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### V6 Resource File                             ###
### generated on: Mon May 16 10:05:25 EDT 2011   ###
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### This file is designed to be delivered to the ###
### translator. 					###
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5008=Could not read response variable attributes
7619=SENSITIVITIES
10205=Response
11112=Reliability Index (beta)
12208=Reliability Constraint results: 
20028=Could not evaluate the design point.
25066=Could not get random variable metamodel
32228=Could not read random variable attributes
35045=Input arguments cannot be null
35772=Reliability Constraint: 
37746=Std. deviation
39383=Could not evaluate design point
42341=MPP - Most Probable Point of failure
42862=Reliability Constraint
43464=Actual Reliability
43774=Failure function gradient value array cannot be null.
45592=MVP - Mean Value Point
47045=Value has to be greater than 0 for option {0}
48961=Nominal Value
57518=MPP in x-space
61759=Failure function gradient value array is not of the correct size.
62615=Gradient at MVP in x-space
66002=Failure function value array cannot be null.
68527=Random Variable
70880=Responses at Mean Value Point: 
74993=Gradient at MPP in u-space
78813=Gradient at MPP in x-space
80763=Bound Value
85333=Bound Type
85443=Fractional Effect
86063=Outer dimensions of array arguments must match.
88713=Mean
94691=Could not clone context for mean value point
99187=Could not evaluate the design point -  response value is null.
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###   Meta Model I18N string                       #
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prop.dispname.minimumfinitedifferencestep=Minimum Finite Difference Step
desc=First Order Reliability Method
dispname=First Order Reliability Method (FORM)
prop.dispname.finitedifferencestepsize=Finite Difference Step Size
prop.dispname.mppmaxiterations=MPP Maximum Iterations
prop.dispname.mpprelconvergence=MPP Relative Convergence
longdesc=<b>FORM - First Order Reliability Method</b><br><br> The <i>First Order Reliability Method (FORM)</i> is a probabilistic method that comes from civil engineering, originally developed for performing structural reliability analysis. Given one or more identified random variables, the focus in structural reliability analysis is to assess the <i>probability of failure</i> - the probability of violating a constraint - of a structural component or system, resulting from performance (output) variation caused by the variation of uncertain, random (input) variables. The structural reliability is then defined as the probability of satisfying a constraint, and is equal to 1-probability of failure.\t<br><br> FORM takes advantage of the desirable properties of the standard normal probability distribution. Hasofer and Lind (1974) defined the reliability index as the shortest distance from the origin of the standard normal space (U-space) to a point on the failure surface. Mathematically, determining the reliability index is a minimization problem with one equality constraint(shortest distance such that the solution point is on the constraint, g(<b>X</b>)=g(<b>U</b>)=0). <br><br> A transformation is introduced to map the original random vector <b>X</b> (in X-space) to the standard, uncorrelated normal vector using <b>U</b>=T(<b>X</b>). The solution of the minimization problem in U-space, U*, is called the <i>Most Probable Point (MPP)</i>. <br><br> If the failure function g(<b>U</b>) is linear in terms of the normally distributed random variables U<sub>i</sub>, the failure probability is calculated as: <br><br> P<sub>f</sub> = \u03A6(-\u03B2) <br><br> where, \u03A6 is the standard normal distribution function and \u03B2 is the distance to the MPP. If the failure function is nonlinear, or the random variables are not normally distributed, a good approximation can still be obtained using the equation above, provided that the curvature of the failure surface at the MPP is not too large in magnitude.
prop.dispname.mppabsconvergence=MPP Absolute Convergence
