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Appendix B Discussion on accuracy of measurement

The basic causes of inaccuracies in the measurement of physical properties by sensors are the physical characteristics of the sensors and signal conditioners themselves, especially with respect to manufacturing tolerances and changes of characteristics of usage and time, and by any mechanical or electrical connections that are present

Some vocabulary for measurement and error should be clarified before an error analysis is considered.

All errors can be classified into two categories according to their performances:

systematic error and random error. If the quantity and direction of errors in the process concerned are fixed or vary according to a specific rule, these errors are called systematic errors. Furthermore, if the quantity and direction of the errors are fixed, they are called constant systematic errors, such as zero offset of an instrument Whereas if the systematic errors vary in the process, for example, zero drift of an instrument, they are called variable systematic errors. O n the other hand, if the quantity and direction of all the errors d o not agree exactly, these errors are called random error. T h e total error is the standard s u m of systematic error and random error and can be written in the following form,

e = ule T e

total \/ system random

where, e


is the total error of a measurement system


system *

s m e

systematic error

Appendices 188

erandom k m e random error

Accuracy is the closeness of measurement value to the true value. If an experiment has small systematic error, it is said to have high accuracy. Precision is the closeness of grouping of measurement values. If an experiment has small random error, it is said to have high precision.

Accuracy describes the amount of systematic error or the bias of measurement value distribution. It is usually denoted to be the difference between the measurement value and the "true" value which is always an average value of a large number of samples in practice. Precision describes the amount of random error, or measurement value dispersion, or sometimes is called estimated uncertainty. It is usually denoted to be the standard deviation or precision index.

Accuracy and precision are obviously different concepts. A measurement may be accurate but not precise, while another measurement m a y be precise but not accurate.

Systematic error mainly comes from,

calibrating error

experimental condition which is different from calibration condition imperfect technique or measurement theoretic error

h u m a n error

R a n d o m error mainly c o m e s from,

A p p e n d i c e s 1 g 9 error of judgement

fluctuating experimental condition

small disturbance of mechanical and electrical system

It is very difficult to decrease the random error. The only way is to enhance the performance of measurement system and improve the measurement condition. In the past years, there have been m a n y improvements in sensor design and manufacturing technology along with the development of various techniques to reduce these errors.

These methods are expensive because additional special electronic circuits are needed and each circuit is usually designed for only one class of sensors. A n d these methods generally have been limited to a certain extent by current technology. Systematic error, on the other hand, m a y be decreased by suitable methods, because it either remains constant or varies according to a rule. T h e normal w a y to eliminate the constant systematic error is the opposite offset or zero-adjustment before using system. Regular opposite offset in the process of running the system is a c o m m o n w a y to decrease the variable systematic error, in which s o m e subsidiary hardware and software will be needed.

In the measurement and control system based on microcomputer where the output of the sensors will be transferred into a computer, digital table calibrating method and its combination with regular on-line zero offset correction is a good method to obtain the accurate values of physical properties.

For dial indicator instrument, non-linearity is a systematic error, which is a typical imperfect technique error. M u c h w o r k has been done in the past to improve the linearity of sensor, amplifier and instrument, since the relationship between the physical value and the sensing value is usually not linear. But non-linearity is not a factor to influence the

A p p e n d i c e s 1 9 0 measurement accuracy in computer based measurement system. H u m a n error is not a

factor of measurement accuracy, either. And regular on-line zero offset correction can also minimise the error caused by a difference of experimental conditions. The important factors for this kind of system are the sensitivity and the stability of the measurement system which cause random error.

Application of A/D converter introduces quantisation error, which is generally determined by the bit of A/D. For example, the error for 8-bit A/D converter is ±0.2%, and the error for 12-bit A/D converter is ±0.012%. High bit A/D converter is much more expensive

than low bit A/D converter. So, the bit of A/D converter should be low upon the

permission of accuracy. The bit of A/D can be selected to guarantee the quantisation error less than one third to one fifth of the random error. Then, the quantisation error will influence the measurement very slightly according to Equation A.l.

For example, if the quantisation error is 1/3 of the random error, the total error will be,

V 2 , 2

e quantisation + e random

= ^J(|)





= 105.4% e random

therefore the quantisation error only increases 5 . 4 % of the total error. If the quantisation error is 1/4 of the random error, the total error will increase 3.1%, while if the

quantisation error is 1/5 of the random error, the total error will increase 2.0%. So, one third to one fifth of the random error is the most economic value for additional error including quantisation error.

A p p e n d i c e s