Uncertainty evaluation

Uncertainty is a consequence of the unknown sign of random effects and limits to corrections for systematic effects and is therefore expressed as a quantity, i.e. an interval about the result. It is evaluated by combining a number of uncertainty components. The components are quantified either by evaluation of the results of several repeated measurements or by estimation based on data from records, previous measurements, knowledge of the equipment and experience of the measurement.

In most cases, repeated measurement results are distributed about the average in the familiar bell-shaped curve or normal distribution, in which there is a greater probability that the value lies closer to the mean than to the extremes. The evaluation from repeated measurements is done by applying a relatively simple mathematical formula. This is derived from statistical theory and the parameter that is determined is the standard deviation.

Uncertainty components quantified by means other than repeated measurements are also expressed as standard deviations, although they may not always be characterised by the normal distribution. For example, it may be possible only to estimate that the value of a quantity lies within bounds (upper and lower limits) such that there is an equal probability of it lying anywhere within those bounds. This is known as a rectangular distribution. There are simple mathematical expressions to evaluate the standard deviation for this and a number of other distributions encountered in measurement. An interesting one that is sometimes encountered, e.g. in EMC measurements, is the U-shaped distribution.

The method of combining the uncertainty components is aimed at producing a realistic rather than pessimistic combined uncertainty. This usually means working out the square root of the sum of the squares of the separate components (the root sum square method). The combined standard uncertainty may be reported as it stands (the one standard deviation level), or, usually, an expanded uncertainty is reported. This is the combined standard uncertainty multiplied by what is known as a coverage factor. The greater this factor the larger the uncertainty interval and, correspondingly, the higher the level of confidence that the value lies within that interval. For a level of confidence of approximately 95% a coverage factor of 2 is used. When reporting uncertainty it is important to indicate the coverage factor or state the level of confidence, or both.

Sector-specific guidance is still needed in several fields in order to enable laboratories to evaluate uncertainty consistently. Laboratories are being encouraged to evaluate uncertainty, even when reporting is not required; they will then be able to assess the quality of their own results and will be aware whether the result is close to any specified limit. The process of evaluation highlights those aspects of a test or calibration that produce the greatest uncertainty components, thus indicating where improvements could be beneficial. Conversely, it can be seen whether larger uncertainty contributions could be accepted from some sources without significantly increasing the overall interval. This could give the opportunity to use cheaper, less sensitive equipment or provide justification for extending calibration intervals.

Uncertainty evaluation is best done by personnel who are thoroughly familiar with the test or calibration and understand the limitations of the measuring equipment and the influences of extemal factors, e.g. environment. Records should be kept showing the assumptions that were made, e.g. concerning the distribution functions referred to above, and the sources of information for the estimation of component uncertainty values, e.g. calibration certificates, previous data, experience of the behaviour of relevant materials.

EXERCISE 1

Translate and remember the following words:

uncertainty, define, definition, defined, imperfection, perfect, fluctation, variability, variable, drift, quantity, quality, assess, assessment, access, sample, complaint, complain, evaluate, evaluation, deviation, bound, square, square root, highlight, improvements, improve, improved, prove, assumption, assume.

EXERCISE 2

Find pairs of antonyms and synonyms:

1. import

2. increase

3. obligatory

4. vendor

5. limited

6. requirement

7. help

8. constant

9. due to

10. drastically

11. advantage

12. thus

1. plus

2. facilitate

3. need

4. export

5. voluntary

6. thanks to

7. extremely

8. decrease

9. unlimited

10. customer

11. so

12. permanent

EXERCISE 3

Answer the following questions to the texts

1. What is called “measurement uncertainty”?

2. Are there any random effects influencing imperfect measurement?

3. Will the result of measurement done by few laboratories be the same on the same product?

4. What is known to be a coverage factor?

5. What is the reason of encouraging laboratories to evaluate uncertainty?

EXERCISE 4

Transform the following active sentences into passive ones

1. Nobody will know the result of the election until late tonight.

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2. The hotel staff clean the rooms thoroughly every day.

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3. They have postponed the match until next Saturday.

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4. They were raising money during the evening for charity.

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5. Someone is repairing the video at this very moment.

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6. They should have posted the parcel on Thursday.

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7. They are going to redecorate the college during the holidays.

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8. They discovered some Roman treasure in the middle of a cornfield in Sussex last week.

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