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Multiple degradation paths arise when systems operate under uncontrolled, uncertain environmental conditions at customers' hands in the field. This paper presents a design stage method for assessing performance reliability of systems with competing time-variant responses due to components with uncertain degradation rates. Herein, system performance measures (e.g. selected responses) are related to their critical levels by time dependent limit-state functions. System failure is defined as the non-conformance of any response, and hence unions of the multiple failure regions are formed. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region that emerges from a safe region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory is manifest through evaluating probabilities by Monte Carlo simulation. Error analysis suggests ways to predict and minimize errors. An electrical temperature controller shows the details of the method, and the potential of the approach. It is shown that the proposed method provides a more realistic way to predict performance reliability than either worst-case, or simple average-based approaches that are available in the open literature.
Date of Publication: June 2008