reliability of coherent threshold systems

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Double-threshold system

X X X1 3 5

X X X2 3 4

X X4 5

X X3 5

X3X3

X1

X1

X5

X X X1 2 5

X X X1 3 5

X4

X2

T = 0

T = 1

T = 2

T = 3

T = 5

[1] [1, 2] [1, 2, 2] [1, 2, 2, 3] [5, 1, 2, 2, 3]

p2

p3p4

p3

q4p5

p1

p4

q2

q4 q5

q2

q3

q3

q1

11

1

1

1

1 1 1 1

1111

1

1

1

1

1

1

11

1

p2q p p1 4 5

p4

q q1 2 3 4 5p p p

q p q1 3 4 5p

p5

p3

p1p1p3

T = -4

T = -3

T = -2

T = -1

T = 0

T = 1

T = 2

T = 3

T = 4

T = 5

P1

P1

P1

P5

P5

P4

P4

P3

P3

P4

P2

P4

P5

P5

P5

P1

P1

q1

q1

q1

q1 q5

q5

q5

q5 q4 q3

q3 q2

q4

q4

q4q5

q1

[5] [5, 3] [5, 2, 3] [5, 2, 2, 3] [5, 1, 2, 2, 3]

1 1

1 1 1

1

1 1

1 1 1 1

1111

1 1 1

111

p3 p3

p1

p4

p2

p5