2.2 Physical-metrological fundamentals of constructing the RUTS systemsthe RUTS systems
2.2.3 Foundations of the description of RUTS systems
2.2.3.5 Environment and boundaries of a RUTS system
As is clear from merits of case, a RUTS system is the main constituent of the system of ensuring the uniformity of measurements, which, in its turn, is the main component of the system of metrological measurement assurance, etc. However, for a more detailed (formalized) description let us consider the issue from another point of view.
Let the concept“generalized system of measurements”be the set of all measure- ments performed within some finite time interval (T) in space (P), i.e., within the limits of a definite space–time continuum (P,T). Using the presentation of a sepa- rate measurement in the form of measuring system (2.2.4), it is possible to present the
generalized system in the following form:
X
0
.P,T /D[
k
ạIzi.'k/º, Izi.'k/D
'ki,oi, i,ıi,gi,ti,ti,pi: : :jŒ'k ij,mi,si,vi,wi,: : : , 1i jạzi.'k/jº ti 2T, pi 2P, 1k jạ.'k/ºj. (2.2.16) Localizing the space–time continuum.P,T /we will pass on to the quite definite systems of measurements. So, confiningPwithin the framework of a country, we have anational system of measurements(NSM). The latter is a concept which has already been put into practice by metrology:
NSMDX
NSM
.T /. (2.2.16.1)
Let us try to formulate the conditions which would reflect the role of metrology with regard to the state of NSM, i.e., the influence that proper metrological systems (2.2.2.4) upon the NSM. Obviously, the set of measurement problems
Zi.'k/DZ.'ki,oi, i,ıi,gi,ti,ti,pi,: : :/ (2.2.17) is determined by the needs of all spheres of societal activities (science, industry, main- tenance, etc.), and it is possible to consider that practically this does not depend on pa- rameters of proper metrological systems, although as was shown below the problem of optimizing the set of measurement problems (for both the given measurand and their totality) is of current importance and can have an appreciable economic effect.
In their work (where such systems are called metrological chains or networks) the authors V. N. Sretenskiy and others consider the general character of the influence of the generalized system of measurements and proper metrological systems on the spheres indicated. For the sphere of science the availability of a strong positive feed- back is characteristic. It causes the acceleration of its development in connection with the fact that “science moves forward proportionally to the mass of knowledge inherited from the preceding generation” (F. Engels).
Metrological systems have both positive components (of development) and nega- tive (components of stability and quality) feedbacks. Therefore, here there should be an optimal relationship between the costs for metrological systems and industrial losses due to inefficiency and poor quality. Linking metrological systems with the sphere of maintenance has a pronounced negative feedback (absorption of measurement infor- mation), since the problem of supporting the stability of consumer properties (parame- ters) of operated objects is solved. Here the problem of optimization is connected with parameters of the proper metrological systems.
Thus, in all cases the influence of the proper metrological systems is reduced to the influence on the quality and efficiency of measurements performed in the NSM (and
Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 123 of theirs results). This is natural for metrology as the science of measurements and corresponding practical activity (see 2.2.4).
At the same time, there is no doubt that the main “responsibility” for proper metro- logical systems is above all to ensure the quality of measurements, since their effi- ciency has a great influence on other spheres of activity (primarily on the production of the measurement technique itself). Therefore, let us choose the quality criterion of measurements performed in the NSM as the main index of the efficiency of proper metrological operation.
Indices of measurement quality[438] are: accuracy, trustworthiness, measurement trueness, measurement repeatability and reproducibility.
Accuracy of measurementscharacterizes the closeness of a measurement result to a true value of a measurand.
Trueness of measurementsis determined by the closeness of a systematic error to zero as a consequence of measurements.
Trustworthiness of a measurement is determined by the degree of confidence in its result and is characterized by the probability of the fact that the true value of a measurand is in real value neighborhoods with indicated boundaries.
Repeatability of measurementsreflects the closeness of results of measurement of one and the same measurand (of the same dimension), carried out under similar conditions.
Reproducibilty of measurementsreflects the closeness of results of measurement of one and the same measurand carried out under different conditions (according to a method, measuring instruments being applied, conditions and observer).
The first two definitions are given in accordance with GOST 16263, the third and last two definitions were taken from [230] and [438] respectively. Let us note that the evaluation of measurement reliability is a merely mathematical maneuver using the sufficiently developed probability theory and always has to be performed in evaluating the results of measurements due to the inevitably probabilistic (random) character of measurements (measurement results and their errors). Therefore, this index cannot be applied to the number of those which are controllable from “within” a metrological system, although it is important from the point of view of customer of measurement information.
From the remaining four indices the first three (accuracy, trueness, and repeatabil- ity) are completely determined by one index, i.e., by the measurement accuracy as an integral index characterizing the closeness to zero of systematic and random compo- nents of a separate measurement error (in single and repeated observations).
