This preview shows pages 1–3. Sign up to view the full content.
Rev: 33004
Chapter 21
21.1
No.
It is desirable that the minimum value of the output signal be greater
than zero, in order to readily detect instrument failures.
Thus, for a
conventional electronic instrument, an output signal of 0 mA indicates that
a malfunction has occurred such as a power failure.
If the instrument
range were 020 mA, instead of 420 mA, the output signal could be zero
during normal operation.
Thus, instrument failures would be more
difficult to detect.
21.2
The difference between a measurement of 5.9 and the sample mean, 5.75,
is 0.15 pH units.
Because the standard deviation is
s
= 0.05 pH units, this
measurement is three standard deviations from the mean.
If the pH
measurement is normally distributed (an assumption), then Fig. 21.3
indicates that the probability that the measurement is less than or equal to
three standard deviations from the mean is 0.997.
Thus, the probability
p
of a measurement being greater than three standard deviations from the
mean is only
p
=10.997=0.003.
21.3
Make the usual SPC assumption that the temperature measurement is
normally distributed.
According to Figure 21.3, the probability that the
measurement is within two standard deviations from the mean is 0.95.
Thus, the probability that a measurement is beyond these limits, during
routine operation is
p
=10.95=0.05.
From (2119), the average run length
ARL
between false positives is,
1
20
ARL
p
=
=
samples
Thus, for a sampling period of one minute, on average we would expect a
false positive every 20 min.
Consequently, we would expect an average of
3 false alarms per hour or 24 false alarms over an eight hour period.
Solution Manual for Process Dynamics and Control, 2nd edition,
Copyright © 2004 by Dale E. Seborg, Thomas F. Edgar and Duncan A. Mellichamp
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 21.4
The CUSUM and EWMA control charts for the sample means are shown
in Figure S21.4. The Shewhart chart is also shown for the sake of
This is the end of the preview. Sign up
to
access the rest of the document.
This homework help was uploaded on 04/10/2008 for the course CHE 242 taught by Professor Cummings during the Spring '08 term at Vanderbilt.
 Spring '08
 Cummings
 Electron

Click to edit the document details