Measurement: Past,Present and Future: Part 1 Measurement History and Fundamentals

Abstract

In this article, the importance of measurement and measurement fundamentals is briefly discussed. Measurement helped our ancestors of several million years ago to develop skills to survive, then in relatively recent times to obtain the knowledge for scientific endeavour and to industrialise and very recently still to introduce automatic control and to underpin innovation. The basis of measurement scales and measurement standards has often changed, and now, there are agreed means for estimating measurement uncertainty and stating measurement accuracy with a given confidence. Measurement now has a solid basis in theory and practice and has developed into a systematic discipline.

I. The Measurement Hand Maiden

‘Measurement began our might’ wrote the poet W.B. Yeats. If anything separates humans from the animal kingdom, it is the quantitative approach to conceptualising the world around us. Of course, it has not been modern science, electronics, computers, television or mobile phones that have made the fundamental difference, but the use the body shape of Homo sapiens. It is not really the relatively big human brain that did it, but our hands and feet that got us here. Human hands provided a means for measurement.

A measuring instrument extends our sensing and becomes the ‘primary observer’, normally at one or two points in space and at one point in time. At this and other points, in space and at other times, the numbers will always be different, whether this is indicated by the particular measuring instrument output or not. The particular observation will catch a momentary difference-points value or a single-point value of what we may think we are interested in but also probably combined with what we are not perhaps conscious of or indeed interested in. We call the quantities being measured as measurands.

Nobody can actually define the material world. In sub-atomic cases, we might first observe a wave and then a particle depending on the measuring instrument used. Also, we now know that our current measurement methods only allow us to ‘see’ about 4% of physical reality – matter and energy – in the cosmos. The rest is ‘dark’ to us. Therefore, really very small and really very big things seem to be outside the human realm – a humbling thought indeed for the scientific priesthood!

Also, we can often forget that the instrument itself will normally make a contribution to what we observe. It may directly affect the quantity observed, and it may itself restrict and contaminate the result because of design and construction inadequacies. The human observer of the result or the following equipment using the result may also restrict and contaminate the result.

How we see the world in our conscious being and our understanding of nature itself have become intertwined with our measuring instruments, although we often forget this. Some 3500 years ago, the Israelite leader Moses commanded the people to ‘use true and honest weights and measures’. Later, prophets Ezekiel and Zechariah had visions of the new Jerusalem, which included tape-measure, measuring rod and measuring line. Later still, the Qur’an gave verses ‘Woe to those who give less [than due], who, when they take a measure from people, take in full, but, if they give by measure or weight to them, they cause loss’. In 1196, during the reign of Richard the Lionheart in Britain, The Assize of Measures stated that ‘Throughout the realm there shall be the same yard of the same size and it should be of iron’. The Constitution of the United States in 1789 stated that ‘The Congress shall have the power … to fix the standard of weights and measures’. Good and fair measurement was at the core of these societies, and so it had been in earlier and later societies.

Measurement can be understood as the hand-maiden of Homo sapiens. Failure to make good measurements and then to learn how to respond wisely to what we understand about them is to quickly move down a path of unfairness, declining economic prosperity, reduction in quality of life, social chaos and eventual society decline.

II. Forest to Civilisation

Several million years ago, the Earth’s climate devastated the forests of central Africa and some of our long-lost predecessors survived through a by-chance big change in their behaviour. Survival was more likely if they came down from swinging in the trees, where they used their hands, arms, feet and legs to hang and move, and instead stood upright and used their legs to run after prey on the grassy savannah. Now by good fortune, they had hands free to collect berries and fruits, to hold spears and to distribute fruits, nuts, meat, bones and skins. But how to distribute among the group so as to keep them working together to help survival?

From handfuls, to hand size, finger numbers and widths and arm and foot lengths, it seems most likely that the path of measurement and numbers began. Certain spear head shapes and spear lengths were found to be better than others. It was better to pass-on the information by mouthing noises and eventually speaking and making pictures and symbols, and therefore, eventually, Homo sapiens arrived and became different, developed, flourished and conquered.

The hand of an African man is shown in Figure 1 . Aristotle characterised the human hand ‘as an instrument that represents many instruments’. Erasmus Darwin, the grandfather of Charles Darwin, expressed, in verse, ‘The hand, first gift of Heaven! To man belongs’.

Figure 1.

