CHAPTER 27 • Statistical Process Control

27-16 CHAPTER 27 • Statistical Process Control
TABLE 27.2 Three sets of x _ ’s from 20 samples of size 4
SAMPLE DATA SET A DATA SET B DATA SET C
1 11.602 11.627 11.495
2 11.547 11.613 11.475
3 11.312 11.493 11.465
4 11.449 11.602 11.497
5 11.401 11.360 11.573
6 11.608 11.374 11.563
7 11.471 11.592 11.321
8 11.453 11.458 11.533
9 11.446 11.552 11.486
10 11.522 11.463 11.502
11 11.664 11.383 11.534
12 11.823 11.715 11.624
13 11.629 11.485 11.629
14 11.602 11.509 11.575
15 11.756 11.429 11.730
16 11.707 11.477 11.680
17 11.612 11.570 11.729
18 11.628 11.623 11.704
19 11.603 11.472 12.052
20 11.816 11.531 11.905
s CHARTS FOR PROCESS MONITORING
The x charts in Figures 27.4(b), 27.5, and 27.6 were easy to interpret because
the process standard deviation remained fixed at 43 mV. The effects of moving
the process mean away from its in-control value (275 mV) are then clear to see.
We know that even the simplest description of a distribution should give both a
measure of center and a measure of spread. So it is with control charts. We must
monitor both the process center, using an x chart, and the process spread, using a
control chart for the sample standard deviation s.
The standard deviation s does not have a Normal distribution, even approximately.
Under the process-monitoring conditions, the sampling distribution
of s is skewed to the right. Nonetheless, control charts for any statistic are
based on the “plus or minus three standard deviations” idea motivated by
the 68–95–99.7 rule for Normal distributions. Control charts are intended to
be practical tools that are easy to use. Standard practice in process control
therefore ignores such details as the effect of non-Normal sampling distributions.
Here is the general control chart setup for a sample statistic Q (short for
“quality characteristic”).