Reliability modelling and self-healing policy design for systems with limited resources

•Systems subject to environmental shocks with limited self-healing resources are studied.•Two self-healing policies are proposed to allocate the limited resources over time. Accordingly, two new reliability models are developed.•Reliabilities of the system under different self-healing policies are derived in a recursive way.•Four new indexes are proposed and derived, based on which the performance of the self-healing policies could be evaluated, compared and further optimized.