Novelty detection, or one-class classification, is of particular use in the analysis of high-integrity systems, in which examples of failure are rare in comparison with the number of examples of stable behaviour, such that a conventional multi-class classification approach cannot be taken. Support Vector Machines (SVMs) are a popular means of performing novelty detection, and it is conventional practice to use a train-validate-test approach, often involving cross-validation, to train the one-class SVM, and then select appropriate values for its parameters. An alternative method, used with multi-class SVMs, is to calibrate the SVM output into conditional class probabilities. A probabilistic approach offers many advantages over the conventional method, including the facility to select automatically a probabilistic novelty threshold. The contributions of this paper are (i) the development of a probabilistic calibration technique for one-class SVMs, such that on-line novelty detection may be performed in a probabilistic manner; and (ii) the demonstration of the advantages of the proposed method (in comparison to the conventional one-class SVM methodology) using case studies, in which one-class probabilistic SVMs are used to perform condition monitoring of a high-integrity industrial combustion plant, and in detecting deterioration in patient physiological condition during patient vital-sign monitoring.