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19. Application Characteristics

Design, weight, and overall dimensions are geared to specific areas of applications. Price may be a secondary issue when the sensor’s reliability and accuracy are of paramount importance. If a sensor is intended for life-support equipment, weapons or spacecraft, a high price tag may be well justified to assure high accuracy and reliability. On the other hand, for a very broad range of consumer applications, the price of a sensor often becomes a cornerstone of a design.

20. Uncertainty

Nothing is perfect in this world, at least in the sense that we perceive it. All materials are not exactly as we think they are. Our knowledge of even the purest of the materials is always approximate; machines are not perfect and never produce perfectly identical parts according to drawings. All components experience drifts related to the environment and their aging; external interferences may enter the system and alter its performance and modify the output signal. Workers are not consistent and the human factor is nearly always present.

Manufacturers fight an everlasting battle for the uniformity and consistency of the processes, yet the reality is that every part produced is never ideal and carries an uncertainty of its properties. Any measurement system consists of many components, including sensors. Thus, no matter how accurate the measurement is, it is only an approximation or estimate of the true value of the specific quantity subject to measurement, (i.e., the stimulus or measurand). The result of a measurement should be considered complete only when accompanied by a quantitative statement of its uncertainty.We simply never can be 100% sure of the measured value.

When taking individual measurements (samples) under noisy conditions we expect that the stimulus s is represented by the sensor as having a somewhat different value s', so that the error in measurement is expressed as:

     d  = s' - s        (27)

The difference between the error specified by Eq. (27) and uncertainty should always be clearly understood. An error can be compensated to a certain degree by correcting its systematic component. The result of such a correction can unknowably be very close to the unknown true value of the stimulus and, thus, it will have a very small error.Yet, in spite of a small error, the uncertainty of measurement may be very large so we cannot really trust that the error is indeed that small. In other words, an error is what we unknowably get when we measure, whereas uncertainty is what we think how large that error might be.

The International Committee forWeight and Measures (CIPM) considers that uncertainty consists of many factors that can be grouped into two classes or types:

  A: Those evaluated by statistical methods
  B: Those evaluated by other means.

This division is not clear-cut and the borderline between Types A and B is somewhat illusive. Generally, Type A components of uncertainty arise from random effects, whereas the Type B components arise from systematic effects.

Type A uncertainty is generally specified by a standard deviation Si , equal to the positive square root of the statistically estimated variance Si² and the associated number of degrees of freedom νi  . For such a component, the standard uncertainty is ui=Si . Standard uncertainty represents each component of uncertainty that contributes to the uncertainty of the measurement result.

The evaluation of a Type A standard uncertainty may be based on any valid statistical method for treating data. Examples are calculating the standard deviation of the mean of a series of independent observations, using the method of least squares to fit a curve to data in order to estimate the parameters of the curve and their standard deviations. If the measurement situation is especially complicated, one should consider obtaining the guidance of a statistician.

The evaluation of a Type B standard uncertainty is usually based on scientific judgment using all of the relevant information available, which may include the following:

• Previous measurement data
• Experience with or general knowledge of the behavior and property of relevant sensors, materials, and   instruments
• Manufacturer’s specifications
• Data obtained during calibration and other reports
• Uncertainties assigned to reference data taken from handbooks and manuals

For detailed guidance of assessing and specifying standard uncertainties one should consult specialized texts. When both Type A and Type B uncertainties are evaluated, they should be combined to represent the combined standard uncertainty. This can be done by using a conventional method for combining standard deviations. This method is often called the law of propagation of uncertainty and in common parlance is known as “rootsum-of-squares” (square root of the sum-of-the-squares) or RSS method of combining uncertainty components estimated as standard deviations:

uc = √[u1² + u2² + · · · + ui² + · · · + un²]       (28)

where n is the number of standard uncertainties in the uncertainty budget.

Table 1 shows an example of an uncertainty budget for an electronic thermometer with a thermistor sensor which measures the temperature of a water bath. While compiling such a table, one must be very careful not to miss any standard uncertainty, not only in a sensor but also in the interface instrument, experimental setup, and the object of measurement. This must be done for various environmental conditions, which may include temperature, humidity, atmospheric pressure, power supply variations, transmitted noise, aging, and many other factors.

No matter how accurately any individual measurement is made, (i.e., how close the measured temperature is to the true temperature of an object), one never can be sure that it is indeed accurate. The combined standard uncertainty of 0.068°C does not mean that the error of measurement is no greater than 0.068°C. That value is just a standard deviation, and if an observer has enough patience, he may find that individual errors may be much larger. The word “uncertainty” by its very nature implies that the uncertainty of the result of a measurement is an estimate and generally does not have well-defined limits.

Reference Books About Sensor



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