The authors derive an online multiple hypothesis Shiryayev Sequential Probability Ratio Test (SSPRT) by adopting a dynamic programming approach. It is shown that for a certain criterion of optimality, this generalized Shiryayev SPRT detects and isolates a change in hypothesis in the conditionally independent measurement sequence in minimum time, unlike the Wald SPRT, which assumes the entire measurement sequence to correspond to a single hypothesis. They consider the measurement cost, the cost of a false alarm, and the cost of a miss-alarm in our dynamic programming analysis. The algorithm is shown to be optimal in the infinite time case. Finally, the performance of the algorithm is evaluated by using a few examples. In particular, they implement the algorithm in a fault detection and identification scheme for advanced vehicle control systems.