ECE-C690: Dependable Computing
Homework 1
January 13, 2009
The homework is due in class Monday, January 26, 2009.
Each problem is worth 10 points.
1. The lifetime (measured in years) of a processor is exponentially distributed with a mean lifetime of 2
years. You are told that a processor failed sometime in the interval [4, 8] years. Given this information,
what is the conditional probability that it failed before it was 5 years old?
2. Argue that the bathtub curve, used to represent the failure-rate trend in hardware components, is applica-
ble to software as well with the proper interpretation. For example, let time t= 0 represent the completion of
the first prototype of the software, which is then followed by various pre-release beta versions and, eventually,
the first released version, with the latter ideally occurring at the end of infant mortality.
3. For the combinational circuit shown below, use the D-algorithm to determine a test for line 5 being stuck-
at-0. Show all steps of the algorithm. What other (if any) stuck-at-1 or stuck-at-0 faults will be detected by
the resulting test pattern.
4. For the combinational circuit shown below, use the PODEM algorithm to determine tests for line Lbeing
stuck-at-1 and Mstuck-at-0. Show all steps of the algorithm.
5. Generate a self-dual function f(X) of three variables X= (x1, x2, x3). Recall that a self-dual satisfies the
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