An Extreme-Value Event Approach for Frequency-Domain Performance Reliability

With time and usage, systems become less reliable as performance measures continuously degrade. In frequency-domain design, a sufficiently large number of performance measures are selected at discrete frequencies to act as surrogates for the frequency bands. Over discretized life-time, the system failure event grows into an ever larger number of highly correlated elementary failure events in terms of both frequency and time. This paper replaces the complex system failure event with an equivalent minimum extreme-value event: it is shown that this single event retains all of the original correlation information and is invariant to the number of elemental events. The novelty of the new and elegant approach is that it standardizes the failure probability evaluation via one-dimensional pdfs at either selected times, or importantly, selected frequencies. Further, pdfs of the frequencies causing failure over life-time are shown to be a useful design tool. The pdfs are easily represented by sampling techniques. Error analysis identifies three errors and the paper gives strategies to control. Case studies of an analogue filter show the proposed methodology has engineering applications. The impact of the proposed methodology is two-fold: it presents a standard way to assess and manage the uncertainty in the degradation process, and it provides a launching platform for timely design optimization.