A building system for detecting faults in an operation of building equipment. The building system comprising one or more memory devices configured to store instructions thereon that cause the one or more processors to perform a cumulative sum (CUSUM) analysis on actual building data and corresponding predicted building data to obtain cumulative sum values for a first plurality of times within a first time period; analyze cumulative sum values associated with a second plurality of times occurring before the first time to identify a second time of the second plurality of times at which a second cumulative sum value is at a local minimum; and determine that a first fault began at the second time.