Titel_SS06

Finally the probability of failure for the mixed system is given by:

PPIIUIUS,0 1  (123 4 56) 1(1210)(1110) 2.0110>? > > ??  ^797

Now if full correlation is assumed, the system failure probability can be calculated in a simlar
way using the Equations (9.5)-(9.6) as:

The system’s reliability is seen to depend very much on the correlation structure between the
failure modes of the system. However, as nothing is known about the correlation between the
individual elements of the system the lower and upper bounds on the system’s failure
probability are not necessarily identical to the values corresponding to zero and full
correlation of all failure modes.

These may be found to be:

2.01 10^75 1 10

PS



It is seen that the difference in this case is negligible.

1

2

3

4

1

2

3

56

4 (5 6)

123 4 (5 6)

Figure 9.4: Illustration of scheme for successive reduction of a system based on the simple bounds.

9.3 Mechanical Modelling of Structural Systems

Having discussed the basics of the probabilistic characteristics of systems it is important to
address the mechanical aspects of the modelling of structural systems. To this end it is useful
to start by the identification of the mechanical behaviour of the individual failure modes.

P(1 2 3) min(110,110,110) 110^225 ^5

P(5 6) max(1 10 ,1 10 ) 1 10^55 ^5

P(4    >5 6 ) min(110 ,110 ) 110? ^25 ^5

,1 >? > > ??^55

5

,1

(1 2 3 4 5 6 ) max(110 ,110 )

110

S

S

PP

P

1

1