Report Number: CSL-TR-74-75
Institution: Stanford University, Computer Systems Laboratory
Title: Influence of fault-detection and switchinig mechanisms on the reliability of stand-by systems
Author: Losq, Jacques
Date: July 1975
Abstract: This paper concerns the reliability of stand-by systems when
switch reliability is taken into account. It is assumed that
failures obey a Poisson distribution for modules and
switches. A very detailed method is given to model stand-by
systems. Several cases are investigated: ideal systems, real
systems with fault-detection mechanisms that can detect any
module error and systems for which the fault-detection
mechanisms detect only some of the module errors. The
reliability versus time curves are determined for each value
of the number of spares. It is shown that the best number of
spares increases as the length of the mission increases.
Systems with extremely short mission time have the best
reliability when they have only one spare. The limit when the
number of spares increases is the reliability obtained with
simplex systems. Whatever the number of spares is, the
reliability of stand-by systems goes to zero as time goes to
infinity. For a given mission time, it is possible to
determine the best number of spares and the best possible
reliability. For a given reliability, it is possible to
compute the number of spares that gives the longest mission
time. These models can be used to determine whether or not
there exists a stand-by system that meets the requirements of
a given reliability and a given mission time. If such
stand-by system exists, its characteristics (minimum number
of spares and reliability) can be derived.
http://i.stanford.edu/pub/cstr/reports/csl/tr/74/75/CSL-TR-74-75.pdf