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3.4 Sensitivity
The sensitivity indicates how much the output of an instrument system or system element changes when the quantity being measured changes by a given amount, i.e. the ratio output/input. For example, a thermocouple might have a sensitivity of 20 uV/C and so give an output of 20 uV for each IT change in temperature. Thus, if we take a series of readings of the output of an instrument for a number of different inputs and plot a graph of output against input (FIG. 19), the sensitivity is the slope of the graph.
FIG. 19 Sensitivity as slope of input-output graph
Application---An iron-constant an thermocouple is quoted as having a sensitivity at 0 degr. C of 0.05 mV/ degr. C.
The term is also frequently used to indicate the sensitivity to inputs other than that being measured, i.e. environmental changes. For example, the sensitivity of a system or element might be quoted to changes in temperature or perhaps fluctuations in the mains voltage supply. Thus a pressure measurement sensor might be quoted as having a temperature sensitivity of ±0.1% of the reading per degree C change in temperature.
Example
A spring balance has its deflection measured for a number of loads and gave the following results. Determine its sensitivity.
Load in kg: 0 1 2 3 4
Deflection in mm: 0 10 20 30 40
FIG. 20 shows the graph of output against input. The graph has a slope of 10 mm/kg and so this is the sensitivity.
FIG. 20 Example
Example
A pressure measurement system (a diaphragm sensor giving a capacitance change with output processed by a bridge circuit and displayed on a digital display) is stated as having the following characteristics. Explain the significance of the terms:
Range: 0 to 125 kPa and 0 to 2500 kPa
Accuracy: ±1% of the displayed reading
Temperature sensitivity: ±0.1% of the reading per °C
The range indicates that the system can be used to measure pressures from 0 to 125 kPa or 0 to 2500 kPa. The accuracy is expressed as a percentage of the displayed reading, thus if the instrument indicates a pressure of, say, 100 kPa then the error will be ±1 kPa. The temperature sensitivity indicates that if the temperature changes by PC that displayed reading will be in error by ±0.1% of the value.
Thus for a pressure of, say, 100 kPa the error will be ±0.1 kPa for a PC temperature change.
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Application -- A commercial pressure measurement system is quoted in the manufacturer's specification as having:
Range 0 to 10 kPa
Supply Voltage ±15 V dc
Linearity error ±0.5% FS
Hysteresis error ±0.15% FS
Sensitivity 5 V dc for full range
Thermal sensitivity ±0.02%/degr. C
Thermal zero drift 0.02%/^C FS
Temperature range 0 to 50 degr. C
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3.5 Stability
The stability of a system is its ability to give the same output when used to measure a constant input over a period of time. The term drift is often used to describe the change in output that occurs over time. The drift may be expressed as a percentage of the full range output. The term zero drift is used for the changes that occur in output when there is zero input.
FIG. 21 Oscillations of a meter reading
3.6 Dynamic characteristics
The terms given above refer to what can be termed the static characteristics. These are the values given when steady-state conditions occur, i.e. the values given when the system or element has settled down after having received some input. The dynamic characteristics refer to the behavior between the time that the input value changes and the time that the value given by the system or element settles down to the steady state value. For example, FIG. 21 shows how the reading of an ammeter might change when the current is switched on. The meter pointer oscillates before settling down to give the steady-state reading.
The following are terms commonly used for dynamic characteristics.
1. Response time
This is the time which elapses after the input to a system or element is abruptly increased from zero to a constant value up to the point at which the system or element gives an output corresponding to some specified percentage, e.g. 95%, of the value of the input.
2. Rise time
This is the time taken for the output to rise to some specified percentage of the steady-state output. Often the rise time refers to the time taken for the output to rise from 10% of the steady-state value to 90 or 95% of the steady-state value.
3. Settling time
This is the time taken for the output to settle to within some percentage, e.g. 2%, of the steady-state value.
