In this paper, design issues of data-driven optimal dynamic fault detection systems for stochastic linear discrete-time processes are addressed without precise distribution knowledge of unknown inputs and faults. Concerning a family of faults with different distribution profiles in mean and covariance matrix, we introduce a bank of parameter vectors of parity space and construct the parity relation based residual generators using process input and output data. In the context of minimizing the missed detection rate for a prescribed false alarm rate, the design of fault detection system is formulated as a bank of distribution independent optimization problems without posing specific distribution assumption on unknown inputs and faults. It is proven that the optimal selection of individual parameter vector can be formulated as a generalized eigenvalue-eigenvector problem in terms of the means and covariance matrices of residuals in fault-free and each faulty cases, and is thus solved via singular value decomposition. The tight upper bounds of false alarm rate and missed detection rate are simultaneously achieved quantitatively. Besides, the existence condition of the optimal solutions is investigated analytically. Experimental study on a three-tank system illustrates the application of the proposed scheme. (C) 2020 Elsevier Ltd. All rights reserved.