Our aim is to propose a new approach for estimating survival functions (SFs) to obtain more individualized predictions than classic estimators based on considering a learning sequence as one entity. The idea is to split this sequence into more homogenous clusters and estimate SFs for each separately. The last step is combining these SFs into one adequate for each newly coming feature vector. As a vehicle for presenting the ideas, we have selected the Kaplan-Meier SFs estimator, since it also covers censored data, frequently met in medical applications. The spectral method is used for clustering – the reasons for this are explained in the text. The case study of applying the proposed approach to the data from nephrology is an essential part of the paper. However, our approach is also applicable in other disciplines, particularly engineering, for estimating SFs of devices and tools.