4. Reliability
If you toss a coin ten times you might find, for example, that it lands heads uppermost six times out of the ten. If, however, you toss the coin for a very large number of times then it is likely that it will land heads uppermost half of the times. The probability of it landing heads uppermost is said to be half
The probability of a particular event occurring is defined as being:
probability = number of occurrences of the event / total number of trials
when the total number of trials is very large. The probability of the coin landing with either a heads or tails uppermost is likely to be 1, since every time the coin is tossed this event will occur. A probability of I means a certainty that the event will take place every time. The probability of the coin landing standing on edge can be considered to be zero, since the number of occurrences of such an event is zero. The closer the probability is to 1 the more frequent an event will occur; the closer it is to zero the less frequent it will occur.
Reliability is an important requirement of a measurement system. The reliability of a measurement system, or element in such a system, is defined as being the probability that it will operate to an agreed level of performance, for a specified period, subject to specified environmental conditions. The agreed level of performance might be that the measurement system gives a particular accuracy. The reliability of a measurement system is likely to change with time as a result of perhaps springs slowly stretching with time, resistance values changing as a result of moisture absorption, wear on contacts and general damage due to environmental conditions. For example, just after a measurement system has been calibrated, the reliability should be 1. However, after perhaps six months the reliability might have dropped to 0.7. Thus the system cannot then be relied on to always give the required accuracy of measurement, it typically only giving the required accuracy seven times in ten measurements, seventy times in a hundred measurements.
A high reliability system will have a low failure rate. Failure rate is the number of times during some period of time that the system fails to meet the required level of performance, i.e.:
Failure rate = number of failures / [number of systems observed x time observed]
A failure rate of 0.4 per year means that in one year, if ten systems are observed, 4 will fail to meet the required level of performance. If 100 systems are observed, 40 will fail to meet the required level of performance. Failure rate is affected by environmental conditions. For example, the failure rate for a temperature measurement system used in hot, dusty, humid, corrosive conditions might be 1.2 per year, while for the same system used in dry, cool, non-corrosive environment it might be 0.3 per year.
With a measurement system consisting of a number of elements, failure occurs when just one of the elements fails to reach the required performance. Thus in a system for the measurement of the temperature of a fluid in some plant we might have a thermocouple, an amplifier and a meter. The failure rate is likely to be highest for the thermocouple since that is the element in contact with the fluid while the other elements are likely to be in the controlled atmosphere of a control room.
The reliability of the system might thus be markedly improved by choosing materials for the thermocouple which resist attack by the fluid.
Thus it might be in a stainless steel sheath to prevent fluid coming into direct contact with the thermocouple wires.
Example
The failure rate for a pressure measurement system used in factory A is found to be 1.0 per year while the system used in factory B is 3.0 per year. Which factory has the most reliable pressure measurement system?
The higher the reliability the lower the failure rate. Thus factory A has the more reliable system. The failure rate of 1.0 per year means that if 100 instruments are checked over a period of a year, 100 failures will be found, i.e. on average each instrument is failing once. The failure rate of 3.0 means that if 100 instruments are checked over a period of a year, 300 failures will be found, i.e. instruments are failing more than once in the year.
5. Requirements
The main requirement of a measurement system is fitness for purpose.
This means that if , for example, a length of a product has to be measured to a certain accuracy that the measurement system is able to be used to carry out such a measurement to that accuracy. For example, a length measurement system might be quoted as having an accuracy of ±1 nun.
This would mean that all the length values it gives are only guaranteed to this accuracy, e.g. for a measurement which gave a length of 120 mm the actual value could only be guaranteed to be between 119 and 121 mm. If the requirement is that the length can be measured to an accuracy of ±1 mm then the system is fit for that purpose. If, however, the criterion is for a system with an accuracy of ±0.5 mm then the system is not fit for that purpose.
In order to deliver the required accuracy, the measurement system must have been calibrated to give that accuracy. Calibration is the process of comparing the output of a measurement system against standards of known accuracy. The standards may be other measurement systems which are kept specially for calibration duties or some means of defining standard values. In many companies some instruments and items such as standard resistors and cells are kept in a company standards department and used solely for calibration purposes.
