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Three Analysis Types:

•  Probability Analysis

•   Inverse Probability Analysis

• CDF/PDF Analysis

Two Design Types:

•  Robust Design

•   Optimization Analysis

  Probability Analysis

This is the conventional reliability analysis that calculates the probability (i.e., reliability and failure probability), the associated sensitivities and the most likely conditions (MPP) for a specified level of limit-state function. This analysis can be applied to both component and system probability problems.

 Input of Probability Analysis:

• Definition of random variables

•  Definition of failure domain by limit-state functions

Typical Output of Probability Analysis:

• MPP

• Failure probability

• Sensitivity of failure probability with respect to random variables and their parameters

• Mean and standard deviation of limit-state functions

The concept of probability analysis is illustrated in the following two figures:

Figure 1. Illustration of Probability Analysis for Calculating the Probability of g(x) <= g_0 (CDF View)

Figure 2. Illustration of Probability Analysis for Calculating the Probability of g(x) <= g_0 (PDF View)

Inverse Probability Analysis

Inverse Probability Analysis identifies the limit-state function level and the most likely conditions that will produce a predefined probability or a predefined reliability index. The associated sensitivities of probability with respect to random variables and distribution parameters are also calculated in this analysis. The inverse probability analysis can only be performed on component probability problems.

 Input of Inverse Probability Analysis:

• Definition of random variables

• Definition of the limit-state function

• Either the predefinition of failure probability or the predefinition of a reliability index

Typical output of Inverse Probability Analysis:

• The value of limit-state function, c, that the probability of g(x)-g_0 £ c is equal to the predefined failure probability

•   MPP

• Sensitivity of failure probability with respect to random variables and their parameters

•  Mean and standard deviation of limit-state function

The concept of Inverse Probability Analysis is illustrated in the following two figures:

Figure 3. Illustration of Inverse Probability Analysis to Find g_0 Such That the Probability of g(x)<=g_0 is P

Figure 4. Illustration of Inverse Probability Analysis to Find g_0 Such That the Probability of g(x)<=g_0 is Pf (PDF View)

 CDF/PDF Analysis

You should establish the CDF/PDFof limit-state function in the predefined range of probabilities or levels of limit-state function. The CDF/PDF Analysis can only be applied to component probability problems.

Input of CDF/PDF Analysis:

•  Definition of random variables

• Definition of the limit-state function

•  Input one of the following:

  • Upper and lower bounds of failure probability

  • Upper and lower bounds of reliability index

  • Upper and lower bounds of limit-state function

  • Individual failure probability values

  • Individual reliability indexes

  • Individual g values

Typical output of CDF/PDF Analysis:

• PDF of limit-state function

• CDF of limit-state function

• MPPs corresponding to different levels of limit-state function in constructing the PDF/CDF curves

The CDF/PDF Analysis is illustrated in the following two figures:

Figure 5. Illustration of CDF/PDF Analysis Such That the Probability of g(x)<=c is between P_flow  and P_fup (CDF View)

Figure 6. Illustration of CDF/PDF Analysis Such That the Probability of g(x)<=c is between P_flow  and P_fup (PDF View) 

Last Updated 02/08/10

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