Stochastic Models and Inference for the Reliability of Complex Systems

University South Carolina Research Foundation, Columbia SC

Investigators

Abstract

Important aspects of modeling the failure or reliability of complex systems are (i) the modeling of the component interactions and (ii) incorporating information about each component into the system. Both are needed to relate the system damage caused by component failure to the failure of the entire system. Here, new approaches to these problems are taken. The first approach is based on load-sharing systems of components, where the interactions among components are modeled by load-sharing rules. For examples, for a mechanical system undergoing an increasing load, such as a fibrous composite material under tensile loading where fiber segments are the components, or a routing system under increasing "traffic" where the nodes are components, the load-sharing rule describes how the tensile load or traffic is transferred/redistributed from failed components to working components. The second approach is based on an entropy/information formalism where damage/destruction in the system is quantified in terms of hazard and reverse hazard functions. These new approaches should lead to more realistic stochastic or probabilistic models for the failure of general systems such as those mentioned. In addition, many complex systems, or pieces of equipment, degrade over time or under increasing load before they fail, and modeling such degradation for prediction of failure is an important part of this project. Engineering degradation tests can often be performed at regular intervals to measure the levels of the degradation processes of such systems. The resulting degradation data, along with any actual failure data, can be used to fit models which provide estimates of the failure distributions or give a basis for prediction of a degradation threshold that causes system failure. Analogously, the same approaches to degradation modeling can be utilized in the progression of a disease toward a meaningful endpoint in medical or health settings. Hence, in this research project, development of models for degradation and failure will be undertaken that involve cumulative damage concepts and result in tractable approaches for statistical inference based on known, but perhaps little-used, distributions, such as inverse Gaussian-type or Birnbaum-Saunders-type distributions. In particular, covariates, or acceleration variables, will be included in the models, and classical inference, as well as Bayesian analysis, will be investigated for these general cases. Accurate prediction of the failure of pieces of equipment or general systems is essential in decision making concerning maintenance or replacement policies for such systems. This is an especially important factor in preventing catastrophic failures of key systems or equipment during critical operations. The overall objective of this research project is to address the above issue by (1) developing new mathematical models for system failure under more realistic conditions and assumptions about the system, taking into account physics-of-failure considerations, and (2) developing new procedures to make inferences about system failure based on either observed failures of such systems or observed levels of the degradation of the system over time, or both.