We here analyze the parity space approach to fault detection in a stochastic setting. Using a state space model with both deterministic and stochastic unmeasureable inputs we show a formal relationship between the Kalman filter and the parity space. Based on a stochastic fault detection and diagnosis algorithm, the probability for incorrect diagnosis is computed explicitly, given that only a single fault with known time profile has occured. An example illustrates how the matrix of diagnosis probabilities can be used as a design tool for performance optimization with respect to, for instance, design variables and sensor placement and quality.