Hand of an African man illustrating the early means for measurement by Homo sapiens

Practical skills and intuition drove inquisitiveness and helped conceptualisation and experimentation. Eventually, reasoning helped to provide explanation and knowledge to pass-on through the generations. At all stages, measurement was critical. And the rest is human civilisation. The relatively recent science endeavour has been built on the cornerstone of measurement, and more recently, measurement has allowed automatic control of machinery and processes to become possible. No automatic control can be better than the measuring instruments used, and most measurements are not used for automatic control purposes at all. Indeed, measurement is ubiquitous.

The importance of measurement was well understood by the song writer of this chorus:

Then swell the chorus heartily, Let ev’ry Saxon sing,

‘A pint’s a pound the world around’, Till all the earth shall sing;

‘A pint’s a pound the world around’, For rich and poor the same:

Just measure and a perfect weight, Call’d by their ancient name.

No science, microelectronics, computers, televisions, mobile phones, Internet operation, automobiles, ships, aircraft – no trust in business, fair trading and global economic progress – no advanced manufacturing, product quality control, process condition monitoring or industrial plant preventative maintenance – no non-destructive testing of materials – no improvements to health or the environment are possible without good and improving measurement and the underpinning world of better measurement standards and global traceable measurements.

Yet, this underpinning world is little known to the average citizen, business manager, company executive or political leader. There are plenty of science, technology, engineering and mathematics (STEM) students, engineers and technologists who fail the test of good measurement knowledge and skills. Indeed, people with good measurement knowledge and skills are relatively rare. However, a great deal depends upon them.

III. Good Measurement Knowledge and Practical Skills

But what is good Measurement Knowledge and what are good Measurement Skills one may ask?

Let us remember that a measurement appears to be simply a number. Therefore, we must ask, does this number mean anything? Well it will only mean anything at all if we are careful in how we obtained the number and if the number is specified as probably being within a range of numbers with a given degree of confidence. The numbers usually have units of measurement, they relate to a scale of numbers, and there is a beginning point to the scale of numbers. Some physical quantities can be reliably recreated, and therefore, they can be used as defined points for a scale of numbers for the particular quantity. It is desirable for the scale of numbers to have a direct proportionality to the quantity.

Choosing a useful measurement scale for a given quantity is not as easy as it might appear at first. Take, for example, the well-known measurement scale for earthquakes. Charles Richter (1900–85) gave his name to a scale of 0–10 and above, where magnitude zero is defined as an earthquake 100 km from a seismometer (measuring movement amplitude) that produces a maximum peak of 1 µm. The units are dimensionless, and the scale has to be logarithmic to accommodate the range of movements. Nonetheless, today, it is found to be better to use a modern intensity-based scale (details published in 1998), the European Macroseismic Scale, as this tells one more about earthquake energy and likely damage.

A measure then, put most simply, is a standard or mark against which we gauge or evaluate something. It is the result of a human decision on how to quantify things to provide information to share. One person may quantify something one way, while another person may choose to quantify the same thing in a different way. Humans and measuring are integral, and it was found to be a good idea to get agreement on how to quantify things, so people could interact in a sensible and profitable way. The need for measurement ‘standards’ was to provide stability, not necessarily precision or accuracy. Measurement ‘standards’ used throughout human history have gone through three stages of development: improvised body measures, disconnected artefacts and physical constants.

If individuals are not careful when taking a measure, and if the measurement number is not carefully qualified in regard to the conditions under which it was taken, then the number may be quite useless. There are plenty of examples of useless measurements. Some of these useless measurements have been made by eminent scientists, engineers and technologists and not just by students in learning and training.

A. The Clock

Let us consider an example of a good measurement. The marine chronometer invented by a self-taught clockmaker, John Harrison, in 1761 lost just 5 s when it travelled by a ship between England and Jamaica and resulted in safe long-distance travel.

It is now planned that by the year 2020, European satellite navigation will be improved by the use of 30 Galileo satellites in orbit above the Earth, each with the most accurate atomic clocks on any spacecraft. The best of these clocks have stability such that they will lose only 1 s in 3 million years. This high level of stability is needed since an error of only a few nanoseconds would produce a positioning error of metres. Such clocks are based on frequency standards.

How do we know this uncertainty (and so called accuracy)? Because there are primary standard atomic clocks in national measurement institutes across the globe for inter-comparison and calibration purposes, and uncertainty of measurement for the satellite atomic clocks has been determined to give us confidence in their time measurement results. If, by chance, these atomic clock standards are lost to the Earth, provided some knowledgeable and skilful measurement experts remain, the standards can be recreated to provide exactly the same timing.

