The present study analyses in depth the algorithms of change point detection in time series for the prediction of failures through the monitoring of mini-terms in real time. The mini-term is a new concept in the area of failure prediction that is based on the measurement of the time it takes for a component to perform its task. The simplicity of the technique has made it feasible to build industrial Big Data for the prediction of failures based on this concept. There are currently more than 11,000 sensorized mini-terms at Ford factory in Almussafes (Valencia). For the present study, 10 representative real cases of the different change points that have been detected up to the present were selected and, these cases were analysed by using the change point algorithms, which are representative of the great majority of algorithms described in the literature in their different versions. As a result, their accuracy was measured when detecting the change point and its computational cost. A discussion of the results is shown at the end of the paper.