We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway.Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling. We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidates pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to one-step process with a single pathway .terestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibited an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.