Performance in an engineering system tends to degrade over time due to a variety of wearing or ageing processes. In supervisory controlled processes there are typically many signals being monitored that may help to characterize performance degradation. It is preferred to select the least amount of information to obtain high quality of predictive analysis from a large amount of collected data, in which labeling the data is not always feasible. To this end a novel unsupervised feature selection method, robust with respect to significant measurement disturbances, is proposed using the notion of ``weak monotonicity'' (WM). The robustness of this notion makes it very attractive to identify the common trend in the presence of measurement noises and population variation from the collected data. Based on WM, a novel suitability indicator is proposed to evaluate the performance of each feature. This new indicator is then used to select the key features that contribute to the WM of a family of processes when noises and variations among processes exist. In order to evaluate the performance of the proposed framework of the WM and suitability, a comparative study with other nine state-of-the-arts unsupervised feature evaluation and selection methods is carried out on well-known benchmark datasets. The results show a promising performance of the proposed framework on unsupervised feature evaluation in the presence of measurement noises and population variations.