Page 100 - Uninterruptible Power Supplies

Additional Information Relating to the Standby Supply Installation
98 Chapter Three

probability of a failure to start, rather than the mean time before fail-
ure which is applicable to continuously running equipment.

The Statistics of Redundancy
At the planning stage it may be necessary to calculate the increase in
the probability of a successful start that can be achieved by providing
redundant generating sets. The calculation is straightforward, the dif-
ficulty is at the beginning where it is necessary to assume a figure for
the probability of a failure to start for a single engine. As stated at the
start of this section, the reliability of a power supply is dependent on
many factors, some of which require a good-quality crystal ball to
assess and quantify.
Consider an installation of two equally sized sets (100 percent redun-
dancy), each with a probability of a failure to start of 1 in 100, and a
probability of a successful start of 99 in 100. On receipt of a start sig-
nal the following probabilities arise:

Event Probability
2
Two sets start 0.99 0.9801
One set starts, one fails 2 0.99 0.1 0.0198
2
Two sets fail 0.01 0.0001
One of these events must result from the start signal and the arith-
metic may be checked by addition: 0.9801 0.0198 0.0001 1.0. The
probability of a successful start is obtained by the addition of 0.9801
and 0.0198 0.9999. These figures may be compared with the results
for a single set which are:
Single set starts 0.99
Single set fails 0.01
It can be seen that the probability of total failure is reduced by 100
by the addition of the second set.
Most standby power installations use one or two generating sets, and
the above calculations will be sufficient for most purposes. Where there
are more than two sets the calculations follow a similar pattern and
invoke the binomial theorem, which may be expressed as:
y
(a b) 1 (3.3)
where a is the probability of a successful start for a single set
b is the probability of a failed start for a single set
y is the number of sets installed

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