5.1 Calibration
Calibration should be carried out using equipment which can be traceable back to national standards with a separate calibration record kept for each measurement instrument. This record is likely to contain a description of the instrument and its reference number, the calibration date, the calibration results, how frequently the instrument is to be calibrated and probably details of the calibration procedure to be used, details of any repairs or modifications made to the instrument, and any limitations on its use.
The national standards are defined by international agreement and are maintained by national establishments, e.g. the National Physical Laboratory in Great Britain and the National Bureau of Standards in the United States. There are seven such primary standards, and two supplementary ones, the primary ones being:
1. Mass
The mass standard, the kilogram, is defined as being the mass of an alloy cylinder (90% platinum-10% iridium) of equal height and diameter, held at the International Bureau of Weights and Measures at Sevres in France. Duplicates of this standard are held in other countries.
2. Length
The length standard, the meter, is defined as the length of the path travelled by light in a vacuum during a time interval of duration 1/299 792 458 of a second.
3. Time
The time standard, the second, is defined as a time duration of 9 192 631 770 periods of oscillation of the radiation emitted by the caesium-133 atom under precisely defined conditions of resonance.
4. Current
The current standard, the ampere, is defined as that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one meter apart in a vacuum, would produce between these conductors a force equal to 2 x 10^-7 N per meter of length.
5. Temperature
The kelvin (K) is the unit of thermodynamic temperature and is defined so that the temperature at which liquid water, water vapor and ice are in equilibrium (known as the triple point) is 273.16 K. A temperature scale devised by Lord Kelvin forms the basis of the absolute practical temperature scale that is used and is based on a number of fixed temperature points, e.g. the freezing point of gold at 1337.58 K.
6. Luminous intensity
The candela is defined as the luminous intensity, in a given direction, of a specified source that emits monochromatic radiation of frequency 540 x 10^12 Hz and that has a radiant intensity of 1/683 watt per unit steradian (a unit solid angle, see below).
7. Amount of substance
The mole is defined as the amount of a substance which contains as many elementary entities as there are atoms in 0.012 kg of the carbon 12 isotope.
The supplementary standards are:
1. Plane angle
The radian is the plane angle between two radii of a circle which cuts off on the circumference an arc with a length equal to the radius (FIG. 22).
2. Solid angle
The steradian is the solid angle of a cone which, having its vertex in the center of the sphere, cuts off an area of the surface of the sphere equal to the square of the radius (FIG. 23).
FIG. 22 The radian
FIG. 23 The steradian
FIG. 24 Traceability chain
Primary standards are used to define national standards, not only in the primary quantities but also in other quantities which can be derived from them. For example, a resistance standard of a coil of manganin wire is defined in terms of the primary quantities of length, mass, time and current. Typically these national standards in turn are used to define reference standards which can be used by national bodies for the calibration of standards which are held in calibration centers.
The equipment used in the calibration of an instrument in everyday company use is likely to be traceable back to national standards in the following way:
1. National standards are used to calibrate standards for calibration centers.
2. Calibration center standards are used to calibrate standards for instrument manufacturers.
3. Standardized instruments from instrument manufacturers are used to provide in-company standards.
4. In-company standards are used to calibrate process instruments.
There is a simple traceability chain from the instrument used in a process back to national standards (FIG. 24). In the case of, say, a glass bulb thermometer, the traceability might be:
1. National standard of fixed thermodynamic temperature points
2. Calibration center standard of a platinum resistance thermometer with an accuracy of ±0.005 C.
3. An in-company standard of a platinum resistance thermometer with an accuracy of ± 0.1 C.
4. The process instrument of a glass bulb thermometer with an accuracy of +/- 0.1 C.
5.2 Safety systems
Statutory safety regulations lay down the responsibilities of employers and employees for safety in the workplace. These include for employers the duty to:
• Ensure that process plant is operated and maintained in a safe way so that the health and safety of employees is protected.
• Provide a monitoring and shutdown system for processes that might result in hazardous conditions.
Employees also have duties to:
• Take reasonable care of their own safety and for the safety of others.
