This paper introduces the concept of a process capability matrix — an ordered set of dimensionless parameters that capture information on a manufacturing system’s response to noises. The matrix captures information on the magnitude of noise, sensitivity to noise, and tolerance to variation. Algorithms and equations are presented that use the matrix to compute the yield of a manufacturing system. The method proves to be accurate on real engineering problems for which existing techniques are inadequate due to statistical correlation among product acceptance criteria. The process capability matrix also proves useful in a new type of block diagram of production systems. The block diagrams are shown to be useful in evaluating the effectiveness of feedforward control strategies for variation reduction. An electronics assembly process serves as an example of the algorithms and their use in design decision making.