$\beta$-decay half-lives of neutron-rich nuclei at $A\sim110$ on r-process path

About half of the elements heavier than iron are thought to be produced by rapid-neutron capture process (r-process). The observed natural abundance in solar system was underestimated by a theoretical model at $A\sim 110$, which uses $\beta$-decay half-lives. In the present study, we measured new $\beta$ half-lives of neutron-rich nuclei on r-process path at RIBF in RIKEN. The nuclei of interest were produced by in-flight fission of uranium beam in beryllium target. The WAS3ABi detector which was 5 stacked double-sided silicon strip detectors ($60 \times 40 \times 1$ mm$^3$), was used for the implantation of ions and the detection of both the implanted ions and the subsequently-emitted $\beta$ rays. It is essential to make a position correlation between the mother nucleus and the $\beta$ rays. In this talk, the analysis of the position correlation will be presented in detail. Preliminary results will be also shown.