# local_reliability

Local reliability method

**Topics**

uncertainty_quantification, reliability_methods

**Specification**

*Alias:*nond_local_reliability*Arguments:*None

**Child Keywords:**

Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|

Optional |
Specify which MPP search option to use |
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Optional |
Values at which to estimate desired statistics for each response |
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Optional |
Specify probability levels at which to estimate the corresponding response value |
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Optional |
Specify reliability levels at which the response values will be estimated |
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Optional |
Specify generalized relability levels at which to estimate the corresponding response value |
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Optional |
Selection of cumulative or complementary cumulative functions |
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Optional |
Number of iterations allowed for optimizers and adaptive UQ methods |
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Optional |
Stopping criterion based on objective function or statistics convergence |
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Optional |
Output moments of the specified type and include them within the set of final statistics. |
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Optional |
Identifier for model block to be used by a method |

**Description**

Local reliability methods compute approximate response function distribution statistics based on specified uncertain variable probability distributions. Each of the local reliability methods can compute forward and inverse mappings involving response, probability, reliability, and generalized reliability levels.

The forward reliability analysis algorithm of computing reliabilities/probabilities for specified response levels is called the Reliability Index Approach (RIA), and the inverse reliability analysis algorithm of computing response levels for specified probability levels is called the Performance Measure Approach (PMA).

The different RIA/PMA algorithm options are specified using the
`mpp_search`

specification which selects among different limit state
approximations that can be used to reduce computational expense during
the MPP searches.

**Theory**

The Mean Value method (MV, also known as MVFOSM in [HM00]) is the simplest, least-expensive method in that it estimates the response means, response standard deviations, and all CDF/CCDF forward/inverse mappings from a single evaluation of response functions and gradients at the uncertain variable means. This approximation can have acceptable accuracy when the response functions are nearly linear and their distributions are approximately Gaussian, but can have poor accuracy in other situations.

All other reliability methods perform an internal nonlinear optimization to compute a most probable point (MPP) of failure. A sign convention and the distance of the MPP from the origin in the transformed standard normal space (“u-space”) define the reliability index, as explained in the section on Reliability Methods on the Uncertainty Quantification page. Also refer to Variable Support for additional information on supported variable types for transformations to standard normal space. The reliability can then be converted to a probability using either first- or second-order integration, may then be refined using importance sampling, and finally may be converted to a generalized reliability index.