## Guardbands in Random Testing

Günter Kemnitz
Technische Universität Clausthal
gkemnitz@informatik.tu-clausthal.de

The most important parameter of a digital test is the fault coverage. Using random patterns as stimuli the fault coverage depends mainly on the number of test patterns and less on the test patterns itself. Defining the test by only one number has a lot of advantages over the alternative, computing, storing and processing a large quantity of exactly defined patterns [1]. Random patterns are often used in self test functions, but also in low cost test systems. During the test of a circuit under operation, randomly selected input patterns are a good, and generally the only model to estimate the fault coverage. The term guardband originates from analog testing. Testing a parameter such as a voltage, the measured value must be better than the value that should be guaranteed by the test [2]. The difference, the so called guardband, is to reduce the probability that noise and other disruptions cause that bad devices will be classified as good ones. There is a similar problem with random test. If the fault coverage is estimated (e.g. by a simulation with a fault sample, with simplified fault assumtions or other random patterns than used under test, ...) the estimated value must be larger or equal than the value to be guaranteed plus a guardband. The calculation of the size of the guardband needs the distribution function of fault coverage. The paper derives an algorithm to calculate it under the assumption that the faults in the circuit are detected independently of each other. The later assumption is of cause a compromise. The calculation itself based upon convolutions of elementary distributions relating to single faults [4]. To evaluate the approach, for some common used benchmarks the theoretical distributions are compared to frequency functions produced by fault simulation using several hundred different random sequences.

The results are easy usable formula to calculate the size of guardbands from the desired fault coverage, the number of faults, a level of confidence and some information about the 'experiment' of estimating the fault coverage. They will generally work and are a great advantage over having no formula. However, as one of our experiments shows, the dependencies between the faults relating from the circuit structure can cause strange distributions, where our formulas do not describe the worst case. This effect will only be described as a starting point for further investigations.

1. Lombardi, F.; Sami, M. (eds): Testing and diagnosis of VLSI and ULSI. Kluwer Academic Publishers, 1988

2. Williams, R. H.; Hawkins, C. F.: The effect of guardbands on errors in production testing. European Test Conf., 1993, p. 2-7

3. Brglez, F.; Fujiwara, H.: A neutral netlist of 10 combinatorial benchmark circuits and a target translator in FORTRAN. Int. Symposium on Circuits and Systems; Special Session on ATPG and Fault Simulation, 1985

4. Kemnitz, G.: Test and self test of digital circuits. Habilitationsschrift Dresden University of Technology, 1995 (in german)