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Sensors: ‘specmanship’ versus reality

04 January 2012

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

Sensors and transducers are used throughout the worlds of science, technology, and industry to measure and control physical events. They range from simple devices such as thermocouples to sophisticated sensors used in aerospace applications. Most sensors provide data in an electronic form and it is this signal that forms the analogue of the physical quantity being monitored.

When specifying a sensor, its accuracy and precision are paramount among a multitude of other parameters. These terms are often used interchangeably but it’s critical to recognize the fundamental differences between the two. Accuracy indicates the proximity of measurement results to the true value, while precision reflects the repeatability or reproducibility of the measurement.

Nevertheless, precision is often taken to mean repeatability. The terms precision, accuracy, repeatability, reproducibility, variability, and uncertainty represent qualitative concepts and thus should be applied with care. 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 being measured.

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 and this implies that we are confident of the precision of the measurement to 1 part in 61,058,948. An accurate instrument is not necessarily precise, and instruments are often precise but far from accurate.

Concepts of accuracy
Sensor manufacturers and users employ one of two basic methods to specify sensor performance: parameter specification and 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 Band or Error Envelope into which all data points must fit regardless of their origin. As long as the sensor operates within the parameters specified in the data sheet, the sensor data can be relied on.

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 how the product will respond during real-world use. Instead, commercial pressures result in manufacturers portraying their sensors in the most favourable light when compared to those of their competitors. If you are selecting a sensor, you must carefully examine all performance parameters with respect to the intended application to ensure the sensor you choose is suitable for its specific end use.

Predictable error sources
A typical sensor data sheet will list individual error sources, not all of which affect the device in a particular situation. Given the plethora of data provided, you may find it difficult to decide whether a sensor is sufficiently accurate for your application.

Ideally, the mathematical relationship between a change in the measure and the output of a sensor over the compensated temperature and operational range should include all errors due to parameters such as zero offset, span rationalisation, non-linearity, hysteresis, repeatability, thermal effects on zero and span, thermal hysteresis, and long-term stability. Typically, users will focus on just one or two of these parameters, using them as benchmarks with which to compare other products.

A commonly selected parameter is non-linearity, 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 accuracy improvements of an order of magnitude.

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

These examples illustrate that you can improve both accuracy and precision because you can minimise predictable errors mathematically. Stability errors and errors that are unpredictable and non-repeatable present the largest obstacle to achievable accuracy.

Unpredictable errors
Unpredictable errors - such as long-term stability, thermal hysteresis, and non-repeatability - cannot be treated mathematically to improve accuracy or precision. Various statistical tools are available to help define long-term stability, but routine re-calibration may be the only reliable way of eliminating the consequences of long-term deterioration. Here are some 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 over-specify 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 the effect of the sensor's long-term stability. Progressive deterioration in sensor characteristics can have disastrous consequences and this emphasises the need for periodic re-calibration.
- For any given application, calculate the total error that can be expected from the sensor by 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. After all, the computer provides numbers that appear, and are commonly assumed, to be unquestionably correct. To avoid costly errors, carefully study the accuracy parameters pertinent to your particular application before you select the sensor. An error or misjudgment at the outset may prove very costly indeed.

Mike Baker is with Sherborne Sensors

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