Near-extreme system condition and near-extreme remaining useful time for a group of products

When a group of identical products is operating in field, the aggregation of failures is a catastrophe to engineers and customers who strive to develop reliable and safe products. In order to avoid a swarm of failures in a short time, it is essential to measure the degree of dispersion from different failure times in a group of products to the first failure time. This phenomenon is relevant to the crowding of system conditions near the worst one among a group of products. The group size in this paper represents a finite number of products, instead of infinite number or a single product. We evaluate the reliability of the product fleet from two aspects. First, we define near-extreme system condition and near-extreme failure time for offline solutions, which means no online observations. Second, we apply them to a continuous degradation system that breaks down when it reaches a soft failure threshold. By using particle filtering in the framework of prognostics and health management for a group of products, we aim to estimate near-extreme system condition and further predict the remaining useful life (RUL) using online solutions. Numerical examples are provided to demonstrate the effectiveness of the proposed method.