SFWRENG 4AA4 Lecture Notes - Lecture 12: Mathtype, Cosmic Ray, Checksum
11 Oct 2016
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Assume one or more units (sensor, computer system, etc. Given 1 unit that produces an output with probability p, output is incorrect (fault); with probability (1 p), output is correct. Problem: no way to know if output is incorrect. Given 2 units, output is incorrect with probability, p, for both, but outputs are independent. If results are different, one has to be incorrect. If results are same, either both correct or both incorrect: both incorrect: probability p2, p = 1 10 3 => p2 = 1 10 6, both correct: probability (1 p)2, disagree: 2(1 p)p. Choose the correct value to be the value on which at least 2 units agree: pro: always make a decision (fault masking) P(wrong) = p(2 wrong) + p(3 wrong) = 3p2(1 p) + p3 = 3p2 3p3 + p3 = 3p2 2p3. Any even number could result in a tie. Suppose that units output values, i. e. real numbers.
