General principles and an algorithm for constructing RUTS systems

2.2 Physical-metrological fundamentals of constructing the RUTS systemsthe RUTS systems

2.2.4 Fundamentals of constructing a RUTS system

2.2.4.3 General principles and an algorithm for constructing RUTS systems

In view of the huge volume of initial data and the complexity of the general structure of the RUTS system, a solution to the problem of constructing this system in a general form is not possible. It should be taken into account that a large part of the initial data, as a rule, is either entirely absent or known to have a significant degree of uncertainty (inaccuracy), which for a multifactor problem can reduce to zero the efforts spent to solve it.

Therefore, it is useful to choose principles and methods which allow a real effect from the fairly general approach suggested here.

The principle of successive approximationis the most natural. Some assumptions, i.e., restrictions, which simplify the problem and decrease its dimension, are succes- sively introduced.

In the case given the method of ranking and gradationhas to be efficient. In the system there are selected separate blocks (subsystems) or classes (groups) of prob- lems which are ranked according to both their degree of generality and algorithmic sequence, and then theprinciple of stage solutionis realized, i.e., the sequence of the problem solution “by parts” is determined.

At last, for solving the problems of such a kind it is efficient to use the “shuttle method”, i.e., a repeated solution of direct and inverse problems, verification of solu- tions by several “cuts”.

On the basis of these principles we offer a scheme and algorithm of problem solu- tion for theoretical constructing the total RUTS system.

At the first stagethe problem of constructing a system in a “bottom-up” manner is solved. At the same time the system is disjoined into subsystems connected with the definite measurand', and the problems are solved for each particular subsystem P

RUTS.'/, i.e., the “'i problems”.

In these problems the concept “chain of transferring” a unit dimension, i.e., the chain of subsequent elements of the system (means of transferring the dimensionSn), connecting reference metrological measuring instrument of the system with some def- inite group (some type) of working measuring instruments (see Figure 2.4). The use of the graph theory apparatus for formalizing the connections between the adjacent levels can appear to be useful here.

The algorithm of the “problem'i” solution consists of the following.

1) Initial data (see Section 2.2.4.2) for the given measurand 'i are grouped into blocks and “tied to” the WMI typeSpi. At the same time it is assumed that the nomen- clature (types) of working measuring instruments has been optimized earlier according to measurement problems.

2) Types of working measuring instruments are grouped in accordance with the accuracySp.ı1/,Sp.ı2/,: : :,Sp.ım/, and

ı1> ı2> > ım. (2.2.26) Ranking the working measuring instruments according to their accuracy is performed for two reasons: firstly, because the goal of the RUTS system is the maximum approx- imation of a real unit dimension of working measuring instruments to an ideal one (according to the definition). This is achieved above all at the expense of measure- ment accuracy. Secondly, among the remaining parameters of WMI only the range of measurements is essential for constructing a system. It is quite correct to assume that the influence of other parameters (above all the conditions of measurements) on the accuracy of working measuring instruments is foreseen by a normative document. As to the measurement range of a particular working measuring instrument, its ranking

Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 135 takes place “automatically”, while the working measuring instruments are subjected to the accuracy ranking procedure. This follows from the most general ideas about in- formation (or resolution) capability of these instruments. The measuring instruments having the widest measurement range appear to have the least accuracy.

3) The longest chain of transfer is chosen. Paradoxical as it may seem at first glance, the chain of such a type can be determined a priori before constructing the system. It is the transfer chain aimed at the least accurate group of working measuring instruments Sp.ı1/. It is clear first of all from the fact that transferring the unit dimension to a more accurate working measuring instrument will require fewer transfer steps (levels) at a reference MMI accuracy equal for all working measuring instruments. Moreover, the most numerous group of working measuring instruments consists of less accurate ones, i.e., the expression given below is true almost without exception:

Np.ı1/ > Np.ı2/ > > N.ım/, (2.2.27)

whereNp.ı1/is the number (park) of working measuring instruments of the given accuracy group. So, from the point of view of the productivity (passing capacity), the chain of transferring the unit to the less accurate working measuring instruments has to be the longest one.

4)Constructing the longest transfer chainto the first approximation is performed.

The construction methond depends on the choice (the availability) of initial data and vice versa. In any case it is necessary to know the park of working measuring instru- mentsNp1. The following versions are possible:

Version 4a. Given

tiC1: the verification time for one measuring instrument at the .i C1/-th level performed with a metrological measuring instrument of thei-th level;

li: the number of measuring instruments of the.iC1/-th level that can be verified with a metrological measuring instrument of thei-th level;

qiC1: the part of measuring instruments of the.iC1/-th level, which are recog- nized in accordance with verification results as unsuitable, restored, and verified again;

TiC1: the verification interval (an average time of faultless operation with regard to the metrological reliability) for a measuring instrument of the.iC1/-th level;

i: the part of time within which a metrological measuring instrument of thei-th level is used for verification (within the frames of a given operation period, i.e., within the frames ofTi).

