The present manuscript provides the design of a residual generator using the Markov Jump Linear System framework as a base. During the residual generator design process, the H-infinity norm and the index H- are considered, to improve residual generator performance. This improvement is achieved using the H-infinity norm to increase the residual generator robustness and the H- index to increment the system sensibility for a specific signal, which is a desirable trait depending on the task where the residual generator is implemented. A numerical example is also provided to illustrate the proposed approach.