From the point of view of the issue under consideration the last index of measure- ment quality, i.e., the reproducibility, from all those listed above, is much more in- teresting, since it characterizes the “collective properties” of a generalized system of
measurements (including the NSM). This index can be called the comparability of measurements (or more precisely, the comparability of measurement results) which is in our opinion a better term than the “reproducibility of measurements”, since the latter has a hint of the repeatability of a measurement problem. This contradicts the content of the concept. Hereinafter we will use the short term “comparability of mea- surements” (with the meaning given above for the term “reproducibility”).
Taking into account the above, as the basic indices of the measurement quality which is the main criterion of efficiency of the proper metrological system influence on the NSM, we chose two: accuracy and comparability of measurements. A high degree of measurement comparability can be provided at a significant systematic errorc(a deviation of measurement result, i.e., a real measurand value from a true measurand one). At the same time the valueccan known or unknown, but it must be the same in all measurements. It goes without saying that the comparability will “automatically”
increase when the accuracy of all the measurements increases. However in practice both problems are of current importance.
In Figure 2.5 an attempt is made to illustrate the relationship between the different quality indices.
Let us consider NSM (2.2.16.1) to be a closed system (without inputs and outputs).
This corresponds to the choice of a comparably short time intervalT when a set of mea- surement problemszi, as well as components needed to solve them [on the right of a vertical line in the expression forzin equation (2.2.16)] remain unchanged (constant).
Obviously, for the first stage of the description of such a large system this assumption is quite defensible.
Now it is possible to consider the formulation of conditions for providing a required level of measurement quality in the NSM for both indices of quality: accuracy and comparability.
1) Since the condition of separate measurement correctness (2.2.10), as indicated in Section 2.2.3.3, means the condition of the maximum likely closeness to a given accu- racy of measurement by way of taking into account all the measurement components of the system, then condition (2.2.10) can be used to formulate aconditionof reaching thegiven(required)measurement accuracywithin the framework of the NSM.
In a given measurement system of the NSM (see equation (2.2.16) and equation (2.2.16.1))
for any measurement problemzi.'k/(see equation (2.2.17)) there exists a set of controllable parameters of the system
Ui.'k/D.Œ'k i,mi,si,vi,wi,: : :/, (2.2.18)
as well as a volume of a priori informationIaat which the performance of condition (2.2.10) is provided.
Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 125
T2 Tn
Accuracy-1 Trueness
Trustworthiness
True value of measurand Repeatability
Reproducibility
b) a)
T1 T2...
Rn Δc
Rb
≤ R n
Figure 2.5.Illustration of the relationships of various indices of measurement quality: (a) accu- racy, trueness, repeatability, and trustworthiness of a measurement results of one measurement problem solution; (b) reproducibility and accuracy of results of a solution of various measure- ment problems, performed at a different “visible” accuracyT1> T2> T3> > Tn. In formal logic language this condition is expressed as
8zi.'k/9 i 2Ui.'k/ & Ia!.2.2.10/ (2.2.18a) It is clear that a priori information has to be related first of all to knowledge about the kinds and parameters of dependencies (2.2.9.1)–(2.2.9.7), linking parameter values of a given measurement system.
2)The measurement comparability conditionwithin the framework of the NSM is formulated in the following way. On a given setạzi.'k/ºof measurement problems in a given system of measurement at anyi ¤ j but when'kr.oi/D 'kr.oj/, there is a group of controllable system parameters such as
hŒ'ki,Œ'kj,mi,mj,si,sj,vi,vj,wi,wj,: : :i, (2.2.19)
which allows the condition to be met
'kmeas.zj/'kmeas.zi/q
ıi2Cıj2. In formal logic language this condition is expressed as 9i 2zi.'k/ANi ¤j & Œ'kr.oi/D'kr.oj/ !
8N Œ'kmeas.zj/'kmeas.zi/ q
ıi2Cıj2. (2.2.19a) Thus, a simultaneous fulfillment of conditions (2.2.18) and (2.2.19) within the framework of the general measurement systems being considered, i.e., the NSM, pro- vides a corresponding quality measurement of the NSM on the whole. This makes it necessary to speak about the necessity of having one more subsystem within the framework of the NSM. This system can be called thesystem of ensuring measure- ment quality(SEMQ). It is used to control the measurement quality in the NSM, i.e., to achieve the fulfillment of conditions (2.2.18) and (2.2.19) in this system.
Unfortunately, at this stage of metrology development the formalization of the SEMQ has not succeeded, but this does not affect the task of our investigation. An attempt has been made to determine (merely intuitively) those proper metrological systems (or more precisely, the problems) which have to be included into the SEMQ.
Here, on the basis of condition (2.2.18) it can be more definitely be said that the SEMQ has to provide the solution of the following problems (general requirements to SEMQ):
research, development and output of working measuring instruments of a needed nomenclature and accuracy, as well as of computer engineering products (the task of the instrument-making industry on the basis of an analysis of “blanks” (unsolved problems) in equation (2.2.18) for componentssi andwi);
manpower training (operators, observers) of a corresponding qualification (compo- nentvi);
development of corresponding methods of measurements (mi);
introduction of required measurand units (componentsŒ'ki/;
Undoubtedly the last three problems concern first of all the proper metrological sys- tems (to all appearance, to the system of metrological assurance SMA).
