The origin of the heavy elements is one of the most fundamental open questions in modern astrophysics, with a notable difficulty being the lack of a complete description of the rapid neutron-capture process (r-process), a process thought to be responsible for the production of around half of all isotopes heavier than iron. One of the major limitations preventing a detailed understanding of the r-process is the lack of nuclear physics inputs for the nuclei involved. Three key quantities used in r-process calculations are nuclear masses of involved nuclei, their β-decay half-lives and β-delayed neutron emission probabilities. The work herein focuses on measuring decay half-lives. This thesis details the commissioning of and first experiments carried out with the Advanced Implantation Detector Array (AIDA). AIDA features large-area double-sided silicon strip detectors with a high degree of segmentation in combination with purpose-built instrumentation, and is capable of making reliable implant-decay correlations at the high beam currents now available at fragmentation beam facilities. Thanks to the large yields of neutron-rich isotopes available at the Radioactive Ion Beam Factory (RIBF), in June 2016 AIDA was used to study r-process nuclei in the vicinity of 90/34Se, using a novel method in which nuclear masses and β-decay half-lives were measured simultaneously. Presented within are the first half-lives obtained through the analysis of the data collected during this experiment, five of which have been measured for the first time. Going forward, AIDA will be used with the β-delayed neutron emission at RIKEN (BRIKEN) detector to measure β-delayed neutron emission probabilities of r-process nuclei and at the Facility for Antiproton and Ion Research (FAIR) at GSI as part of the Decay Spectroscopy (DESPEC) experiments.