This study addresses challenges in measuring spatial accessibility to grocery stores accurately. By enhancing an existing radiation model with different transportation modes and time use diaries, we aim to provide a more realistic estimation of accessibility. We introduce a novel approach using survival analysis, specifically the Cox proportional hazard model, to develop a cost decay function based on time use diaries. Additionally, a multinomial logit model estimates the proportion of people walking, using cars, and using buses. Using grocery stores in Travis County, Texas, as a case study, our results show that most zip codes have low to moderate walking accessibility to grocery stores, with transit accessibility being very low in many western zip codes. However, accessibility in some areas improves due to car availability.