Page 169 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
138
control within 95% confidence but not within 97.5% confidence. The
sample process average taken yesterday results in t = 2, and this
number can be used to compare the variability in production to a nor-
mally occurring variability. The probability that t will exceed 1.860 is
0.05 (1 in 20 times will occur in this manner naturally), whereas the
probability that t will be greater than 2.306 is 0.025 (1 in 40 times will
occur in this manner naturally).
Example 5.2
A manufacturing process for batteries has an average battery voltage
output of 12 volts, with production assumed to be normally distrib-
uted. It has been decided that if a sample of 21 batteries taken from
production has a sample average of 11 and sample standard deviation
of 1.23, then production is declared out of control and the line is
stopped. What is the confidence that this decision is a proper one to
take?
11 – 12
t = = – 3.726 and = 20

1.23/ 21
Since the t distribution is symmetrical, the absolute value of t can
be used. The calculated value of 3.726 falls between the t ,20 for =
0.001 and = 0.0005. The probability that t will exceed –3.552 is
0.001, and the probability that t will be greater than –3.849 is 0.0005.
Thus, the decision is proper, since the significance of the sample oc-
curring from the normal distribution is less 0.001 or 99.9% confi-
dence.
5.1.2 Other statistical tools: Point and
interval estimation
The previous section has introduced some statistical terms that are
not widely used by engineers but are very familiar to statisticians.
This section is a review of some of the statistical terms and proce-
dures dealing with error estimation for the average and standard de-
viation as well as their confidence limits.
A good number to use for statistically significant data is 30. It is a
good threshold when using some of the six sigma processes such as
calculating defect rates. This is based on the fact that a t distribution
with degrees of freedom = 29 approaches the normal distribution. It
can be from Table 5.2 that the data for the value of t ,30 is close to the
value of the standard normal distribution. The error E is calculated as
the difference between the t ,30 value and the z value from the normal
distribution. For a significance of 0.025, or confidence of 97.5%, the er-
ror is less than 5%. Note that this point of z = 1.96 is close to the z = 2