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Six Sigma for Electronics Design and Manufacturing
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process capability population data is greater than 30, and the ca-
2
pability update data is less than 30, then the test can be used.
To compare current value of to the initial process capability
when both data sets are under 30, the F test should be used. F
tests can test for a level of significance (5% or 1%) to determine if
the ’s between the two data sets are statistically different. De-
pending on the results of these tests, the six sigma attributes are
either retained or recalculated. The F test can also be used when
two or more sample data sets originate from a common popula-
tion. In that case, the differences between sample variability are
either due to natural variation or a deviation in the product.
More details on the F test are given in Chapter 7.
5.2.2 Determination of standard deviation for
process capability
There are four different methods for determining the standard devia-
tion of the population for process capability studies:
1. Total overall variation. All data is collected into one large group
and treated as a single large sample with n greater than 30.
2. Within-group variation. Data is collected into subgroups, and a dis-
persion statistic is calculated (range). All ranges of each subgroup
are averaged into an R . The is calculated from an R estimator
(d 2 ). This method is the basis for variable control chart limit calcu-
lations and discussed in Chapter 3.
3. Between-group variation. Data is collected into subgroups, and an
average (X ) is calculated for each subgroup. The standard devia-
tion s of sample averages is calculated. The population is esti-
mated from the central limit theorem equation, = s · n . This
method can be used to obtain process capability from control chart
limits.
4. Moving range method. In this method, data is collected into one
group of small numbers of data, over time. A range (R) is calculat-
ed from each two successive points. All ranges of each pair are av-
eraged into an R . The is calculated from an R estimator (d 2 ) for n
= 2, which is equal 1.128. Method 4 is the preferred method for
time series data and small data sets from low-volume manufactur-
ing.

For processes that are in statistical control, these methods are equiv-
alent over time. For processes not in control, only Method is 2 insensi-
tive to process variations of the average over time. The estimate is
inflated or deflated with Method 1 and could be severely inflated/de-