Age-based maintenance under population heterogeneity: Optimal exploration and exploitation

We consider a system with finite lifespan and single critical component that is subject to random failures. An age-based replacement policy applied preventively replace the before its failure. The components used for come from either weak population or strong population, referred as heterogeneity. However, true type unknown decision maker. By considering maker has belief on probability of having we build partially observable Markov process model objective minimizing total cost over system. resulting optimal updates variable in Bayesian fashion by using data obtained course lifespan, it denotes when execute preventive replacement. It optimally balances trade-off between learning (via deliberately delaying time better learn type) maintenance activities. addressing this so-called exploration-exploitation trade-off, generate insights compare performance existing heuristic approaches literature. also characterize lower bound cost, allowing us determine value resolving uncertainty type.