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ACTA IMEKO 
May 2014, Volume 3, Number 1, 16 – 18 
www.imeko.org 

 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 16 

The measurement chain and validation of experimental 
measurements 
R.J. Moffat 

Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States of America 

 

 

Section: RESEARCH PAPER  

Keywords: measurement chain, uncertainty propagation 

Citation: R.J. Moffat, The measurement chain and validation of experimental measurements, Acta IMEKO, vol. 3, no. 1, article 5, May 2014, identifier: 
IMEKO-ACTA-03 (2014)-01-05 

Editor: Luca Mari, Università Carlo Cattaneo 

Received May 1st, 2014; In final form May 1st, 2014; Published May 2014 

Copyright: © 2014 IMEKO. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits 
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 

 

 
An experienced human operator can often recognize an 

anomalous combination of data even upon its first occurrence, 
and may save an apparatus from a serious failure by this 
“intuition”. The human operators ability to identify trends and 
anomalies is based not only upon the instantaneous value of a 
measurand but upon its context (the other associated 
measurands including prior values). Decisions are made based 
on groups of data, some of which may even be non-quantitative 
(i.e. sound, smell, color etc.). 

The advent of automated data acquisition and computer 
control opens the door to this same type of decision making by 
a control system. Certain requirements must be met: (1) the 
measured data must accurately reflect the state of the system (2) 
the computer must “know what to expect” over the range of 
normal operation and, (3) the computer must be able to 
distinguish between allowable deviations due to experimental 
uncertainty and deviations which signify trouble. 

These are the same problems which face an experimental 
research program and it seems likely that the nomenclature and 
methodology developed for research experiments will be 
helpful in discussing measurements for computer-aided control. 
This paper presents three ideas found useful in planning 
experimental programs: (1) the nomenclature of the 
measurement chain, (2) the data reduction program considered 
as a mathematical model of the real system and, (3) the use of 

uncertainty analysis to predict the allowable scatter in an 
experimental result. 

The process of finding the numerical value of a measurand is 
illustrated in Figure 1. 

Five potentially different values exist for each measurement. 
The various terms will be illustrated in terms of  a hypothetical 
experiment: determining the exhaust gas temperature of  a small 
engine. The Principal Measurand, in this example, is Temperature; 
all other descriptors of  the system are Peripheral Measurands. The 

Figure 1. The measurement chain. 

This is a reissue of a paper which appeared in ACTA IMEKO 1973, Proceedings of the 6th Congress of the International Measurement 
Confederation, “Measurement and instrumentation”, 17-23.6.1973, Dresden, vol. 1, pp. 45–53. 
The paper witnesses the sophisticated discussion that, well before the publication of the Guide to the Expression of Uncertainty in 
Measurement (GUM), was active in the measurement science community around the subject of error and uncertainty, and its 
consequences on the structure of the measuring process and the way it is performed. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 17 

Real Value of  the principal measurand is the value the measurand 
would have if  the system were not affected by the measurement process. In 
the present example, the Real Value would be the temperature 
of  the exhaust in an uninstrumented engine, running at some 
stated speed and load. 

The Available Value is the value of  the measurand in the system, at 
the location of  the sensor, while the measurement is being taken. There 
will always be some difference between the Available Value and 
the Real Value, though It may be small, since it is impossible to 
change the state of  the sensor without also changing the state 
of  the system. In addition, the presence of  the sensor may 
cause the system to move to a new operating point, resulting in 
a still further change in the value of  the measurand. The 
Available Value is the one to which the sensor is exposed: a 
“perfect sensor” would equilibrate at the Available Value. 

In the example, the presence of  the temperature sensor in 
the exhaust duct will raise the engine back-pressure, requiring a 
slight increase in fuel flow to maintain the same nominal speed 
and load. This will result in an increase in the exhaust gas 
temperature. The Available Value will be higher than the Real 
Value for this case. 

The Achieved Value is the value the measurand has in the sensor, 
while the measurement is being made. If  the calibration of  the sensor 
were perfectly known, then this is the value which would be 
measured. Many sensors, and particularly thermal sensors, 
respond to more than one aspect of  their surroundings. These 
system/sensor interactions cause the sensor to equilibrate with 
its entire environment rather than just the principal measurand 
and gives rise to what is known as “Environmental Error”. 

In the present example the temperature sensor is subject to 
radiation error, conduction error, and velocity error. Thus the 
temperature level in the sensor (the Achieved Value) will be 
lower than the temperature of  the gas stream at the sensor 
location (the Available Value) due to system/sensor interaction. 
The difference will depend upon the velocity and composition 
of  the exhaust gases as well as the materials and temperatures 
of  the surrounding duct work and hardware. 

The Measured Value is the value which is attributed to the measurand 
when the output of  the sensor is interpreted using the best estimate of  the 
calibration of  the sensor. If  the calibration were without error the 
Measured Value would be equal to the Achieved Value. If  the 
calibration of  the sensor is affected by the conditions of  use in 
a manner which is not known to the user, then the Measured 
Value will be different from the Achieved Value. 

In the present example assume the temperature sensor to be 
a thermocouple whose elements are exposed directly to the gas 
streams. After a period of  time there may be sufficient chemical 
reaction with the exhaust gases to cause a change in the 
calibration of  the wire. Use of  standard tables of  EMF–
Temperature on such a thermocouple would result in Measured 
Values which might be significantly different from Achieved 
Values. The Corrected Value is the engineer’s best estimate of  the 
Real Value, accounting for all of  the recognized sources of  
error: system disturbance, system/sensor interactions, and 
calibration change. 

