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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 46E

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Question

The limit state equation for a particular failure mechanism is:
Z = 50+
The variables have the following values:
Variable
X₁
X₂
X3
5X₁-4X2-2X3 + X4
Mean
X₁ [12.25
15
10
15
5
s.d.
The variables X1, X₂ and X3 are correlated and the covariance matrix is:
X₁ X₂ X3
-5
2
X₂ -5
9-4
X3 2 -4 6.25
3.5
3.0
2.5
1.5
Determine the reliability index of the system: (i) assuming no correlation
effects; and (ii) allowing for correlation.

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