Page 109 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
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UCL x = X – A 2 R = 12.62 – 0.73 · 4.44 = 9.38
R Control limits
Upper control limit (UCL R ) = D 4 R = 2.28 · 4.44 = 10.12
Lower control limit (LCL R ) = D 3 R = 0
Since the measurements were recorded in thousands of an inch, the
centerline of the X control chart is 0.01262 and the control limits for X
are 0.01586 and 0.00938. For the R chart, the centerline is set at
0.00444 and the limits are 0.01012 and 0.
These numbers form the control limits of the control chart. After
the limits have been calculated, the control chart is ready for use in
production. Each production day, four readings of the part dimension
are to be taken by the responsible operators, with the average of the
four readings plotted on the X chart, and the range or difference be-
tween the highest and lowest reading to be plotted on the R chart.
The daily numbers of X and R should plot within the control limits. If
they plot outside the limits, the production process is not in control,
and immediate corrective action should be initiated.
3.2.5 Alternate methods for calculating control limits
The control limits are set to three times standard deviation of the
sample distribution (s). s can be calculated from the population
standard deviation using the factor d 2 according to the central limit
theorem:
= R /d 2 = 4.44/2.059 = 2.156
s = / n = 2.156/2 = 1.078
± 3 s = 1.078 · 3 = 3.23, which is close to the A 2 · R value of 3.24,
which corresponds to the distance from the centerline to one of the
control limits in the variable control charts.
It is interesting to note that of the total population of 100 numbers
(Table 3.2), then the standard deviation is = 2.156, which is exactly
the one predicted by the R estimator. If the specifications limits are
given, then the Cp, Cpk, and reject rates can be calculated as in the
example in the previous chapter.

3.2.6 Control chart guidelines, out of control
conditions, and corrective action procedures
and examples
Figures 3.2 and 3.3 are examples of X and R charts showing the solder
paste height deposition process for a surface mount technology (SMT)