JOTP-011
5 December 2014
APPENDIX G. MARGIN OF SAFETY CALCULATIONS FOR PRESSURE VESSELS
- average static fire maximum operating pressure (estimate of μy)
Y
- standard deviation of the maximum operating pressure (estimate of σy)
Sy
ny
- maximum operating pressure sample size
fy
- degrees of freedom of estimate Sy
fx-y - degrees of freedom for X and Y
Sx-y - standard deviation of the difference X - Y
and
XY X- Y
(G1)
S2y S2 S2
(G2)
x
x
y
When applying tolerance limits to determine the probability that X-Y>0, it is necessary to
determine a sample size, nx-y, to be used in the computation. If nx = ny, then set nx-y = nx = ny. If
nx does not equal ny, then the following shall be used to determine nx-y.
s2 s2
x
y
n xy
(G3)
S2
S2
y
x
nx
ny
The procedure used to determine equation G3 is as follows:
a.
The t-test for the equality of two means with unequal variances is:
(x y) (μ x μ y )
t
(G3a)
1
S2
2
S2
nx
y
x
ny
b.
If nx = ny = n, the formula becomes:
(x y) (μ x μ y )
t
(G3b)
1
S2 S2
2
x
y
n
G-2
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