In order that experimental data properly describe the state 
of  a system, the Corrected Values must be acceptably close to 
the Real Values. Recognition of  the many ways in which 
unwanted effects can enter a measuring chain is important in 
devising systems which return valid measurements. Too often, 
principal emphasis is placed on the calibration of  the sensor 
(the link between the Achieved Value and the Measured Value). 
The state of  the instrumentation art is so well advanced now 

that, in general, the principal remaining difficulties are caused 
by the system/sensor interactions. Errors due to system/sensor 
interactions can be controlled by either of  two techniques: (1) 
design of  a system which minimizes system disturbance and 
system/sensor interactions or, (2), use of  a data processing 
program prior to the control mode which applies the required 
corrections. The data reduction program and the apparatus 
must be considered together. The data reduction program may 
require peripheral data to be gathered (i.e. wall temperature, gas 
velocity etc.) in order to properly correct the control data. This 
relationship is illustrated in Figure 2. 

Consider a general question “What is the value of  ?” A test 
apparatus and its associated data program together must 
account for all system disturbances and system sensor 
interactions with a minimum of  uncertainty. Large corrections 
tend to be uncertain, hence the system should be designed to 
minimize the disturbances and interactions. Whatever cannot be 
accomplished by the system design must be done by the data 
processor. If  the combination is properly matched then the 
corrected value will be independent of  the peripheral effects: 
they will be suppressed by the system and corrected for by the 
program. Only significant information will be passed to the 
control block. If, for instance, the temperature of  the duct walls 
decreased due to a drop in ambient air temperature, the 
increased radiation error would cause the Measured Value of  
temperature to go down, even though the Available Value of  
temperature remained constant. A properly written data 
processing program would, however, return the same Corrected 
Value, since it would properly compute the new radiation 
correction. 

One further problem remains: tolerance on the set point. 
There is an uncertainty in any physical measurement and a 
result compute from several measurements is affected by the 
uncertainty in each of  its inputs. It is desirable to be able to 
anticipate the uncertainty interval associated with a computed 
result, R, which results from the recognized uncertainty in each 
of  its inputs. This describes the interval within which the 
computed result must lie as a result of  purely random variations 
of  each of  its input variables. The uncertainty interval 
represents a “tolerance” on the computed result. For purposes 
of  uncertainty analysis, a single measurement can be regarded 
as bearing the following information: x x δx     (20/1) (1) 

where: x  is the most probable mean value of  x  which would be 

Figure 2. The experimental loop. 



 

ACTA IMEKO | www.imeko.org May 2014 | Volume 3 | Number 1 | 18 

observed if  it were measured many times x  is the presently recorded value of  one measurement of   x  δx is the interval within which the most probable mean is 
felt to lie 

(20/1) are the “odds” which the experimenter believes apply 
to the preceding statement: i.e., a measure of  confidence. 

One frequent technique for estimating the uncertainty in a 
computed result is that of  Kline and McClintock [1] which 
propagates the uncertainty at constant probability. Consider a 
result, R, computed from several variables, the x , where: (1) 
each x  is independent and (2) each x  displays a Gaussian 
distribution of  uncertainty. The uncertainty in the result is then 
given by: δR ∂R∂x1 δx1 2 ∂R∂x2 δx2 2 … ∂R∂xn δxn 2 /  (2) 

  
The computing equation R=R(x1, x2, x3, ..., xn) is the data 

reduction equation by which R is calculated from its inputs, x . 
The various partial derivatives usually have different values in 
different parts of  the operating range. The uncertainty in the 
result R is, therefore, governed sometimes by one variable and 
sometimes by another. Active computer control permits the use 
of  “variable tolerances” which are consistent with the physical 
laws governing the uncertainty. 

The principal problem which arises is: What value of  δx  
should be used? The answer depends upon the use to which the 
final result will be put. A general answer is shown in Figure 3. 

If  an uncertainty calculation is being made in order to plan a 
system then the only component of  δx  would be the 
“resolution” of  the sensor or the ability to interpolate data 
from its output (Zeroth Order Uncertainty). Any real system 
tends to have small disturbances which vary randomly with time 
(a timewise “Jitter” or unsteadiness) and different sensors have 
different dynamic characteristics and may introduce different 
phase shifts into their outputs when exposed to the same 
process stream. One way to deal with this is to treat the 
unsteadiness as an uncertainty and add its effect to that of  the 
interpolation problem (First Order Uncertainty). If  the final 
result is to be used in such a way that the absolute level would 
be important (for example by subtracting two computed results 
to determine a difference) then the uncertainties in the 
calibrations must be included (Nth Order Uncertainty). 

With the use of  uncertainty propagation it becomes possible 

to set floating limits on the control variables to account for the 
changing sensitivity of  the process to its variables. 

SUMMARY 

In many respects, the advent of computer based control 
brings closer together the areas of measurement for research 
and measurement for control. If computer control is carried to 
its logical end, the control function should be preceded by a 
data reduction program which corrects for the disturbance 
effect of the sensor, and all of the recognized interactions 
between the system and the sensors. A data reduction program 
which completely models the behavior of the system will return 
correct measurement data to the control unit, regardless of the 
peripheral conditions on the system. Development of the data 
reduction program should complement and accompany the 
development of the hardware system. Uncertainties in the 
measured data will cause uncertainties in the computed result. 
This requires establishment of “tolerances” on the control 
parameters. Uncertainty analysis techniques based on constant 
probability propagation provide a rational basis for establishing 
limits for acceptable excursions. 

REFERENCES 

[1] S.J. Kline, F.A. McClintock, “Describing Uncertainties in Single 
Sample Experiments” Mechanical Engineering, January, 1953. 
 

 

Figure 3. The levels of uncertainty analysis.