In some complicated cases, a multivariate process/product can be characterized better by a combined technical specification vector. A combined technical specification vector is referred to as the case that the quality of a process/product is evaluated by different continuous and discrete random variables at the same time. In this case that there is also the covariance condition, the vector could not follow a single joint distribution. This research approaching kernel method and support vector data description (SVDD) proposes a new multivariate cumulative scheme named MK‐CUSUM to monitor the random vector of a process/product with combined technical specifications. The numerical analysis indicates that the proposed scheme is capable of detecting out‐of‐control conditions effectively when the process experiences different shifts in the random mean vector. The comparative performance report addresses that the proposed scheme is superior compared to the models of literature.