Application of Probability to Mechanical Design
45
Start
1/2~2
Urn 1 i
AUrn 2
Draw2
R
W R
W
R
W R
W
Figure 2.3 Successive draws from a supply box.
assembly and the associated costs. The following example depicts some
of the concerns during manufacturing assembly.
EXAMPLE 2.7 12.39l. An automatic assembly machine positions
board A on top of board B, both nominally one inch thick with a properly
drilled hole, and a machine screw, nominally 2¼ inches long, with a controlled ~ inch thick nut torqued on at final assembly. Upon assembly for
boards A and B the machine also selects an oversized 1 ~ inch board 1
in 100 times, and undersized 2~ inch screws C are selected 1 in 50 times.
The nuts have a sorter to maintain ¼ inches thickness, and, the drill
holes are also controlled.
There are three assembly failures
AB-2(I~" over sized) and nut can’t be started on 2¼ inch screw.
BC-B(I~" over sized) and C-2½ rt allows half engagement of nut.
l~t
CA-A(lg over) and C-2g allows half engagement of nut.
Therefore how many failures may occur.
1
Then P(A)=~ = P(B) with P(C)= 1/50. Make the substitution
x = AB
y= BC
z = CA
P(AB + BC + CA) = P(x + y +