Cause-Effect Analysis for Multiple Fault Detection in Combinational Networks

Bosson and Hong' have developed an effective procedure for multiple fault detection. However, their claim that their procedure gives near-minimal results is not necessarily the case. Poage [1] has considered the problem of generating test patterns for multiple fault detection. His method can be used to find a minimal set of fault-detection tests; however, it has the drawback that it is computationally complex. Bossen and Hong1 claim to have a considerably simpler procedure which gives near-minimal results. To illustrate their procedure, they worked out an example which generates six test patterns for a circuit whose known minimum is five. By their nonredundant (NR) procedure, the example should have given eight test patterns, not six. Since eight is considerably more than five, the ability of the procedure to generate near-minimal results is questionable. In order to demonstrate the errors, Example 2 considered by Bossen and Hong will be worked out in detail using their own procedures (General (G) and NR). The circuit is given in Fig. 1. By algorithm G, F' = i = wxy + wxz + wlvyz + xyz F' = wxy + wxz + wiyz + xyz = wxyz + y)Z + YZz + WWX +WY +WZ + WXX + Xy +* = wxyz ± 8 + +IZ + :t +XZ X {wx, wy, xy, x,x w, ?w,y, wz, yz, xy, tz Xm {wxy, WXZ, wyz, xyz, yz, yz, yz, ix, WX, WX, W, X, y, Z, W, X, y, Z|. Computing Xi =Xj, i= wxyz, ixy. W)3XP2, ti3lZ, ?&gz, tbxgl, WIXZ, 751y2, tby2, Wtg, WtPj, ?DXtZ, tgZ, mfg2, WXZ, tffY2, tY2I Abnormal true tests are therefore twxyz, wxyz, wxyz, wxyz, wxyz I Manuscript received January 15, 1974; revised April 17, 1974. The authors are with the Department of Electrical Engineering, Pennsylvania State University, University Park, Pa. 16802. 1 D. C. Bossen lnd S. J. Hong, IEEE Trans. Comput. (Special Issue on Fault-Tolerant Computing), vol. C-20, pp. 1252-1257, Nov. 1971. Fig. 1. Circuit considered by Bossen and Hong. which is the same as in the paper. Computing Xm = 5FXm, Xm {WXyz, wxyz, wxyz, wxyz, wxyz, wxyz, * *. Abnormal false tests are therefore {wxyz, wxyz, wxyz, wOxyz, wxy2, wxyz }. The terms wxyz and zwyz were not included in the paper. These terms represent wxy z., wxy E f and z G Xm wDyz x, w7vyz E IY and x fE Xm. The preceding implies eleven test patterns, not nine as Bossen and Hong claim. The aforementioned omissions cited also increase the NR result by two test patterns as can be easily shown. The solution can be reduced to seven terms if the F simplified cause-effect equation is used.