The concept “comparability of measurements” closely correlates with the concept
“uniformity of measurements”. This is confirmed by an analysis of literature data where understanding the uniformity of measurements is identified with a state of the system where a given accuracy is provided in different places, time, conditions, meth- ods, operators, and measuring instruments. In other words, it is possible to give the following initial definition.
Measurement is the state of a general system of measurements at which any two measurements of PQ, having the same dimension, carried out within the framework
Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 127 of this system, give results which do not overstep the limits of the evaluated errors of these measurements. It is therefore naturally possible to define a system of ensuring the measurements uniformity as a system that provides fulfillment of condition (2.2.19) in the system (2.2.16.1).
It is possible to say a bit more about this system (SEMU) than about the SEMQ.
First of all, measurement comparability condition (2.2.19) is not really a part of any measurement problem in the NSM. There whould be still be a need of a problem situation on ensuring the uniformity of measurements (or comparability of measure- ment results, which is the same thing). A typical (and maybe simply characteristic, i.e., determining) practical case of such a problem situation consists of the following.
Let acustomerAbe situated in a space–time continuum similar to that where the NSM is, but, having his own coordinates.Pa,Ta/, needs an object (product) “a”
characterized by a set of consumption properties (measurable indices of quality)'k.a/, k 2 .1,n/. At the same time the product (object) “a” satisfies desires (problems) of the customerAonly in the case where the values of each consumption property do not overstep the definite limits within the tolerance valuestol'k.a/at the confidence probabilityftol.'k/.
AsupplierB (manufacturer) with his own coordinates (Pb,Tb), should set up the manufacturing of product “a” with the values of indices'k.a/within the limits of the indicated (given) tolerance and confidence probability values.
Since both customerAand supplierBhave their own interests and are able to use their own set of methods and means for determining the consumption properties'k.a/
of the product, then the main problem for settling their interpersonal relations (and for the whole economy of their country) consists of achieving a guarantee which will allows the supplier and customer to obtain comparable measurement results relative to the corresponding indices'kin spite of the different ways (methods) they use for one and the same measurand'k. To achieve this means meeting condition (2.2.19).
It is clear that the system providing the measurement uniformity between the sys- temsB(the supplier) andA(the customer) has to be “external” with respect to both of them, but to belong to a common space–time continuum. It should be remarked that the described problem situation “supplier–customer” can take place between enterprises of a region or country, as well as between different countries.
From this it follows that for constructing a system of ensuring the uniformity of measurements not so much the quality of measurements carried out or the solution of measurement problems in the common system of measurements is important, as the number of interrelations “supplier–customer” for each measurable property'k, i.e., the number of problem situations in a system considered (for example, in some NSM).
From the point of view of economics this is determined by the degree of specialization and cooperation of social manufacturing.
Now let us consider the interpretation of the measurement result comparability con- dition with regard to problemszi andzj:
'meas.zj/'meas.zi/q
ıi2Cıj2 (2.2.19b) under the condition'r.zi/D'r.zj/.
In accordance with equation (2.2.8) the results of solving these problems are 'meas.zj/Dn'.zj/Œ' sj; 'meas.zi/Dn'.zj/Œ' si. (2.2.20) They correspond to the true dimensions of the unitsŒ' sjandŒ' siwhich are realized insj andsi, but which are unknown.
Observers in zi andzj believe that both of these express the results in terms of
“accepted units”Œ' 0, i.e., they have the “seeming” results
'seemmeas.zj/Dn'.zj/Œ' 0; 'seemmeas.zi/Dn'.zi/Œ' 0, (2.2.20a) the difference between which is
'seemmeas.zj/'seemmeas.zi/D ạn'.zj/n'.zi/º Œ' 0Dn'.zj,zi/Œ' 0, and it is compared withq
ı2i Cıj2, i.e., the comparison is performed according to in- dications of the corresponding measuring instruments. As to a real difference of the values, it can differ from the seeming one due to the difference between the real unit dimensions realized insi andsj and the accepted dimension:
'realmeas.zj/'measreal .zi/Dn'.zj, zi/Œ' real.
We can see this atŒ' real¤Œ' 0,'realmeas¤'seemmeas. In other words, the reproducibility (the comparability) of measurements depends on the dimension of the unit realized in measuring instruments. From this it follows that the validity of meeting condition (2.2.19) can be secured only in the case when the units in the measurement systems ziandzj being compared are similar and equal to (close to) the dimension of the unit acceptedin the given system of measurements.
This means that SEMU has to include a subsystem which would not only provide the uniformity of units (from the point of view of the dimensions realized in the measuring instruments of the generalized system of measurements) but also their compliance with conventionally accepted units (with their definition).The RUTS system plays this role in accordance with the essence that was prescribed to it earlier in Section 2.2.3.4. Thus, the following interrelation of systems has been established:
NSM$SEMQSMASEUMRUTS system. (2.2.21)