Page 182 - Six Sigma for electronics design and manufacturing

The Use of Six Sigma with High- and Low-Volume Products and Processes
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period of time. It is very useful when there is only one number to de-
scribe a particular condition or situation. It can be used to estimate
production variables such as temperature, pressure, humidity, volt-
age, or conductivity. It can also be used for production support efforts
such as costs, efficiencies, shipments, and purchasing activities. The
moving range charts can also be used for attributes. Instead of count-
ing defects, the time between defects can be counted and entered as
the variable in the chart.
The moving range stands for the difference between successive
pairs of numbers in a series of numbers. The absolute value of the dif-
ference is used, creating a new set of range numbers, each with two
successive elements. The number of differences or “ranges” is one less
than the individual numbers in the series. The chart is built up from
the following:
The centerline of the chart is the average of all the individual
measurements.
The average of the ranges of the successive numbers is called the
M R . The control limits are set by multiplying M R by the number
2.66. This is the result of using the factor d 2 for n = 2 (1.128) esti-
mation of the in the following equation:
– – – –
MR control limits = X ± 3 · M R /1.128 = X ± M R · 2.66 (5.12)
Note that the conversion from the standard deviation of sample av-
erage to population that is performed on X , R charts is not neces-
sary here, since the moving range charts use the actual distribution of
data, not those from sample distributions.
Example 5.11
Days between defects were counted as a measure of the quality of a
manufacturing process. They occurred on the following production cal-
endar days: 23, 45, 98, 123, 154, 167, 189, 232, 287, 311, and 340. Cal-
culate the data for the moving range chart for days between defects.
Days between defects: 22, 53, 25, 31, 13, 22, 43, 55, 24, 29; average
= 31.70
Moving ranges (R’s): 31, 28, 6, 18, 9, 21, 12, 31, 5; R = 17.89
MR x control limits = 31.70 ± 2.66 · 17.89 = 17.89 ± 47.59 days
R chart control limits: UCL R = D 4(n=2) · R = 3.27 · 17.89 = 58.5;
LCL R = 0
Another method to plot this defect data would be defects/month, ob-
tained by dividing the data by 30.