Order-preserving submatrices (OPSM's) have been shown useful in capturing concurrent patterns in data when the relative magnitudes of data items are more important than their exact values. For instance, in analyzing gene expression profiles obtained from microarray experiments, the relative magnitudes are important both because they represent the change of gene activities across the experiments, and because there is typically a high level of noise in data that makes the exact values untrustable. To cope with data noise, repeated experiments are often conducted to collect multiple measurements. We propose and study a more robust version of OPSM, where each data item is represented by a set of values obtained from replicated experiments. We call the new problem OPSM-RM (OPSM with repeated measurements). We define OPSM-RM based on a number of practical requirements. We discuss the computational challenges of OPSM-RM and propose a generic mining algorithm. We further propose a series of techniques to speed up two time dominating components of the algorithm. We show the effectiveness and efficiency of our methods through a series of experiments conducted on real microarray data.