Data pooling for multiple single-component systems under population heterogeneity

We consider multiple newly designed single-component systems with a known finite lifespan. The component in each system can be replaced preventively to avoid a costly failure. This component is also in use for the first time, and therefore, there is no historical data on the lifetime of the component. In this case, the probability distribution of the component lifetime can be estimated based on expert opinions. However, there can be different opinions on the lifetime distribution. There are two populations where components can come from: a weak and a strong population. We assume that the components always come from the same population. However, the true type of the population is unknown. We build a discrete-time partially observable Markov decision process model to find the optimal replacement policy which minimizes the expected total cost throughout the lifespan. To resolve the uncertainty regarding population heterogeneity, we update the belief by using the data collected from all systems, allowing us to investigate the effect of so-called data pooling. First, we generate insights about the structure of the optimal policy. We then compare the cost per system under the optimal policy with the cost per system under two benchmark heuristics that follow the single-system optimal policy with and without data pooling, respectively. In our numerical experiments, we show that the cost reduction relative to the worst benchmark heuristic can be up to 5.6% for data pooling with two systems, and this increases up to 14% for 20 systems. Additionally, the effect of various input parameters on the costs is analyzed.