On ageing concepts for repairable items from heterogeneous populations

Ageing concepts are very important in lifetime modeling and analysis. Monotonic failure rates are the simplest and most popular manifestations of aging properties of items in applications (IFR and DFR, accordingly). However, they are usually discussed for homogeneous populations, whereas heterogeneity can change dramatically the shape of the corresponding failure rate. In this paper, we suggest a new measure of ageing for items from heterogeneous populations based on the described process of information-based minimal repairs. We also show and illustrate, by several examples, that the conventional measure of aging based on the shape of the (population) failure rate is unrealistic in this case and can lead to wrong decisions, e.g., in burn-in procedures and optimal maintenance.