Measurement is the process of comparison between the unknown physical quantity to its predefined standard so as to find the value of unknown physical quantity. The measurement is said to be less erroneous if measured value is closed to the true value of the system. To make the error-free measurement, the user must know the characteristics and operation of instruments, basic laws to handle the instrument and cause of errors in measurement. Hence , in the theory of measurement, we are studying about the characteristics of the instrumental error and its analysis, statistical analysis of error and minimization of error etc.
The performance characteristics of an instrument can be divided into two distinct categories as:
The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant i.e. do not vary with time, is called Static characteristics.
The various static characteristics are
xii) Range or span
It is the degree of closeness with which the reading approaches the true value of the quantity to be measured. The accuracy can be expressed in following ways:
a) Point accuracy:
Such accuracy is specified at only one particular point of the scale.
It does not give any information about the accuracy at any other Point on the scale.
b) Accuracy as percentage of scale span:
When an instrument as uniform scale, its accuracy may be expressed in terms of scale range.
c) Accuracy as percentage of true value:
The best way to conceive the idea of accuracy is to specify it in
terms of the true value of the quantity being measured.
It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. The precision is composed of two characteristics.
Consider a resistor having true value as 2385692 , which is being measured by an ohmmeter. But the reader can read consistently, a value as 2.4 M due to the non availability of proper scale. The error created due to the limitation of the scale reading is a precision error.
b) Number of significant figures:
The precision of the measurement is obtained from the number of significant figures, in which the reading is expressed. The significant figures convey the actual information about the magnitude & the measurement precision of the quantity. The precision can be mathematically expressed as:
Where, P = precision
Xn = Value of nth measurement
Xn = Average value the set of measurement values
The sensitivity denotes the smallest change in the measured variable to which the instrument responds. It is defined as the ratio of the changes in the output of an instrument to a change in the value of the quantity to be measured. Mathematically it is expressed as,
Thus, if the calibration curve is linear, as shown, the sensitivity of the instrument is the slope of the calibration curve. If the calibration curve is not linear as shown, then the sensitivity varies with the input. Inverse sensitivity or deflection factor is defined as the reciprocal of sensitivity. Inverse sensitivity or deflection factor = 1/ sensitivity = Δqi/Δqo.
It is defined as the ability to reproduce the input characteristics symmetrically and linearly. The curve shows the actual calibration curve and idealized straight line.
It is the degree of closeness with which a given value may be repeatedly measured. It is specified in terms of scale readings over a given period of time.
It is defined as the variation of scale reading & random in nature Drift:
Drift may be classified into three categories:
a) zero drift:
If the whole calibration gradually shifts due to slippage, permanent set, or due to undue warming up of electronic tube circuits, zero drift sets in.
b) span drift or sensitivity drift
If there is a proportional change in the indication all along the upward scale, the drifts are called span drift or sensitivity drift.
c) Zonal drift:
In case the drift occurs only a portion of the span of an instrument,it is called zonal drift.
If the input is slowly increased from some arbitrary input value, it will again be found that output does not change at all until a certain increment is exceeded. This increment is called resolution.
If the instrument input is increased very gradually from zero there will be some minimum value below which no output change can be detected. This minimum value defines the threshold of the instrument.
It is the ability of an instrument to retain its performance throughout is
specified operating life.
The maximum allowable error in the measurement is specified in terms of some value which is called tolerance.
The minimum & maximum values of a quantity for which an instrument is designed to measure is called its range or span.
1.S.morris.alan(2001). Measurement and Instrument principle(3 ed.).A division of Reed Educational and Professional Publishing Ltd
2.nderson, Norman A. (1998). Instrumentation for Process Measurement and Control (3 ed.). CRC Press.