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ABSTRACT Unmanned aerial vehicles (UAVs) are revolutionizing a wide range of military and civilian applications. Since mission failures caused by malfunctions of UAVs can incur significant economic losses, modeling and ensuring the reliability of UAV‐based mission systems is a crucial area of research with challenges posed by multiple dependent phases of operations and collaborations among heterogeneous UAVs. The existing reliability models are mostly applicable to single‐UAV or homogeneous multi‐UAV systems. This paper advances the state of the art by proposing a new analytical modeling method to assess the reliability of a multi‐phased mission performed by heterogeneous collaborative UAVs. The proposed method systematically integrates an integral‐based Markov approach with a binary decision diagram‐based combinatorial method, addressing inter‐ and intraphase collaborations as well as phase‐dependent configurations of heterogeneous UAVs for accomplishing different tasks. As demonstrated by a detailed analysis of a two‐phase rescue mission performed by six UAVs, the proposed method has no limitations on UAV's time‐to‐failure and time‐to‐detection distributions. Another contribution is to formulate and solve UAV allocation problems, achieving a balance between mission success probability and total cost. Given the uncertainties inherent in the mission scenario, the random phase duration problem is also examined. 

Dynamic topography refers to vertical deflections of Earth’s surface from viscous flow within the mantle. Here we investigate how past subduction history affects present dynamic topography. We assimilate two plate reconstructions into TERRA forward mantle convection models to calculate past mantle states and predict Earth’s present dynamic topography; a comparison is made with a database of observed oceanic residual topography. The two assimilated plate reconstructions ‘Earthbyte’ and ‘Tomopac’ show divergent subduction histories across an extensive deep-time interval within Pacific-Panthalassa. We find that introducing an alternative subduction history perturbs our modelled present-day dynamic topography on the same order as the choice of radial viscosity. Additional circum-Pacific intra-oceanic subduction in Tomopac consistently produces higher correlations to the geoid (more than 20% improvement). At spherical harmonic degrees 1–40, dynamic topography models with intra-oceanic subduction produce universally higher correlations with observations and improve fit by up to 37%. In northeast Asia, Tomopac models show higher correlations (0.46 versus 0.18) to observed residual topography and more accurately predict approximately 1 km of dynamic subsidence within the Philippine Sea plate. We demonstrate that regional deep-time changes in subduction history have widespread impacts on the spatial distribution and magnitude of present-day dynamic topography. Specifically, we find that local changes to plate motion histories can induce dynamic topography changes in faraway regions located thousands of kilometres away. Our results affirm that present-day residual topography observations provide a powerful, additional constraint for reconstructing ancient subduction histories.