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Difference between Accuracy and Precision

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To most people, accuracy and precision mean the same thing: to someone involved in the field of instrumentation and measurement, the two terms should be considered as different. In basic mathematics, we are taught to count, but not taught to measure. One way in which this distinction is known is through the difference between a poll (a measurement) and a vote (a count). The result obtained from counting will be an exact result (barring blunder), while the result obtained from a measurement will only approach the truth. We are taught how to deal with exact numbers, but are sometimes not aware of the nature of results we obtain from approximated or measured values.
Measurement, by its nature, is not exact; the magnitude of that “inexactness” is the error. This is distinguished from a blunder, which is the introduction of an error that can be traced back to its source, and therefore an error that may be detected, quantified and corrected. A blunder is an actual mistake in the application of a measurement, such as misreading a scale or mis-adjustment of an instrument. Error is inherent in measurement, and incorporates such things as the precision of the measuring tools, their proper adjustment, and competent application. The analysis of the magnitude of probable error is appropriate in examining the suitability of methods or equipment used to obtain, portray and utilize an acceptable result.
The best way to show the difference between both the parameters is through the eyes of a marksman, to whom the “truth” represents the bullseye.
Precision
The degree of refinement in the performance of an operation, or the degree of perfection in the instruments and methods used to obtain a result is called precision. It mainly refers to an indication of the uniformity or reproducibility of a result. Precision relates to the quality of an operation by which a result is obtained, and is distinguished from accuracy, which relates to the quality of the result.

Precision
               Precision

In the figure above, the marksman has achieved a uniformity, although it is inaccurate.This uniformity may have been achieved by using a sighting scope, or some sort of stabilizing device. With the knowledge gained by observation of the results, the marksman can apply a systematic adjustment (aim lower and to the left of his intended target, or have his bow and arrow to achieve more accurate results in addition to the precision that his methodology and equipment have already attained.
Accuracy
The degree of conformity with a standard or the truth is called accuracy. Accuracy relates to the quality of a result, and is distinguished from precision, which relates to the quality of the operation by which the result is obtained. In the figur below, the marksman has approached the truth, although without great precision. It may be that the marksman will need to change the bow and arrow or skills used to obtain the result if a greater degree of precision is required, as he has reached the limitations associated with his bow and arrow and current skills.

Accuracy
                Accuracy

Th figure above represents results indicating both accuracy and precision. It differs from the first figure in that the marksman has probably made one of the systematic adjustments that was indicated by his attainment of precision without accuracy. The degree of precision has not changed greatly, but its conformity with the truth has improved over the results obtained in first figure.
If the marksman from the second figure determines that his results are not enough for the task at hand, he has no other choice than to change his current method or his bow and arrow. He has already performed to the limitations of these.
An additional benefit can be obtained by using a methodology that brings great precision. The analysis of results obtained from techniques yielding a high degree of precision will make the detection of blunders easier.

Accuracy with Precision
Accuracy with Precision

In the figures shown below, we have introduced a blunder into the results associated with accuracy and with precision. Given the degree of precision represented in the first figure below, it is easy to detect the blunder. It would be easy to analyze the results represented in the second figure shown below, and overlook the blunder. Without a high degree of precision, the blunder may go undetected and uncorrected, thereby affecting the total accuracy.

Accuracy with Blunder
Accuracy with Blunder
Precision with Blunder
Precision with Blunder

The analysis of precision can be misleading if a certain degree of precision is implied but not actually attained. To overstate an example, suppose someone were to use a vehicle odometer to measure the distance from one town to another, but measure from the last even mile (as indicated on the odometer) with a tape measure. The result could be represented with an implied precision expressed in feet, but the underlying accuracy is no better than the measurement obtained by the least precise method. It is a misleading sense of comfort that is provided when the implied precision expressed is not in agreement with actual methodology used.
In surveying, the need for greater precision usually leads to greater costs. To obtain a higher degree of precision, it may be necessary to use a more complicated/costly equipment or a more time-consuming methodology. The surveyor must determine what methodology and resultant precision is needed to achieve the accuracy required for a task at hand.

Ionization Gauge – Cold Cathode Type

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The cold cathode type ionization gauge is used to replace the hot cathode type, as it produces errors at very high temperatures of the cathode. To overcome this problem, the electrodes must be roperly treated before use. All these problems can be nullified by vacuum measurement using cold cathode ionization gauge.

