Due to the advancements in data measurement and computer technology, automated data collection from multiple sensors has become common in recent years. However, very few papers have dealt with the cost-optimal early fault detection of gearboxes, condition based maintenance policy, and remaining useful life prediction when multiple sensors are used for data collection under varying load. The novel approach presented here is based on vector autoregressive vibration signal modeling and continuous time hidden Markov modeling using the optimal Bayesian control technique. System condition is modeled using a continuous time Markov chain with three states, namely, unobservable healthy state 0, unobservable warning state 1 and observable failure state 2. Model parameters are calculated using the expectation-maximization algorithm. The optimal control policy for the three-state model is represented by a Bayesian control chart for a multivariate observation process. The chart monitors the posterior probability that the system is in the warning state 1 and the system is stopped when this probability exceeds an optimal control limit. Prediction of mean residual life using a posterior probability is also developed in this paper. The validation of the proposed methodologies is carried out using actual gearbox vibration data obtained from multiple sensors.