# ch21 - Rev: 3-30-04 Chapter 21 21.1 No. It is desirable...

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Rev: 3-30-04 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 0-20 mA, instead of 4-20 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 =1-0.997=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 =1-0.95=0.05. From (21-19), 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

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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
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## 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.

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ch21 - Rev: 3-30-04 Chapter 21 21.1 No. It is desirable...

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