CHAPTER 27 • Statistical Process Control

27-32 CHAPTER 27 • Statistical Process Control
gives x and s for the first 21 samples, coded in units of 0.0001 inch from the center
of the specifications. The specifications allow a range of 0.0002 inch about the
center (a range of 2 to 2 as coded).
(a) Make an s chart based on past data and comment on control of short-term
process variation.
(b) Because the data are coded about the center of the specs, we have a given
target 0 (as coded) for the process mean. Make an x chart and comment
on control of long-term process variation. What special x-type cause probably
explains the lack of control of x? CUTTING
27.24 The Boston Marathon. The Boston Marathon has been run each year since
1897. Winning times were highly variable in the early years, but control improved
as the best runners became more professional. A clear downward trend continued
until the 1980s. Rick plans to make a control chart for the winning times from
1950 to the present. The first few times are 153, 148, 152, 139, 141, and 138 minutes.
Calculation from the winning times from 1950 to 2011 gives
x 134.032 minutes and s 6.462 minutes
Rick draws a center line at x and control limits at x 3s for a plot of individual
winning times. Explain carefully why these control limits are too wide to effectively
signal unusually fast or slow times.
COMMENTS ON STATISTICAL CONTROL
Having seen how x and s (or x and R) charts work, we can turn to some important
comments and cautions about statistical control in practice.
Focus on the process rather than on the products. This is a fundamental
idea in statistical process control. We might attempt to attain high quality by careful
inspection of the finished product, measuring every completed forging and reviewing
every outgoing invoice and expense account payment. Inspection of finished
products can ensure good quality, but it is expensive. Perhaps more important, final
inspection comes too late: when something goes wrong early in a process, much bad
product may be produced before final inspection discovers the problem. This adds
to the expense, because the bad product must then be scrapped or reworked.
The small samples that are the basis of control charts are intended to monitor the
process at key points, not to ensure the quality of the particular items in the samples.
If the process is kept in control, we know what to expect in the finished product.
We want to do it right the first time, not inspect and fix finished product.
rational subgroup
Rational subgroups. The interpretation of control charts depends on the distinction
between x-type special causes and s-type special causes. This distinction in
turn depends on how we choose the samples from which we calculate s (or R). We
want the variation within a sample to reflect only the item-to-item chance variation
that (when in control) results from many small common causes. Walter Shewhart,
the founder of statistical process control, used the term rational subgroup to emphasize
that we should think about the process when deciding how to choose samples.