2′×B3′×B4′)+(X9′×B5′×B6′)
=(x 1′X2′X3′X4′X5′X6′X7′X8′)+(X9′x 10′x 1 1′x 12′x 13′)
The minimum cut set found is as follow:
p 1 = { x 1’X2’X3’X4’X5’X6’X7’X8’}
P2 = { X9′x 10′x 1 1′x 12′x 13′}
Structural importance analysis:
The order of structural importance is as follows:
Ⅰφ(9)=Ⅰφ( 10)=Ⅰφ( 1 1)=Ⅰφ( 12)=Ⅰφ( 13)
>Ⅰφ( 1)=Ⅰφ(2)=Ⅰφ(3)=Ⅰφ(4)Ⅰφ=(5)Ⅰφ=Ⅰφ(6)=Ⅰφ(7)=Ⅰφ(8)
Conclusion: There are 40 groups of minimum cut sets in the fault tree. According to the definition of minimum cut set, if the basic events of any group of minimum cut sets occur at the same time, the top event will inevitably occur, indicating that the top event has 40 ways of occurrence. So this system belongs to a more dangerous system. There are two groups of minimum path sets, and the top event cannot occur unless the basic event of any group of minimum path sets occurs. Therefore, the system has two control modes.