It would seem that measurement experts have now become more important than measurement artefacts and as important as natural constants! This is rather sad because measurement science at one time was understood, at least in a general way, by mostly everybody in daily life, while now it has largely become the realm of unknown experts.

The current national primary standard atomic clocks have an extremely low level of uncertainty of about 1 s in 30 million years. This is an uncertainty of about 1 part in 10 to the order 14, or of about 1 ns per day. In 2012, the UK National Physical Laboratory (NPL) confirmed German findings that by using the ytterbium ion for frequency measurement, the uncertainty level for atomic clocks can be 20 times better than is the current situation with the caesium atomic clock.

B. Uncertainty of Measurement

All measuring instruments and measuring systems experience sources of error, both systematic and random. The former should be removed or estimated, but often, there is an unknown fixed or slowly drifting contribution to the final measurement result. The random uncertainty has to be stated in terms of probability using a specified confidence level. The probable range of values within which the true value lies is stated as a range of values for a given confidence level. In fact, a single measurement result gives us the likely value with a degree of uncertainty at a specified level of confidence.

The real questions are these: Is the measurement result just adequate for the purposes required? is it inadequate for the purposes required? or is it far too precise, of too great an accuracy, and therefore, probably far too costly for the purposes required?

The natural environment normally varies and is uncertain, but, at least, we can gain some confidence in how to specify it with one or more numbers. Measurement can be a risky business, and by no means does it fully determine our living environment. However, it can be a good estimate and therefore useful if we are careful! All good measurement practitioners are suspicious observers because they know that a good measurement result is difficult to obtain and to repeat.

A good explanation of the concept of uncertainty – or the complexity of the world – was given by Donald Rumsfield, the US Defence Secretary in 2002 regarding the situation in Afghanistan:

There are known knowns. There are things we know that we know. There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. These are things we do not know we don’t know.

C. Measurement Caution and Confidence

It is unwise to undertake measurements when you have no idea at all how the measuring instrument or measurement system works or some idea of what measurement result to expect. But you can transfer this obligation to another person, for example, a public trading standards officer who confirms that the measuring instrument meets certain required standards of performance when used in the correct way in defined conditions. Next time, at the fuel pump, look for the certified statement. You could be cheated of lots of money if the fuel quantity gauge has been tampered with by the garage retailer.

Measurement affects our pockets every day. Most of our money is given away on the basis of our believing in the fidelity of measuring instruments – if we care to think about these things at all! Business and product and services trading have always suffered from those who set out to overprice, produce shoddy goods or services and cheat customers. Therefore, there is a ubiquitous need for our protection by statutory and measuring instruments as well as real competition between suppliers.

Manufacturers of measurement instruments are keen to convince us of the confidence we can have in the numbers their instruments generate. Often, this confidence is fully justified, but unfortunately, sometimes, the manufacturers unfairly play the instrument specification game to gain market share or increase price. Thus, authorised and independent calibration and testing services are essential so that authorised instrument certificates are provided. This process increases the costs of measurement, but without it, measurement quickly becomes crude and almost arbitrary monitoring. Many manufacturing and process companies still use such monitoring, but the quality of their goods are in doubt. Quality control and quality assurance are based on proper measurement requiring measurement standards and traceability.

D. Measurement Traceability

Today, international trading is only possible because the planet has a multitude of measurement standards throughout the world and worldwide measurement traceability. For example, the basic metre standard maintained in the United Kingdom is the same length as the basic metre standard maintained in Germany, China, India and the United States to an absolute uncertainty of 0.1 nm. Each country transfers this length to calibration laboratories and manufacturing sites throughout its own territory. During each transfer down a measurement distribution chain, the uncertainty of measurement for the transferred metre increases by approximately 5–10 times as shown in Table 1 . Thus, handheld 25-mm-range micrometers with digital readouts used, for example, in workshops in the United Kingdom, Germany, China, India and the United States, can all measure absolute length with the same uncertainty of ±0.002 mm even though the micrometers may be manufactured and calibrated in these countries.

Table 1.

A typical measurement traceability chain showing magnitudes of measurement uncertainty

Mechanical components made in different countries will now fit together, and therefore, automobile parts and sections of an aircraft can be made almost anywhere around the globe. Thus, in large part, the national and international measurement systems are responsible for open markets and globalisation of trade. As a consequence, global capitalism has been confident to invest and international trade has massively expanded.

