With advances in sensing and monitoring techniques, it is increasingly possible to acquire real time multi-sensor monitoring data of stochastic degrading devices. Therefore, it has been attached great importance to effectively fuse these multisensor monitoring data so as to precisely predict the remaining useful life (RUL) in the prognostics field. Toward this end, this paper presents a novel data-model interactive RUL prediction method for multi-sensor monitored linear stochastic degrading devices with random failure threshold. During the offline training part, an optimization objective function synthesizing the mean squared error between the predicted life and the actual life as well as the variance of the predicted life is constructed based on the composite health index extracted from multi-sensor historical data and the associated lifetime prediction via stochastic degradation modeling. As such, a closed-loop feedback mechanism is established for composite health index constructing and stochastic degradation modeling. Based on this feedback mechanism, the fusion coefficients for multi-sensor data and the distribution parameters of random failure threshold of the associated composite health index are optimized to make the constructed composite health index automatically match the adopted stochastic degradation model. During the online prediction part, the composite health index is first constructed based on the multi-sensor data of the device in service and then the linear stochastic degradation model is applied to track the degradation progression. To make the degradation model adapt to the current status of the device, the Bayesian method is proposed to update the model parameters, and then, the RUL distribution with the consideration of the randomness of the failure threshold is derived under the concept of the first passage time. Finally, we validate the proposed method by the multi-sensor data of aircraft gas turbine engines and the results indicate its merits in improving the properties of the composite health index and the accuracy of the prognosis.