On the basis of the achievable performance of the control outputs, fault diagnosis of two cascade control
systems, including series cascade control (SCC) and parallel cascade control (PCC), is developed. Without
any prior knowledge of complicated operating processes and/or external inputs perturbing the operating system,
the accurate fault identification can be achieved by a series of the statistical hypothesis procedures applied to
the currently measured data. To isolate possible faults, the output variances of the primary and secondary
loops are separated into cascade-invariant (CI) and cascade-dependent (CD) terms, respectively, by the
Diophantine decompositions. After a sequence of the hypotheses tests is performed on the CI and the CD
terms of current control and the achievable performance conditions, the hierarchical diagnosis trees for the
primary and secondary outputs are established, respectively, to explore possible faults. The final faults can
be inferred by merging both diagnosis trees. The statistical inference systems for SCC and PCC structures
are the same. The performance of the proposed method is demonstrated via two examples, including a simulation
case with a single fault and a pilot-level tank system with multiple faults.