The number of metrological measuring instruments of thei-th level necessary for ver- ifyingniC1measuring instruments at the.iC1/-th level is determined from the con-

tinuity condition of the unit transfer process within their verification interval:

TiC1ini D tiC1NiC1.1CqiC1/

li . (2.2.28)

Knowing thatNp1 DnmC1we first findnmand then, using the recurrent method, the population of each level (ni) and the number of levelsm, are determined.

Version 4b. Given

n1: the number of subordinate metrological measuring instruments of the 1-st level in the given chain, which are verified withS0(with the reference metrological mea- suring instrument) within its verification intervalT0;

c†: the ratio between an error of the reference metrological measuring instrument to an error of the working measuring instrument;

g0andgp: the student coefficients for confidential errors of the reference metro- logical measuring instrument and working measuring instrument;

the permissible probability of verification defects (preferable ones from the point of view of the aim of the RUTS system with regard to the defect of the second kind).

Using the procedure of the MI 83-76 National System of Measurement Assurance.

Method of Determination of Verification Sceme Parameters, a maximum possible and minimal necessary (under these conditions) number of levelsmis found. At the same time while calculating according to MI 83-76, it is necessary to introduce a correction that is the inverse one with regard to the coefficient of the population level occupied by subordinated MMI, since in the considered case of the linear transfer chain the “side”

flows are absent (see condition (2.2.28)).

Version 4c.Given

n1: the number of MMI of the 1-st level;

tmC1: the time of verifying one working measuring instrument against an MMI of the lowest levelm;

li: the same as in version 4b;

h: the ratio of the verification time of one MMI on the second level against an MMI of the first level to the verification time of one working measuring instrument:

hD ttm2 ;

i: the same as in version 4a;

D .1CqiC1/ D 1.25: the average estimate of metrologically serviceable (fit according to verification results) measuring instruments on all levels;

it is also assumed that verification intervals for all MMI are of a lower level than the first one, and also for working measuring instruments they are similar and equal toTmD1 year andli D1.

Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 137 Then by the procedure outlined in [526], the maximum number of MMI at each level and the minimum number of levels are found.

5) Similar construction procedures are made for the remaining chains relating to the verification of working measuring instruments of the other accuracy groups. On the basis of the results obtained an improvedstructure of the RUTS system of the first approximationis constructed.

At the second stagethe nomenclature of MMI and methods of transferring the unit dimension on each step of the system which satisfy the conditions shown below are constructed:

(a) “compatibility” of the transfer method and types of MMI at the adjacent levels connected by this methodmklij (see Figure 2.4);

(b) problems for which the system construction was performed at the preceding stage (versions 4a–4c).

If it is not possible to satisfy some conditions with an “available” set of means and methods suitable for MMI, then appropriate corrections are introduced into the con- ditions of versions 4a–4c, and the process of constructing is performed anew. This results in an improved structure and composition of a particular concrete specific RUTS system of the first approximation.

An analogous structure according to the first two stages is made for all other mea- surands'k 2 ạ'kºmeasured within the frames of the general measurement system, i.e., NSM. As a result we obtain atotal RUTS system of the first approximationwhich satisfies the goals of this system to a first approximation.

The queue of performingtwo subsequent stagesof constructing the RUTS system can change, depending on the availability of corresponding data, particular aims of further improvement or of the level of the consideration commonness, of available resources, etc.

At one of these stages (for example, at the thirdone) the compatibility of differ- ent particular systems is checked from the point of view of the general properties of the system of unit reproduction (see Section 2.2.5.1). At another stage it is possible to solve a number of optimization problems using economic criteria, registration of performance parameters of the RUTS system (or its subsystems), and optimization by the efficiency criterion of system performance.

At the final,fifth stagesome inconsistency (discrepancy) of solutions obtained to separate conditions at all preceding stages are revealed, the necessary corrections are introduced into the initial data, and corrections are determined for a final solution of the first approximation.

After that we have a complete RUTS system, optimal with regard to the composition and structure and at most corresponding to the goal and quality of this system at an available knowledge level.

In Section 2.2.4.4 some problems of the operation and optimization of the RUTS systems are considered. Then a number of issues connected with the system of unit dimension reproduction as well as the influence of this system on the complete RUTS system construction are analyzed.