By Adam Osborne
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Extra resources for 6800 Programming for Logic Design
4 Other Reliability Evaluation Techniques 33 Similar derivations can be made for M-of-N systems in which failing processors are identified and replaced from an infinite pool of spares. This is left for the reader as an exercise. The extension to the case with only a finite set of spares is simple: the summation in the reliability expression is capped at that number of spares, rather than going to infinity. 2 Markov Models In complex systems in which constant failure rates are assumed but combinatorial arguments are insufficient for analyzing the reliability of the system, we can use Markov models for deriving expressions for the system reliability.
Siewiorek and R. S. Swarz, Reliable Computer Systems: Design and Evaluation, A. K. Peters, 1998.  M. L. Shooman, Reliability of Computer Systems and Networks: Fault Tolerance, Analysis, and Design, Wiley-Interscience, 2001.  A. K. Somani and N. H. Vaidya, “Understanding Fault-tolerance and Reliability,” IEEE Computer, Vol. 30, pp. 45–50, April 1997.  K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, John Wiley, 2002.  M. Weiser, “The Computer for the Twenty-first Century,” Scientific American, pp.
31) where Rcomp is the reliability of the comparator. Assuming a fixed failure rate of λ for each processor and an ideal comparator (Rcomp (t) = 1), the MTTF of the duplex system is c 1 + 2λ λ The main difference between a duplex and a TMR system is that in a duplex, the faulty processor must be identified. We discuss next the various ways in which this can be done. MTTFduplex = Acceptance Tests The first method for identifying the faulty processor is to carry out a check of each processor’s output and is known as an acceptance test.
6800 Programming for Logic Design by Adam Osborne