Basic Math for Process Control
A practical tutorial on the mathematics essential to the process control field, this book is a handy reference for process control engineers and a helpful aid to students in mathematics courses.
TABLE OF CONTENTS Basic Math for Process Control
The Most Representative Value (MRV)
Sometimes a number of measurements of the same entity are made, possibly at different times. This leads to the question: What one value could be chosen as being the most representative value for the entity of concern?
The daily price of gasoline, in cents per litre, over a 15 day period, was noted to be:
| 62.5 | 64.5 | 65.5 | 66.5 | 61.5 |
| 61.5 | 62.5 | 66.5 | 67.5 | 67.5 |
| 68.5 | 68.5 | 66.5 | 65.5 | 63.5 |
Which value would be most representative of the price of gasoline over the 15 day period? There are actually four possibilities.
Average Value
The average value, or what the statisticians call the arithmetic mean, is probably the most familiar. To calculate the average, the 15 readings are summed, and the sum is divided by the number of readings, i.e. 15. For this example, the average turns out to be 65.2 / l.
Although the average value is often used as the most representative value, there is obviously a problem in this case because the value 65.2 does not appear anywhere in the list of readings. This raises some doubt as to its appropriateness as the representative value.
Weighted Average
When a number of readings are taken, it may happen that some readings will be more relevant than others. At the beginning of the year, one might be attempting to estimate how much of one's income will go into paying for natural gas. The cost of gas for each of the last five years is...
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