Fundamentals of Quantitative Design and Analysis - Computer Architecture: A Quantitative Approach - page 36

redundant power supplies. Assume one power supply is sufficient to run the
disk subsystem and that we are adding one redundant power supply.
Answer
We need a formula to show what to expect when we can tolerate a failure and
still provide service. To simplify the calculations, we assume that the lifetimes
of the components are exponentially distributed and that there is no dependen-
cy between the component failures. MTTF for our redundant power supplies is
the mean time until one power supply fails divided by the chance that the other
will fail before the first one is replaced. Thus, if the chance of a second failure
before repair is small, then the MTTF of the pair is large.
Since we have two power supplies and independent failures, the mean time
until one disk fails is MTTF power supply /2. A good approximation of the probability
of a second failure is MTTR over the mean time until the other power supply
fails. Hence, a reasonable approximation for a redundant pair of power supplies
is
Using the MTTF numbers above, if we assume it takes on average 24 hours
for a human operator to notice that a power supply has failed and replace it, the
reliability of the fault tolerant pair of power supplies is
making the pair about 4150 times more reliable than a single power supply.
Having quantified the cost, power, and dependability of computer technology, we are ready
to quantify performance.
1.8 Measuring, Reporting, and Summarizing
Performance
When we say one computer is faster than another is, what do we mean? The user of a
desktop computer may say a computer is faster when a program runs in less time, while an
Amazon.com administrator may say a computer is faster when it completes more transac-