A Philips and Penning cold cathode gauge is shown below. The device consists of two cathodes and a hollow anode in between. An input voltage greater than 2 Kilovolt is applied between them. A strong magnetic field is produced due to the applied voltage and thus the electrons are ejected. This causes the gauge to operate. At pressures below 10-2 Torr, the mean free path of the gas is so large that a collision may not occur at all so that discharge is not sustained or ionization may not be initiated. This problem can be eliminated by a collimating magnetic field. This is shown in the figure below.

Ionization Gauge - Cold Cathode Type
                              Ionization Gauge – Cold Cathode Type

The collimating magnetic field increases the path length for the electrons, enabling discharges possible at pressures down to about 10-5 Torr. It is difficult to obtain linearity between the meter reading and pressure as there occurs interactions between the positive ions and electrons at high electric and magnetic fields.

Ionization Gauge – Hot Cathode Type

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Ionization Gauge is a device that is used to measure vacuum. In the hot cathode type, a column of gas is introduced into which, a potential difference V is applied with free electron in the space. This causes the electron with a charge e to acquire a kinetic energy Ve. If the pressure range of the gas in the column goes below a certain limit, called the critical pressure, then corresponding to a voltage larger than the critical voltage Vc, the energy Ve may be high enough to initiate ionization, and positive ions will be produced when the electrons collide with the gas molecules.

The value of Vc is smallest for cesium (3.88V) and largest for helium (24.58V), among monoatomic gases or vapours. For diatomic gases like N2, H2 and so on, it is roughly about 15V. This is known as the ionization potential and at this potential the pressure is also important.

At very low pressures, during the intervals of time for transit from the cathode to the plate in a vacuum chamber, more than one collision is unlikely for an electron. Then for a fixed accelerating potential V>Vc, the number of positive ions formed would vary linearly with the value of pressure. Thus, a determination of the rate of production of positive ions for a given electron current should give a measure of the pressure.

Working

The construction of a hot cathode type ionization gauge consists of a basic vacuum triode. The figure of an external control type hot cathode gauge is shown below.

External Type Ionisation Gauge
                   External Type Ionisation Gauge

The grid is maintained at a large positive potential with respect to the cathode and the plate. The plate is at a negative potential with respect to the cathode. This method is also known as the external control type ionization gauge as the positive ion collector is external to the electron collector grid with reference to the cathode. The positive ions available between the grid and the cathode will be drawn by the cathode, and those between the grid and the plate will be collected by the plate.

The internal control type is shown below. Here the grid is the positive ion collector and the plate is the electron collector.

Internal Type Ionisation Gauge
Internal Type Ionisation Gauge

One of the most popularly used hot filament gauges for industrial applications is the Bayard – Alpert type filament gauge. It consists of a helical grid with a potential of +150 volts. This huge potential attracts the electrons and thus causes gas ionization. At -30 volts, the gas ions are attracted to the central ion collector, thus producing an ion current of 100mA/Torr. This value is then fed to the electronic systems to be amplified and displayed.

The hot cathode ionization gauge is useful in measuring the total pressure of all the gases present in the system. The biggest advantage of this device is its very small response time. This is because of the devices small inertia. The device is used for pressure measurement between the ranges of 10-8 to 10-3 Torr with an output current varying between 10-9 to 10-4 A.  But this range depends on the gas, other things remaining constant.

Where the pressure is higher than 10-3 Torr, the positive ions make a greater impact on the cathode to heat it up and ultimately destroy it. At pressure ranges below 10-8 Torr, in external control type, the electrons impact over the grid and radiates soft x-rays, which results in the production of electrons from the plates as secondary emission. These electrons produced will be of the same order as that of the positive ion current in the plate circuit and thus neutralizes this current. Thus the internal control type is known to be a better option to measure pressure as low as 10-9 Torr.

When the cathode remains at very temperatures (say 3000 deg C), the gaseous matters present inside may reset with the filament or with themselves particularly at different pressure stages. This may causes the device to produce wrong outputs and may also affect the cathode life. During extreme conditions of high temperatures and low pressures, the presence of any gases inside the device, will be forcefully released, thus causing the pressure to increase. Thus, the electrodes have to be properly treated before use. This can be done only by passing high currents through the electrodes, especially the filament and the grid and by high frequency heating of the plate. To overcome these problems, the cold cathode type ionization gauge is also used by many.

