Distance Leads to Error

Get specific with accuracy in your measurement equipment

by Christopher L. Grachanen

Recently, my pastor delivered a sermon he titled "Distance leads to error." I won’t get into the content of the sermon, but being a calibration professional, I started thinking about this theme from a metrological perspective.

As most measurement-equipment users know (or should know), all measurements have error contributors (often referred to as measurement uncertainties) associated with the measurement values derived by a measurement process. Some of these error contributors are documented in measurement-equipment specifications. Others, such as operator errors and ambient influences, must be determined, estimated and assessed for a particular measurement application.

While I was thinking about some of the error contributors associated with measurement equipment specifications, I found some common ground with my pastor’s sermon.

Check the specs

Manufacturers guarantee their measurement equipment to published specifications. These specifications are used to communicate levels of accuracy that can be expected for a particular piece of measurement equipment’s model type.

These specifications equate to tolerances for calibration purposes that can be classified into three major categories: specifications associated with a unit’s derived measurement value (for example, percentage of reading or output); specifications associated with a unit’s measurement range; and specifications associated with a fixed floor or offset. The final two of that trio—range and fixed floor—will be addressed in this column.

Specifications associated with a measurement unit’s range are typically stated as a percentage or parts per million (ppm) of range, span or full scale. The relationship of measurement range specification to a measurement value can be easily understood through the following example:

A digital multimeter with a 10-volt direct current (VDC) range specification has a value of 2.5%. This results in a yield of 0.25VDC. Comparing 0.25VDC to several measurement value readings makes it possible to determine what percentage 0.25 volts (V) is of each value.

Table 1 shows that as measurement values get farther away from the digital multimeter’s nominal 10V full-scale range, the greater the 0.25VDC percentage becomes when compared to each value. Remember, 0.25VDC is the error associated with measuring the multimeter’s 10VDC range so that as the ratio of 0.25VDC to measurement values increases, so does the error associated with making that measurement.

Table 1

To illustrate this relationship more clearly, carry the example to a 1VDC measurement value and plot the results, shown in Figure 1.

Figure 1 also shows that the relationship of range specification to measurement value is not a linear one. For a 10% full-scale measurement value of 1V, the error contributed to the measurement from the measurement unit’s range specification would be a whopping 25%.

Figure 1

The fix is in

The second type of measurement equipment specification involves a fixed value that is not dependent on a measurement unit’s range or derived measurement value.

A measurement unit’s fixed-floor or offset specification can be expressed as a numeric value with an associated prefix and unit, such as 3 milliamps or 120 microvolt direct current (uVDC). Fixed-floor or offset specifications can also be expressed as a numeric value that references a measurement unit’s resolution, such as number of digits, counts or divisions.

A measurement unit’s fixed-floor specification, given as three counts for a digital multimeter with a 100uV resolution, would equate to 300uV, or three times 100uV. Again, this example shows the relationship of a fixed-floor specification relative to several measurement values.

Keep the digital multimeter in the 10VDC range and compute a fixed-floor specification for 15 counts. With a 100uV resolution, our digital multimeter would have a fixed-floor error of 1.5 millivolt direct current (mVDC), yielding the relationship found in Table 2.

Table 2 shows that as measurement values get farther away from the digital multimeter’s nominal full-scale value, the greater the 1.5mVDC floor percentage becomes when compared to each measurement value. Keeping with this train of thought, noise that might be induced in a measurement process often can be treated as a fixed, averaged and offset value.

Table 2

This is concurrent with the notion that the greater the signal-to-noise ratio is for a measurement, the less likely the error contributor is due to noise when comparing that noise to the measured signal.

From the aforementioned example, it can be seen in the context of a measurement unit’s range and fixed-floor specifications that the farther away a derived measurement value is from a measurement unit’s full-scale value, the bigger the error contributor percentages as related to the final value.

Users of measurement instruments possessing range and fixed offset specifications who are trying to select an appropriate unit for the task at hand should be cognizant of assuring the selected measurement range is as close as possible to the expected measurement. Simply stated, you would not want to use a 100-ampere current shunt to measure an expected current of 1 ampere.

And, as any good engineer—or pastor—would tell you, the farther away you get from your expected target, the more likely you are to introduce error into the situation.

Christopher L. Grachanen is a master engineer and operations manager at Hewlett-Packard Co. in Houston. He earned a master’s in Business Administration from Regis University in Denver. Grachanen is co-author of The Metrology Handbook, a senior member of ASQ, an ASQ certified calibration technician and the Measurement Quality Division Certified Calibration Technician chairman.

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