Hydraulic systems are widely used in the aeronautic, machinery, and energy industries. The functions that these systems perform require high reliability, which can be achieved by examining the causes of possible defects and failures and by taking appropriate preventative measures. One of the most popular methods used to achieve this goal is FMEA (Failure Modes and Effects Analysis), the foundations of which were developed and implemented in the early 1950s. It was systematized in the following years and practically implemented. It has also been standardized and implemented as one of the methods of the International Organization for Standardization (ISO) 9000 series standards on quality assurance and management. Apart from wide application, FMEA has a number of weaknesses, which undoubtedly include risk analysis based on the RPN (Risk Priority Number), which is evaluated as a product of severity, occurrence, and detection. In recent years, the risk analysis has been very often replaced by fuzzy logic. This study proposes the use of matrix analysis and statistical methods for performing simplified RCA (Root Cause Analysis) and for classification potential failures for a variable delivery vane pump. The presented methodology is an extension of matrix FMEA and allows for prioritizing potential failures and their causes in relation to functions performed by pump components, the end effects, and the defined symptoms of failure of the vane pump.