Cointegration testing method from economics area is introduced for condition monitoring and fault diagnosis for nonstationary engineering systems. The cointegration testing method seeks a a linear combination of a set of nonstationary stochastic variables, which describes long-run dynamic equilibrium relation of the nonstationary variables. This feature provides a possibility for researchers in engineering areas to utilize the cointegration testing method for nonstationary system monitoring and fault diagnosis. To verify the feasibility and performance of the cointegration testing method, an example based on a simulated nonstationary fluid catalytic cracking unit (FCCU) system is discussed. The results of the example show that the cointegration testing method has a potential in engineering system monitoring and fault diagnosis.