Chapter 14
Statistical Process Control
142
Control Charts for Variation and Mean
1. No.
Control charts are constructed entirely from the observed data, and they are totally
independent of any product specifications.
The upper and lower control limits of control
charts, for example, are based on the actual behavior of the process under study, and not the
desired behavior.
It is possible for the process of filling 12 oz cans of Coke to be well within
statistical control by consistently filling the cans with, say, 11.5 oz.
2. In this context.
a.
x denotes the mean of the 20 daily means from the daily samples of size 50.
b.
R denotes the mean of the 20 daily ranges from the daily samples of size 50.
c. UCL denotes the value of the upper control limit.
The process is not within statistical
control if there is a data point above the upper control limit.
d. LCL denotes the value of the lower control limit.
The process is not within statistical
control if there is a data point below the lower control limit.
3. Random variation is the natural fluctuation due to chance alone that is inherent in every
process which does not function with perfect precision.
Assignable variation is deviance from
perfect precision that can be attributed to an identifiable source – e.g., machinery that needs
adjustment.
4. The mean and the range are both out of statistical control.
There are longterm cycles, and
there are recent trends showing a significant decrease in the central tendency and significant
increase in the variability.
Both the
x chart and the R chart have points below the lower
control limit and points above the upper control limit.
5. a. Within statistical control.
b. Not applicable; none of the three criteria applies.
c. No; the variability is too large.
Even though the process may be within control statistically,
it is not within control practically.
For the amounts of cola in 12 oz cans to vary from 10 oz
to 13 oz is clearly unacceptable.
6. a. Not within statistical control.
b. Criterion 1 applies; there is a pattern or trend that is not random.
In this case it is clear
that the variability is increasing.
c. No; the equipment appears to be losing its ability to keep within tolerance.
The increasing
variability is a disaster about to happen; if this continues without intervention the process
will soon be producing products outside the control limits.
7. a. Not within statistical control.
b. Criterion 3 applies; there are 8 consecutive points below the centerline.
For these data,
the criterion applies two times – as there are also 8 consecutive points above the
centerline.
c. No; there appears to have been a shift in the process after observation 8, as all the values
before then are below the centerline and all the observations after that are above the
centerline.
It is usually important to identify the cause for such a shift.
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CHAPTER 14
Statistical Process Control
8. a. Within statistical control.
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 Spring '11
 Dr.Kalluri
 Control Chart, UCL, statistical control

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