In this paper, a statistical approach to fault detection and isolation (FDI) of robot manipulators is presented. It is based on a statistical method called partial least squares (PLS) and on the inverse dynamic model of a robot. PLS is a well-established linear technique in process control for identifying and monitoring industrial plants. Since a robot inverse dynamics can be represented as a linear static model in the dynamical parameters, it is possible to use algorithms and confidence regions developed in statistical decision theory. This approach has several advantages with respect to standard FDI modules: It is strictly related to the algorithm used for identifying the dynamical parameters, it does not need to solve at run time a set of nonlinear differential equations, and the design of a nonlinear observer is not required. This method has been tested on a PUMA 560 simulator, and results of the simulations are discussed.