Test efficiency analysis of random self-test of sequential circuits

Motivated by the work of K. Kim et al. (1988) and A. Krasniewski and S. Pilarski (1989), the problem of test efficiency in random testing of sequential circuits using built-in self-test (BIST) techniques is addressed. It is shown that, given a circuit with n primary inputs and the goal of maximizing expected pattern coverage, different pattern-sampling distributions for its 2ⁿ possible patterns can be partially ordered. The exact distributions for pattern coverage for both equiprobable and nonequiprobable pattern-sampling distributions are derived. Approximations for pattern-coverage distributions under equiprobable pattern-sampling conditions and corresponding numerical results are presented. A limiting distribution function for pattern-coverage distribution is derived. The authors also present numerical results on confidence levels for obtaining a specified pattern coverage. The distribution for the number of test cycles (R) required to achieve a specified pattern coverage is also derived. The authors derive and use the expression for the expected value of R to illustrate the increase in the effect of achieving a specified coverage j as j increases