Computing the cdf for degrading dynamic systems

The times and frequencies of inspection, maintenance and replacement in degrading dynamic systems are difficult to determine. Mechanistic computer models are helpful but are inefficient because its complexity and the uncertainties in system characteristics and degradation rates. Probability distributions that are traditionally calculated through Monte Carlo Methods require thousands and thousands of time consuming lifetime simulations, rendering the creation of the cumulative distribution of time to failure onerous. The paper presents a novel methodology that 1) replaces the implicit mechanistic model with a simple explicit model, 2) transforms the dynamic, probabilistic, problem into a time invariant probability problem over each cycle-time, and 3), builds the cumulative distribution function (Cdf) as the summation of the incremental service-time failure probabilities over the planned service time. Error analysis suggests ways to predict and minimize errors. A Case Study of a servo-control mechanism shows how the new methodology builds a Cdf and yet provides controllable accuracy and a substantial time reduction when compared to Monte Carlo sampling with the traditional mechanistic model.