Page 178 - Six Sigma for electronics design and manufacturing

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The Use of Six Sigma with High- and Low-Volume Products and Processes
data. For low-volume production, smaller sample sizes can be used
and deviations tested for the probability that the average or stan-
dard deviation has shifted from the original, given a confidence in-
terval.
3. Correction of process capability based on regular updates. Correc-
tion should only be undertaken if the manufacturing process has
shifted beyond normal statistical significance of 10%, for either
variable or attribute processes, and the population distribution is
assumed to be normal. To check normality, many tests are avail-
2
able, including the graphical and (chi-square) tests discussed in
Chapter 2. The distribution of the data should be symmetrical,
with no skew. If not, the process should be investigated. Changes
to the process capability should be tested as follows:
Testing changes in the average for variable processes. The z
test is used for comparing sample average to the population av-
erage if the sample and population are both greater than 30. The
t test is used to compare sample average to population average if
the sample is < 30 and the population is > 30. If both the initial
process capability and the process update data are less than 30,
then a compound sample standard deviation term can be calcu-
lated to compare the two samples (population is either known
or unknown). The purpose of this test is to determine if the aver-
age has shifted or not and, therefore, whether to recalculate six
sigma process capability data for the average.
The formulas for these tests against original population data are
as follows:
X –
z = (5.10)
/ n
for testing a large sample n with average X against a population (or
large sample) of average and standard deviation ;
X –
t = (5.10)
s/ n
for testing a small sample n, with average X and sample standard
deviation s, against a population (or large sample) of average and
an unknown standard deviation.
The formulas for testing current samples data against original
sample data, when both are < 30 and with known sample sizes,
are given in Section 5.4
For testing changes in the , several tests are available, depend-
ing on the size of the samples taken. If the initial variable