Alphatron Vacuum Gauge

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Alphatron is a type of cold cathode ionization gauge and can also be considered as a radioactive ionization gauge. As the cold cathode and hot cathode types earlier explained, are composition dependent, the transfer characteristics may be obtained relative to air for different gases and the system can be used as a leak detector.

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The device uses alpha particles in order to ionize the gas in the vacuum chamber. The number of ions formed in the chamber is directly proportional to the gas pressure, if the chamber dimensions are shorter than the range of alpha particles. The figure below shows the schematic diagram of an alphatron.

Alphatron Vacuum Gauge

Alphatron Vacuum Gauge

The ions produced by the alpha particles are collected by the collector electrode and a current between 10-13 and 10-9 Amperes will flow though the resistor R. The output voltage e0 is measured using a high input impedance output meter. The device has a range between 103 to 10-3 Torr.

Quartz Reference Vacuum Gauge

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A quartz reference gauge is a device used to measure vacuum. The working principle is pretty much same to that of a bourdon tube. Here, 2 bourdon tubes are used and a formed into a helix. When a pressure difference between the two occurs, the setup begins to rotate. This rotational deflection is picked up using an optical circuit as show in the figure below.

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Quartz Reference Vacuum Gauge
                                     Quartz Reference Vacuum Gauge

The reason for using quartz is that it has good spring characteristics and if the unit is kept at a constant temperature environment, the angular deflection per unit pressure is repeatable. The main disadvantage with the device is that it cannot be used as a vacuum gauge in gases with fluorine content as this erodes quartz.

The rotational deflection is connected into an electronic signal, after it passes through the optical circuit. This electronic circuit is further amplified and then the output is annulled using a servo-control system. The corresponding output is displayed by analogue techniques or counted digitally, which can be directly in pressure units. With a tachogenerator on the servomotor shaft a damping adjustment facility can be provided, if necessary. The device is known to have a resolution of 1 milliTorr for 100 milliTorr full scale reading.

Thermocouple Vacuum Gauge

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The working of a thermocouple type vacuum gauge is very similar to that of a pirani gauge. The only difference is that the hot wire temperature is measured directly with a thermocouple which is attached to a wire. For different pressures, the temperature is measured by the fine-wire thermocouple, the hating current being initially fixed by the resistance as shown in the figure. This device is usually used for comparison purposes. The sensitivity of such an instrument depends on the pressure and the wire current.

Thermocouple Type Vacuum Gauge
                        Thermocouple Type Vacuum Gauge

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The figure below shows the working of thermocouple gauges for comparison purposes. Two sets of thermocouples are used to measure temperatures of heater wires in the two chambers and oppose each other. When there is a difference in pressures, there occurs an unbalance which is measured by a potentiometer circuit. Instead of a single thermocouple per wire, a thermopile is often chosen to increase sensitivity. The thermocouple gauge is also composition dependent and needs empirical calibration for the high vacuum range.

Vacuum Comparison by Thermocouple Gauges
                   Vacuum Comparison by Thermocouple Gauges

Pirani Gauge

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A basic pirani gauge consists of a fine wire of tungsten or platinum of about 0.002 cm in diameter. This wire is mounted in a tube and then connected to the system whose vacuum is to be measured. The temperature range is around (7-400) degree Celsius and the heating current is between (10-100) mA.  A bridge circuit is also used for greater accuracy. The pirani gauge is connected as one arm of the bridge circuit. The figure is shown below. Vacuum measurement is usually taken in three ways.

  • When the pressure changes, there will be a change in current. For this, the voltage V has to be kept constant.
  • The resistance R2 of the gauge is measured, by keeping the gauge current constant.
  • The null balance of the bridge circuit is maintained by adjusting the voltage or current. This change is made with the help of a potentiometer and the change brought will be a measure of the pressure produced.

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Pirani Gauge
Pirani Gauge

An additional reference gauge can also be used in the adjacent arm of another pirani gauge, in the bridge circuit. The additional gauge is evacuated and sealed, which helps in the compensaton for variation in ambient temperature. For commercial use, the range of the instrument can be extended from 10-3 Torr to 1 Torr.

