Reliability Analysis for Industrial Systems with Interdependency

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This grant supports research for the development of statistical models for interdependent systems. Specific systems under investigation are those for which the failure of a component within the system affects the reliability of the remaining components. The main goal of this research is to characterize this dependence statistically, using as few assumptions as needed about the component lifetime distributions. Several tools are used to identify the dynamic nature of a system, including reliability estimation, correspondent reliability uncertainty measurement, and statistical tests for interdependence. The load share model, first derived in textile engineering to describe the failure of individual fibers within a bundle, is used as a basis for characterizing component interdependencies. Statistical tests for load sharing rules include a test to see if the load-sharing environment exists, and a test of whether the system stress causes components to fail at an increasing rate as other components fail. Component classes of interest (e.g., those with increasing failure rate) corresponding to specific applications are emphasized in this research project. Applications of the statistical methods are designed for various industries. The research is motivated by problems in the nuclear industry where components in a power plant can suffer decreased reliability if nearby components are degraded or failed. In the field of software reliability, the time until a program bug is found in the software depends on what other bugs exist in the software. Methods derived here can help in the estimation of dynamic software reliability problems like this one. Other examples include materials testing. Metal fatigue, for example, is often characterized by crack growth. In a given specimen, several cracks can exist in the material, but the largest one inherits most of the applied stress, and thus will grow at a faster rate than the other cracks. This provides a platform for extending the load-share model to degradation models in materials engineering.