This paper deals with a failure diagnosis of a pneumatic directional control valve used in automated production systems. The valve vibration is monitored by an accelerometer : Six parameters characterizing the vibration data are extracted, and fed into multi-layer neural networks to solve four types of diagnosis problems. It is shown that the neural network approach is useful for the failure diagnosis, yielding low failed-safe and low failed-dangerous probabilities. Neural network structures are analyzed through Boolean expressions summarizing relationships between two successive neuron layers. These expressions are obtained by noting that, for learning patterns, occurrences of discrete failure events behind continuous network input parameters are known. For each neuron, its function can be clarified by the structure analysis; irrelevant neurons can be identified and removed without degrading the diagnosis performance; the neural network for a diagnosis of foreign material around a spool utilizes a majority voting mechanism, and attains a 50% reduction of incorrect answers compared with a linear diagnosis. A conjugate gradient followed by a variable metric method is demonstrated as an effective learning algorithm.