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General System Problem

Table of Contents

1. Description

2. Limit State Function

3. Random Variables

4. Analysis

5. Results

  Description:

General system reliability analysis with dependent random variables.

 Limit-State Function: 

Failure domain F(x) is defined as

where

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Random Variables:

Group 1: X₁ and X₂ are defined in terms of marginals and correlation matrix as
X₁ ~ Log Normal(m=100, s=20)
X₂ ~ Log Normal(m=15, s=3)

X₃ and X₄ are defined in terms of marginals and correlation matrix as

X₃ ~ Type II Largest Value(m=7, s=2.1)

X₄ ~ Type II Largest Value(m=5, s=1.5)

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 Analysis:

Calculate sysrem failure probability by FORM and Monte Carlo simulation

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Results:

By using FORM: Download UNIPASS PAS File

	Reliability Index, b	Failure Probability
	2.4585690E+00	6.9745981E-03
	2.3097249E+00	1.0451694E-02
	3.2946315E+00	4.9275405E-04
	2.9745337E+00	1.4671712E-03
	2.0282776E+00	2.1265962E-02
	2.9608654E+00	1.5338801E-03
	2.8505393E+00	2.1822576E-03
	1.6256116E+00	5.2016157E-02
	-1.8851906E+00	0.970297942963399
System F	2.3253515E+00	1.0026586E-02

End of FORM Analysis                                        
 No. of g-functions calculated up to this point      =      391
 No. of derivatives of g calculated up to this point =       61

By using Monte Carlo simulation: Download UNIPASS PAS File

  Number of g-function calculations                  =      391
 Number of sampling points                          =    39495
 Mean of estimated failure probability              = 1.0026586E-02
 Standard deviation of estimated failure prob.      = 5.0132890E-04
 COV of estimated failure probability               = 4.9999962E-02
 Generalized reliability index of failure prob.     = 2.3253515E+00

 Bounds of mean estimated failure prob. based on 90.00% confident level:
 Lower bound of Pf= 9.2019730E-03, its generated beta= 2.3573892E+00
 Upper bound of Pf= 1.0851198E-02, its generated beta= 2.2955365E+00

End of Simulation Method                                           
No. of g-functions calculated up to this point      = 2918529
No. of derivatives of g calculated up to this point =       0

Finishing 

Last Updated 02/08/10

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