On the Saturation of n-Detection Test Sets with Increased n Irith Pomeranz 1 and Sudhakar M. Reddy 2 School of Electrical & Computer Eng. Electrical & Computer Eng. Dept. Purdue University University of Iowa W. Lafayette, IN 47907 Iowa City, IA 52242 pomeranz@ecn.purdue.edu reddy@engineering.uiowa.edu Abstract An n-detection test set contains n different tests for each target fault. The value of n is typically determined based on test set size constraints, and certain values have become standard. In this work we investigate appropriate values for n by considering the saturation of the n- detection test generation process. As n is increased, even- tually the rate of increase in test set quality starts drop- ping. Saturation occurs when the increase in test set qual- ity with n drops below a certain level. We introduce three parameters of an n-detection test set to measure satura- tion of the test generation process: (1) the fraction of faults detected n times or less by the test set, (2) the frac- tion of faults detected fewer than n times by the test set, and (3) the test set size relative to the size of a one- detection test set. We demonstrate that the behavior of each one of these parameters follows a unique pattern as n is increased, and certain features of this behavior can be used to identify saturation. All the parameters are easy to compute during the test generation process. 1. Introduction In an n -detection test set, each target fault is detected n times, by n different tests. If a fault has only nˆ <n dif- ferent tests among all the input vectors of the circuit, the fault is detected nˆ times by an n -detection test set. Increasing the numbers of detections of target faults was shown to increase the likelihood of detecting untar- geted faults as well as defects. This can be explained as follows. Consider a defect associated with the site of a tar- get fault f . Suppose that the defect has activation and propagation conditions similar (but not identical) to those of f . By including n different tests that detect f in an n - detection test set, different activation and propagation conditions are created around the site of f (and the site of the defect). Therefore, the likelihood that the test set will detect the defect is increased. 1. Research supported in part by SRC Grant No. 2004-TJ-1244. 2. Research supported in part by SRC Grant No. 2004-TJ-1243. Paper 30.1 INTERNATIONAL TEST CONFERENCE 1 1-4244-1128-9/07/$25.00  2007 IEEE Generation of n -detection test sets for a specific fault model requires only minor modifications to a test generation procedure for the same fault model. This is typically simpler than writing a test generation procedure for a new fault model. The generation of n -detection test sets and their advantages in detecting untargeted faults and defects were studied in [1]-[11]. Determining a value for n is typically done based on tester memory and test application time constraints. The size of a compact n -detection test set increases approximately linearly with n , and n ≤ 10 appears to have become the accepted bound on n . Issues that arise when n is restricted were considered in [10]. Among the ques- tions considered in [10] are the following. (1) How much untargeted fault or defect coverage is missed by restricting n . (2) How much higher should n be in order to eliminate the untargeted fault or defect coverage loss. This is impor- tant in deciding whether higher values of n should be con- sidered. (3) How does a given test generation strategy affect the ability of an n -detection test set to detect untar- geted faults. The analysis in [10] considered a specific target fault model (stuck-at faults) and a specific untar- geted fault model (four-way bridging faults [12]-[13]) to provide answers. In this work we address issues related to the value of n used for n -detection test generation from a different point of view. An n -detection test generation process will eventually saturate as n is increased. Saturation implies that continuing n -detection test generation beyond the saturation point is ineffective in improving the coverage of random untargeted faults or defects. We introduce the following parameters to determine the saturation point of an n -detection test generation process. (1) The first parameter is the fraction of faults for which the number of detections under an n -detection test set is smaller than n . For low values of n , only undetectable faults (and in some cases a small number of other faults) are detected fewer than n times by an n -detection test set.