By Topic

Inverting and Minimizing Boolean Functions, Minimal Paths and Minimal Cuts: Noncoherent System Analysis

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Locks, Mitchell O. ; Department of Administrative Sciences; College of Business Administration; Oklahoma State University; Stillwater, OK 74074 USA.

An efficient technique is presented for inverting the minimal paths of a reliability logic diagram or fault tree, and then minimizing to obtain the minimal cuts, or else inverting the minimal cuts for the minimal paths. The method is appropriate for both s-coherent and s-noncoherent systems; it can also obtain the minimized dual inverse of any Boolean function. Inversion is more complex with s-noncoherence than with s-coherence because the minimal form (m.f.) is not unique. The result of inversion is the dual prime implicants (p.i.'s). The terms of a dual m.f., the dual minimal states, are obtained by a search process. First the dual p.i.'s are obtained; then a m.f. is found by an algorithmic search with a test for redundancy, reversal-absorption (r.a.). The dual p.i.'s are segregated into the ``core'' p.i.'s [8,9] essential for every m.f. and the ``noncore'' p.i.'s, by r.a. Then a m.f. is found by repeatedly applying r.a. to randomized rearrangements of the noncore terms. Examples are included, adapted from the fault-tree literature.

Published in:

Reliability, IEEE Transactions on  (Volume:R-28 ,  Issue: 5 )