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Six Sigma for Electronics Design and Manufacturing
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Method 4. Moving range method (n = 2)
For each subgroup, obtain the average range between successive
numbers:
Subgroup I: = R /d 2(n=2) = 1.67/1.128 = 1.48
Subgroup II: = R /d 2 = 1.89/1.128 = 1.68
Subgroup III: = R /d 2 = 1.67/1.128 = 1.48
– –
For the total groups (I–III), = R/d 2 = 1.74/1.128 = 1.54.
As can be seen from Example 5.10, the of the overall 30 numbers
was 1.62 (Method 1). The 30 numbers were made of three subgroups
(samples) with large shifts in sample averages. The closest indirectly
calculated value was obtained by Method 2, between-group varia-
tion from the R estimator of , because it negated the average shifts.
The moving range method (Method 4) was as much as 10% off, even
when using the full 30 numbers. The least accurate value was Method
3, the between-group variation, which derived from a distribution of
sample averages and the conversion of the sample to population .
The number of subgroups (samples) was small and led to the largest
error in determination.
5.2.4 Process capability for low-volume production
When it is not feasible to collect the amount of data required to deter-
mine process capability because of cost or resource issues or produc-
tion volume, reduced data can be used successfully to estimate
process capability, provided that confidence is quantified in the data
analysis. Although 30 points of data are considered statistically sig-
nificant, a smaller number of data points can be taken, using prede-
termined error levels and confidence goals, to obtain a good estima-
tion of process average and variability. Refer to earlier sections in this
chapter for proper methods and examples.
The moving range method provides an alternate mechanism for es-
timating the for small amounts of data, provided that data points
are taken over time for both variable and attribute processes. Ten
data point are required to provide an estimator for with the moving
range method.

5.2.5 Moving range (MR) methodologies for low
volume: MR control charts
The moving range methodology allows for a reasonable estimate of
and process capability for both variable and attribute processes. It
uses individual measurements or defect rates over a representative