Page 101 - Uninterruptible Power Supplies

Additional Information Relating to the Standby Supply Installation
Additional Information Relating to the Standby Supply Installation 99

The results of expanding this expression, using the probabilities of
0.99 and 0.01, for three, four, and five sets are:
For three sets:

2
3
0.99 3 0.99 0.01 3 0.99 0.01 0.01 1
2
3
For four sets:
2
4
0.99 4 0.99 0.01 6 0.99 0.01 4 0.99
2
3
4
.01 0.01 1
3
For five sets:
4
2
3
5
3
2
0.99 5 0.99 0.01 10 0.99 0.01 10 0.99 .01
5 0.99 0.01 0.01 1
5
4
From these expressions, Table 3.2 may be constructed.
This table provides some insight into the working of this aspect of
statistics. It is based on the assumed probabilities of 0.99 and 0.01 and
readers will observe that the figures in column 2, where all sets start,
are the various powers of the probability 0.99 and are independent of
the probability 0.01. Similarly, the figures relating to all sets failing in
columns 3–7, are independent of the probability 0.99 and are the vari-
ous powers of the probability 0.01, which become insignificant in
columns 5–7.
The figures in the other columns, where some sets start and some
fail, are derived from the two probabilities and the binomial coeffi-
cients, which can be calculated somewhat laboriously but which are
available from mathematical textbooks and from Pascal’s triangle.
The probability of successful starting can be obtained from the table
for any arrangement of redundancy. Most installations involving redun-
dancy are arranged in the N 1 form and success is achieved if all sets
start or if one only fails. Thus, the probability of success is the sum of
the figures in columns 2 and 3. For two-, three-, four-, and five-set

TABLE 3.2 Table of Probabilities
1 2 3 4 5 6 7 8
Number Check
of sets All start 1 fails 2 fail 3 fail 4 fail 5 fail total
1 set 0.99000 0.01000 — — — — 1.00
2 sets 0.98010 0.01980 0.00010 — — — 1.00
3 sets 0.97030 0.02940 0.00030 10 5 — — 1.00
4 sets 0.96060 0.03880 0.00058 10 5 10 5 — 1.00
5 sets 0.95099 0.04803 0.00097 10 5 10 5 10 5 1.00

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