McLeod Gauge

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McLeod Gauge is a vacuum gauge that uses the same principle as that of a manometer. By using the pressure dividing technique, its range can be extended from a value of 10-4 Torr. The basic principle is called the multiple compression technique. It is shown in the figures below. If there are two bulbs A and B connected with the McLeod and test gauges through capillary tubings, the pressure on the right hand side of the test gauge is very small and the capillary connection between T and bulb B very long, then the flow law can be written as

V.dp2/dt = K.(p1-p2)

V- Volume of the bulb

dp2/dt – Pressure Gradient in time between the two elements

K – Flow conductance in the capillary.

As p2 is very small when compared to p1, the flow rate remains practically constant and is proportional to the pressure. This forms the basis of the calibration.

There are many variations of the McLeod Gauge. The basic construction is shown in the figure below.

McLeod Gauge
                                            McLeod Gauge

Working

The gauge is used to compress a small quantity of low pressure gas to produce a readable large pressure. Bulb B of the gauge is attached to capillary aa’. The mercury level in the gauge is lowered up to l1 by lowering the reservoir, thereby allowing a little process fluid to enter B. By raising the reservoir, the gas is now compressed in the capillary aa’ till mercury rises to the zero mark in the side tube and capillary bb’. The capillary bb’ is required to avoid any error due to capillary.

The McLeod gauge is independent of gas composition. If, however, the gas contains condensable material and during compression it condenses, the reading of the gauge is faulty. The gauge is not capable of continuous reading and the scale is of square law type. For linearizing the scale at comparatively higher pressures, a second volume is introduced as shown in the figure below, where the scale shown is linear.

McLeod Gauge For Linear Scale
                             McLeod Gauge For Linear Scale

Vacuum Gauge

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For pressure measurement below atmosphere or vacuum, different gauges are available. Manometers and bell gauges can go up to 0.1 Torr. Diaphragm gauges are usable up to a pressure of 10-3 Torr. For pressure below this value, electrical gauges like Pirani or Ionization Gauges are used. Vacuum measurement is broadly classified into Mechanical Type, Thermal Type, Ionization Type, and Radiation Vacuum Gauge.

Thermal Types

The heat conductivity of gases is independent of its pressure, at normal pressure. But, heat conductivity starts falling as the pressure is lowered t 10 Torr and below. The reason behind this is less collision between gas molecules within the wall and also their small number in a specific volume. The energy is carried to the walls of the container due to this collision. Thus, lesser number of molecules will be available to take the heat away from the source.

At low pressures, the heat loss that occurs from a hot wire mounted in a glass or metal tube is due to the following factors.

  • Convection
  • Conduction through the lead mines
  • Radiation
  • Conduction in the gas

Out of these, convection is comparatively negligible. A new clear wire has a small surface emissivity and is god for producing high temperature at low gas pressures. Due to oxidation and carbonization, the surface tends to deteriorate. This causes error of the device at low pressure ranges.

Optical Pressure Sensor

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Optical type pressure measurement is receiving considerable attention in recent years where the movement of a diaphragm, a bellows element or such other primary sensors are detected by optical means. The principle is nothing new, but the technique of adaptation in commercialization is varied in nature. A typical case with a diaphragm and a vane attached to it that covers and uncovers an irradiated photo diode with changing pressure is shown in the figure below.

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Optical Type Pressure Sensor                                      Optical Type Pressure Sensor

The circuit diagram shows that if any instant uncovering area of the photo diode is Am, and that of reference one is Ar, with other notations shown in the figure, the ratiometric output would be

Vf/VR = G(Am/Ar – a)

G – Span adjusted

a – Zero adjustment co-efficient

Calibration may be made directly in pressure. The ratiometric technique is often preferred for avoiding drift error in electronic components as they are likely to be equally affected and cancelled. The vane movement or the diaphragm movement is kept small for negligible hysteresis and good precision. Diode signals have non-linearities which may also vary from unit to unit. The non-linearities are often linearised using look up table in programmable read only memories during A/D conversion process. The range may be adjusted from (0-400)MPa with an accuracy of 0.1 percent scan. Temperature, though compensated, affects measurement to a certain extent which, in zero scale may be compensated by auto-zeroing facility.

This system is often used as a null detecting one in a force balance type pressure measurement, where the servo-system brings the sensor to the zero balance point.