• Avoid misusing or damaging equipment that is designed to protect people's safety.
Thus, in the design of measurement systems, due regard has to be paid to safety both in their installation and operation. Thus:
• The failure of any single component in a system should not create a dangerous situation.
• A failure which results in cable open or short circuits or short circuiting to ground should not create a dangerous situation.
• Foreseeable modes of failure should be considered for fail-safe design so that, in the event of failure, the system perhaps switches off into a safe condition.
• Systems should be easily checked and readily understood.
The main risks from electrical instrumentation are electrocution and the possibility of causing a fire or explosion as a consequence of perhaps cables or components overheating or arcing sparks occurring in an explosive atmosphere. Thus it is necessary to ensure that an individual cannot become connected between two points with a potential difference greater than about 30 V and this requires the careful design of earthing so that there is always an adequate earthing return path to operate any protective device in the event of a fault occurring.
Problems
Questions 1 to 5 have four answer options: A. B, C and D, Choose the correct answer from the answer options.
1. Decide whether each of these statements is True (T) or False (F).
Sensors in a measurement system have:
(i) An input of the variable being measured, (ii) An output of a signal in a form suitable for further processing in the measurement system.
Which option BEST describes the two statements?
A B C D
(OT(ii)T (i)T(ii)F (i)F (iOT (i)F (ii)F
2. The following lists the types of signals that occur in sequence at the various stages in a particular measurement system:
(i) Temperature
(ii) Voltage
(iii) Bigger voltage
(iv) Movement of pointer across a scale
The signal processor is the functional element in the measurement system that changes the signal from:
A (i) to (ii)
B (ii) to (iii)
C (iii) to (iv)
D (ii) to (iv)
3. Decide whether each of these statements is True (T) or False (F).
The discrepancy between the measured value of the current in an electrical circuit and the value before the measurement system, an ammeter, was inserted in the circuit is bigger the larger:
(i) The resistance of the meter,
(ii) The resistance of the circuit.
Which option BEST describes the two statements?
A B C D
(i) T (ii) T (i)T (ii)F (OF (ii)T (i)F (ii)F
4. Decide whether each of these statements is True (T) or False (F).
A highly reliable measurement system is one where there is a high chance that the system will:
(i) Require frequent calibration.
(ii) Operate to the specified level of performance.
Which option BEST describes the two statements?
A (i)T(ii)T B (i)T(ii)F C (i)F(ii)T D (i) F (ii) F
5. Decide whether each of these statements is True (T) or False (F).
A measurement system which has a lack of repeatability is one where there could be:
(i) Random fluctuations in the values given by repeated measurements of the same variable.
(ii) Fluctuations in the values obtained by repeating measurements over a number of samples.
Which option BEST describes the two statements?
A (i)T (ii)T B (i)T(ii)F C (i)F(ii)T D (i)F (ii)F
6. List and explain the functional elements of a measurement system.
7. Explain the terms (a) reliability and (b) repeatability when applied to a measurement system.
8. Explain what is meant by calibration standards having to be traceable to national standards.
9. Explain what is meant by 'fitness for purpose' when applied to a measurement system.
10. The reliability of a measurement system is said to be 0.6. What does this mean?
11. The measurement instruments used in the tool room of a company are found to have a failure rate of 0.01 per year. What does this mean?
12. Determine the sensitivity of the instruments that gave the following readings:
(a)
Load kg 0 2 4 6 8
Deflection mm 0 18 36 54 72 (b)
Temperature X 0 10 20 30 40
Voltage mV 0 0.59 1.19 1.80 2.42 (c)
Load N 0 1 2 3 4
Charge pC 0 3 6 9 12
13. Calibration of a voltmeter gave the following data.
Determine the maximum hysteresis error as a percentage of the full-scale range.
Increasing input:
Standard mV 0 1.0 2.0 3.0 4.0
Voltmeter mV 0 1.0 1.9 2.9 4.0
Decreasing input:
Standard mV 4.0 3.0 2.0 1.0 0
Voltmeter mV 4.0 3.0 2.1 1.1 0
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