Radioactive materials released from a nuclear power plant can degrade the performance of plant operators by disturbing their physical actions, complicating the mitigation procedures, or heightening their psychological stress. This study provides an approach to quantitatively estimate the inter-unit radioactive influence at a multi-unit site by using a conventional probabilistic safety analysis (PSA) model. Three steps are suggested as follows: (1) select the risk-significant core damage sequences of the unit(s) that release radioactive materials, (2) select the risk-significant human failure events (HFEs) at the unit(s) that are affected by the radioactive releases, and (3) develop an integrated PSA model with a fault tree linking approach. The effects of release timing and operator action timing are also considered, called timing effects. To demonstrate the applicability of the approach, the risk of five identical units at a multi-unit site was quantitatively evaluated with a loss of offsite power initiating event as case studies. The multi-unit core damage frequency increased by a maximum factor of 5.7 without consideration of timing effects, while it increased up to 19 percent with consideration of timing effects.