Page 105 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
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on the process, such as a poor repair or maintenance record, un-
trained operators, and nonuniform materials.
The variable control charts are generated by taking a historical
record of the manufacturing process over a period of time. Shewhart,
the father of control charts, recommends that “statistical control can-
not be reached until under the same conditions, not less than 25 sam-
ples of four each have been taken to satisfy the required criterion.”
These observations form the historical record of the process. All obser-
vations from now on are compared to this baseline.
From these observations, the sample average X and the sample
range R, which is the absolute value of highest value minus the low-
est value in the sample, are recorded. At the end of the observation
– –
period (25 samples), the average of X s, designated as X and the aver-
age of R’s, designated as R , are recorded.
3.2.1 Variable control chart limits
The control limits for the control charts are calculated using the fol-
lowing formulas and Table 3.1 for control chart factors. The control
chart factors were designated with variables such as A 2 , D 3 , and D 4 to
calculate the control limits of X and R control charts. The factor d 2 is
important in linking the average range R , and hence the standard de-
viation of the sample (s), to the population standard deviation .
The control chart factors shown in Table 3.1 stop at the number 20
of observations of the subgroup. Control charts are based on taking
samples to approximate a large production output. If the sample be-
comes large enough, there is no advantage to using samples and their
associated normal distributions to generate variable control charts.
Instead, 100% of production could be tested to find out if the parts
produced are within specifications.
3.2.2 Control chart limits calculations
X chart control limits are 3 s of the sample average distribution. This
distribution is always normal, with an average equal to the average of
– –
sample averages X. The range of each sample is called R and the aver-
age of all sample ranges is called R . The distribution of the ranges is
not normal, even if the parent distribution is normal. The control
chart factors in Table 3.1 are approximations to convert the R to the
standard deviation of the sample average distribution s and the popu-
lation distribution .

X Control limits (3 s limits)
– – – –
Upper control limit (UCL X )= X + 3 s = X + A 2 · R (3.1)