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Specmanship vs reality

If you want to either specify a sensor or acquire meaningful data from a sensor, you first need to understand terms such as total error band, accuracy, and precision


In modern vehicles, vast numbers of sensors are used to improve both efficiency and safety in powertrain, chassis, and body applications, and their accuracy and precision are paramount. These terms are often used interchangeably, but it is critical to recognize the fundamental differences between accuracy, (the proximity of measurement results to the true value) and precision, (the measurement reproducibility).

Precision is often taken to mean repeatability, but these terms, together with accuracy, reproducibility, variability, and uncertainty represent qualitative concepts and should be carefully applied. The precision of an instrument reflects the number of significant digits in a reading; the accuracy of an instrument reflects how close the reading is to the true value.

To the decimal point
The precision of a measurement is commonly expressed in terms of significant figures, but this convention is often misused. For example, an electronic calculator may yield an answer of 6.1058948, implying that we are confident of the precision of the measurement to one part in 61,058,948. An accurate instrument is not necessarily precise, and instruments are often precise but far from accurate.

Figure 1 illustrates the difference between accuracy and precision:






Concepts of accuracy
Sensor manufacturers generally employ one of two methods to specify sensor performance:
• Parameter specification
• The Total Error Band envelope

Parameter specification quantifies individual sensor characteristics without any attempt to combine them. The Total Error Band envelope yields a solution nearer to that expected in practice, whereby sensor errors are expressed in the form of a Total Error Envelope into which all data points must fit regardless of origin. As long as the sensor operates within the parameters specified in the data sheet, the sensor data can be relied on. Figure 2 illustrates the total error band concept.

Figure 2: Total error band


However, many manufacturers do not generally specify their products using the error band method, unless there are legislative pressures compelling them to do so, even though it yields results more representative of real-world use. Instead, commercial pressures result in manufacturers portraying their sensors in the most favorable light when compared to those of their competitors.

Predictable error sources
A typical sensor data sheet lists individual error sources, not all of which affect the device in a particular situation. Given the plethora of data provided, it may be difficult to decide whether a sensor is sufficiently accurate for an application. Ideally, the mathematical relationship between a change in the measure and the output of a sensor over its temperature and operational range should include all errors from all sources including stability. Typically, users focus on just one or two parameters, using them as benchmarks to compare other products.

A commonly selected parameter is nonlinearity, which describes the degree to which the sensor's output departs from a straight-line correlation. A polynomial expression describing the true performance of the sensor would, if manufacturers provided it, yield significant accuracy improvements.

If thermal effects contributing to zero and sensitivity errors are stated, then measurement errors may be minimized by considering the actual errors rather than global errors quoted on the sensor data sheet, together with the actual temperature range encountered in the application.

These illustrations show that you can improve both accuracy and precision because you can minimize predictable errors mathematically. Stability errors and errors that are unpredictable and nonrepeatable present the largest obstacle to achievable accuracies.

Unpredictable errors
Unpredictable errors – including long-term stability, thermal hysteresis, and nonrepeatability – cannot be treated mathematically to improve accuracy or precision and routine recalibration may be the only reliable way of reducing the consequences of long-term deterioration.

Top tips for the specifier
• Repeatability is the most important sensor performance parameter; without it no amount of compensation or result correction is going to be meaningful
• Consider the environmental temperature range within which the sensor will operate. Thermal errors will dominate
• Do not overspecify the operating range of the sensor "just to be safe." Manufacturers state the sensor's safe over-range limits and these should be sufficient in themselves
• Do not confuse resolution with accuracy—they have no relation to one another
• If the sensor is to be used long-term, consider long-term stability. Progressive deterioration in sensor characteristics can have disastrous consequences emphasizing the need for periodic recalibration
• For any given application, calculate the total error that can be expected referring to the data sheet performance parameters.

Many sensor users hold quantitative data in awe, particularly when the data are associated with computer-based DA systems. The computer provides numbers that appear, and are commonly assumed, to be unquestionably correct. To avoid costly errors, study the accuracy parameters pertinent to a particular application before sensor selection. An error or misjudgment at the outset may prove very costly indeed.


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