# Integrity Index and Integrity-based Optimal Design of Structural Systems

## Integrity Index and Integrity-based Optimal Design of Structural Systems" Mousavi a, Gardoni b.

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a Texas A&M University,

b University of Illinois at Urbana-Champaign

### Abstract

The reliability of a system is a function of the reliability of each of its components. This paper develops the concept of integrity of a system as a measure of the balance between the reliability of the system components and puts forward the definition of Integrity Index as well as a method to maximize this index in a structural system. The integrity is quantified using the conditional probabilities of failure of the components given that the system has failed to assess the importance of the individual components in system reliability. The Integrity Index is defined as 1 minus the difference between the maximum and minimum conditional probabilities of failure of the system components. Therefore, this index can quantify the integrity of any structural system as long as the conditional probabilities of failure of its components can be calculated. Integrity Index is equal to 1 when all of the system components have the same contribution to the system reliability and it is 0 when there is the maximum imbalance between the contributions of the components to the system reliability. Using the conditional probabilities of failure of the components, a new method is then developed for Integrity-based Optimal Design that maximizes the system integrity giving the maximum Reliability Return on Investment (RROI). This method is first discussed for various systems (series, parallel and general). Then, as an example, the Integrity Index and Integrity-based Optimal Design are presented for an offshore mooring system.

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