Application of Probability to Mechanical Design
51
The end dimension will be
#z = 28 in
~ = C,,~_ ~ ~i
100
~= 0.16404(1~0
)
~ = 0.0459325
the stack up dimension will be
i=7
z = ~ xi -t- 2.576(0.0459325)
i=1
z = 28 in -4- 0.11832 in
for 99% of the assembly.
B. Card Sort Solution Estimate of Variance
The normal functions for z examined have nicely behaved partial
derivatives. However there are functions which can take several pages of
partial derivatives to evaluate.
Therefore it becomes time consuming to obtain an answer when a close
estimate might suffice. Further using a computer to generate distributions
may also be too time consuming. The card sort selects specific values of
the variables to find either or
Zmax -- ,/~z = X}c
(2.25)
~z -- Zmin = X}c
(2.26)
the cards or variables are selected to make z a maximum or minimum. If the
variable appears in the denominator (bottom) a large value card makes
grow toward a minimum while a small value card makes z grow toward
a maximum. If a variable appears in both the denominator and numerator
(top) the Zma x means the large value card is used both places since only
one card or value is used in both places. When more complicated functions
are used the functions or combinations will have to be examined to see
if the cards selected cooperate to yield Zmax or Zrnin.
The variables are between two bounds for 99% for approximately
4-2.576 standard deviations of the data. The probability of being greater
or less than ()C/)ma x or (Xi)mi n is 0.0l/2.