E. Measurement Base Standards

Early standard weights are shown in Figure 2 , while the basis of the definition of the metre length is shown in Table 2 .

Figure 2.

Cubic weights made of stone from the Indus Valley Civilisation 4000 years ago. Weight ratios: 1 to 2 to 4 to 8 and so on. They are still in use in traditional markets in Pakistan and India

Table 2.

Basis of the definition of the metre length from the year 1791 to the present time

There always seems to be a demand in existing measurement applications for greater measurement precision and measurement accuracy, and lower levels of measurement uncertainty. In addition, there are requirements in new applications and also for new kinds of measurement. For all these reasons, it may well be that improved and/or new basic national standards are needed. However, these can take 10–20 years or more to develop and for them to be agreed upon and then be implemented by the international metrology community. Fundamental metrology requires a high degree of forward planning to seek to meet the likely measurement needs in the future. Only governments in partnership with industry and universities and through international collaborations can provide such forward thinking and the required actions.

Major basic science metrology programmes are funded in national measurement laboratories such as the NPL in the United Kingdom, National Institute of Standards and Technology (NIST) in the United States and Physikalisch Technische Bundesanstalt (PTB) in Germany. The scientists cooperate through international metrology organisations and determine when appropriate new basic measurement standards are ready to be introduced. This can result in an actual change in the value of a defined measurement quantity. For example, some years ago, the electrical volt changed its value at the microvolt level.

Why should the value of these basic measurement quantities change? The reason is to allow use of highly stable natural constants that can be determined independently, in principle, anywhere at any time. Also, sometimes, it may prove easier to make measurement determinations in the national measurement institutes. The current definition and the proposed future definition of the International System of Measurement Units (the SI System) are given in Table 3 .

Table 3.

Definition of basic measurement quantities for the current SI units and the proposed new SI units

F. A Good Measurement

What might a typical measurement look like? As a simple example, we take the case of the length of a metal bar of nominal length 140 mm. Poor measurement might give a result as 140 mm (a single number), while the good measurement (taken using a recently calibrated length gauge) might give a result as 140.51 ± 0.02 mm for k = 2 at normal room temperature, that is, in the format as follows: (number ± uncertainty) units with 95% confidence at 20 °C (where k is the level of confidence). Poor measurement could be very misleading, while the good measurement is a ‘best available’ single value, because there is no absolute single value.

Measurement therefore deals with uncertainty in the number and provides a degree of confidence in the number for defined conditions. In fact, the measurement result states a range of values in which the true value probably existed at the time and place it was taken. Different confidence levels can be stated, and the higher the confidence level, the greater the range specified in which the true value probably existed.

In the case of ‘static’ quantities, the dynamic response of the instrument can be restricted so as to smooth-out noisy variations, while period of measurement can be increased to improve measurement confidence by quickly taking a series of readings to average out some of the ‘noisy’ random uncertainty. The majority of measurement signals have frequency components in the bandwidth 0–1 kHz. It is the near zero and direct current (DC) levels in which offsets occur.

IV. Measurement Accuracy

Users require that measurement equipment provide reliable performance over long periods of time and that readings for a fixed input be stable and repeatable. They also look for a degree of ‘accuracy’.

The idea of ‘accuracy’ of a measurement result has always been somewhat misleading, for it tends towards creation of over-confidence in a result (no doubt intended by the instrument manufacturer!). The single accuracy number for a measurement system is supposed to be a ‘catch-all’ of all the different actual causes of measurement uncertainty by use of a single ‘non-measured’ number. A measurement result is usually given in terms of the number with a single specified uncertainty at a given confidence level. This uncertainty contains contributions from many sources. Manufacturers of measurement instruments and measurement systems like to talk of measurement ‘confidence’ as it sounds rather more comforting than talking about measurement ‘error’ or measurement ‘uncertainty’!

A. Precision and Accuracy

Plenty of people believe that high measurement precision means high accuracy. However, the truth is that a measurement result can be highly precise and wholly inaccurate. The precision takes no account of the systematic errors such as offsets created within the measuring instrument. Temperature is the great opponent of good non-temperature measurement because almost all mechanical and electrical components are temperature sensitive to a greater or lesser degree.

