46
Chapter 2
Using Eq. (2.3) with proper substitution
P(x + y + z) = P(x) + P(y) + P(z) - P(x)P(y)
- P(z)P(y) + P(xyz)
Note combination
P(x)P(y)-AB followed BC which can’t happen since ABC are controlled 1 each for an assembly. Therefore only the first three conditions
can occur.
(1)(5~)
1 failures
+
~
- 2000 assemblies
A solution is to sort boards A and B and screw C. However, the cost of
one board sorter and one screw sorter must be compared to the cost of
ending 1/2000 failures. It should be noted that a nut sorter as well as a
check on the drilled holes can be factored into the assembly.
Should the nut be oversized for 1/50 this would add another possible
failure mode.
There are situations when events can happen in several different ways
then the permutations and combinations must be examined.
EXAMPLE 2.8. Find the probability that of 5 cards drawn from a
deck, two will be aces. Proceed knowing the aces can be drawn in several
ways, in fact, the permutations are for 5 cards, n with two of them aces, r.
(~)
n,
[1.2.3.4.
C -r!(g---r)!(i ~-(i~2 ~)
(2.11)
So
,(2
of
5 cards)
i=l~e
=
(any one arrangement)
being aces ~t i=1