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Chapter 19: B. Statistical Process Control 263
2. Enough samples should be collected so that the major source of
variation has an opportunity to occur. Generally, at least 25 samples
of size four or five are considered sufficient to give a good test for
process stability.
3. During the collection of data, a complete log of any changes in the
process, such as changes in raw materials, operators, tools or any
calibration of tools, machines, and so on, must be maintained.
Keeping a log is important for finding the special causes in a process
(Duncan 1986).
Calculation of Sample Statistics
The sample statistics that need to be determined initially to prepare Shewhart
X – and R control chart are the sample mean (x – ) and sample range (R). Thus, for
example, let x 1 , x 2 , . . . , x n be a random sample from the process under investigation.
Then, we have
x + x + ... + x
1 2
x =
n
n
(19.2)
R Max x Min x . (19.3)
= ( ) ( )
i
i
Calculation of Control Limits
Step 1. First calculate x – i and R i for the ith sample, for i = 1, 2, 3, . . . m, where
m is the number of samples collected during the study period.
Step 2. Calculate
R R + R + … +
=
R
1 2
m
x + x + ... + x
1 2
x =
m
m
m
(19.4)
(19.5)
Part IV.B.3
Step 3. Calculate the three-sigma control limits for the X – control chart:
UCL = x + 3sˆ
x
sˆ
= x + 3
n
R
= x + 3
d n
2
= x+
A R
2
(19.6)