A new unsupervised predictive maintenance analysis method based on the renormalization group approach used to discover critical behavior in complex systems has been proposed. The algorithm analyzes univariate time series and detects critical points based on a newly proposed theorem that identifies critical points using a Log Periodic Power Law function fits. Application of a new algorithm for predictive maintenance analysis of industrial data collected from reciprocating compressor systems is presented. Based on the knowledge of the dynamics of the analyzed compressor system, the proposed algorithm predicts valve and piston rod seal failures well in advance.