B. Interference and Noise Signals

Some measuring instruments and measurement systems can also suffer from other quantities, such as humidity, vibration, magnetic and electromagnetic interference quantities, not least at electrical mains frequencies. The magnitude of the quantity to be measured can affect the uncertainty of measurement. It is never a good idea to rely on the bottom third of a measurement scale. Instrument protection for off-scale readings is always desirable. Whether the quantity is increasing or decreasing may affect the uncertainty of measurement. Changing measurement quantities contain frequency content, and therefore, frequency bandwidth of the measurement system is important, particularly the phase characteristic. Waveform distortion caused by a measurement system has fooled many people!

The sensors at the front end of many measurement systems often only produce very small analogue electrical signals at millivolt and microvolt magnitudes, and therefore, it is difficult to design instrumentation to avoid the effects of interference signals. Electrical ground loops pick up electromagnetic mains frequency signals; therefore, they must be avoided. Electrostatic field screening and magnetic field shielding may be essential. Electrical circuit low resistance values reduce pickup and resistance noise but increase power consumption.

Unfortunately, at normal temperatures, electrical circuits and electronic devices create electrical noise mostly of a random kind; therefore, the ratio of the magnitude of the measurement signal to the magnitude of the total interference/noise signal is of significant concern in measurement. The smallest change in the measurement signal that can be observed is taken to be the magnitude of this interference/noise.

Therefore, if the measurement full-scale signal has a magnitude of 1 mV, for a measurement resolution of 1 in 1000 (0.1% of the full-scale reading), the interference/noise magnitude should not be more than 1 µV rms. If the measurement signal is at a fifth of the full-scale value, 200 µV rms, for a resolution of 1 in a 1000 at this value, the interference/noise should not be more than 200 nV rms. At room temperature for typical instrumentation-type electronic components and frequency bandwidths, the random noise level would be below this value.

If 1 in 10,000 resolution is required (0.01% of reading), then at one-fifth of the full-scale reading, the interference/noise should not be more than 20 nV rms. The random noise level in the instrumentation electronics might well be higher than this. Accuracy of 0.01% at one-fifth of full-scale requires DC drift to be not more than 0.2 nV rms/°C for operation in a 100 °C temperature range. Instrumentation amplifiers have differential inputs with high common mode rejection ratios to reject common voltages such as DC and interference pickup on the two input terminals. The differential signal is the measurement signal.

C. Other Issues

It should be obvious why high measurement precision and high measurement accuracy are difficult to obtain and why measurement requires specialist design skills and why high-quality instrumentation becomes expensive!

Before applying measuring apparatus in new applications, particularly if digital instrumentation is to be used, it is wise to take a visual observation of the raw analogue signals using an oscilloscope instrument. Measurement instrumentation can give ‘silly’ results if the measuring signals are not typical of the signals used to calibrate the instrumentation.

In general, digital instrumentation using microelectronic analogue-to-digital converters, microcomputer chips and software programmes can lead to reduction of uncertainty (particularly systematic uncertainty) in the observed measurement number, if care is taken, although digitisation itself does add uncertainties. Nonetheless, plenty of people get over-confident and can be fooled into a sense of measurement security because they can easily read-off from digital displays!

If the quantity to be measured inputs to the measuring system as events, frequency, phase or timing variations or in digital format, this can have advantages over the information coming into the measuring system in the form of amplitude variations. Amplitude signals can be converted to the other formats or, for example, be used to modulate frequency carriers.

Notwithstanding all these problems, it is possible to make good measurement with adequate precision and adequate accuracy!

V. Conclusion

Knowledge and automatic control require measurement, and therefore, measurement concerns are fundamental to all aspects of human life. The enthusiast sees measurement as the ‘spirit of science, engineering and technology’ and as such, to be studied and practised widely in a diligent manner. The subject of measurement has a solid basis in theory and practice and during the past 30 years has developed into a systematic discipline.

It is evident that reliable monitoring, accurate measurement and long-term stability of a measuring instrument or measurement system do not come easily. Good instrumentation design is essential particularly at the sensory input where there is primary transduction and low-signal level, and this will be discussed more fully in the second article of this themed issue (Part 2).

Arguably, the most important measurements that mankind has ever made are those of the amount of carbon dioxide in the Earth’s atmosphere. These measurements continue to show a dramatic increase in magnitude of this atmospheric gas as shown in Figure 3 , and dire consequences for our species could follow.

Figure 3.

Measured growth in carbon dioxide in the Earth’s atmosphere from the year 1980 to the year 2000

Our very early ancestors and then later Homo sapiens developed on planet Earth over long periods of time, partly as a consequence of using essential measurement skills, but could now easily disappear from the planet in a relatively short time by ignoring crucial measurement knowledge.