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262 Part IV: Quality Assurance
3. VARIABLES CHARTS
Identify characteristics and uses of x – – R and
x – – s charts. (Application)
Body of Knowledge IV.B.3
In this section we study various control charts for variables.
Shewhart X – and R Control Chart
Part IV.B.3
Certain rules that are widely used in preparing Shewhart X – and R control charts
are:
1. Take a series of samples from the process that is under investigation.
Samples consisting of four or five items taken frequently are usually
good. This is because:
a. Rational subgroups or samples of size four or five are more
cost-effective.
b. If samples are larger than 10, the estimate of process standard
deviation obtained using the range is not very efficient. Moreover
the R chart is also not very effective.
c. With samples of size four or five, there are fewer chances for
occurrence of any special causes during the collection of a sample.
It is commonly known that if the type of variation is changing
(special cause versus common cause variation) the sample size
should be as small as possible so that the averages of samples do
not mask the changes.
EXAMPLE 19.3
Let 5, 6, 9, 7, 8, 6, 9, 7, 6, and 5 be a random sample from a process under investigation.
Find the sample mean and the sample range.
Solution:
Using the above data, we have
5
x = + 6 + 9 + 7 + 8 + 6 + 7 + 6 + 5
= 59 .
10
R Max x Min x 9 5= 4.
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