2.1 Classification of reproducing physical quantities units and systems for transferring their sizes (RUTS)and systems for transferring their sizes (RUTS)
2.1.6 The technical-economic efficiency of various RUTS systems
This is indeed the reason why the influence of metrology (and of its metrological systems) on the efficiency of all sectors of the national economy is only indirectly apparent, i.e., through the increase in the general level of the measurement quality in the country.
In connection with this, let us consider merely metrological aspects of the technical and economicalefficiency of the RUTS systems which will be conditionally deter- mined as
".Cr/D E.Cr/
E.Cr/, (2.12)
whereE.Cr/is the reduced expenses connected with the creation and operation of theCr system, and".Cr/is the overall index of a metrological effect of applying this system.
The metrological effectcan be determined reasoning from the degree a final aim of the RUTS system has been achieved, which according to Section 2.1.2.6 is reduced to the implementation of the condition of measurements comparability (2.5) if it is considered that within the state system of measurements a unified system of PQ units is operating.
Thedegree of compliancewith condition (2.5) can be determined, certainly, as the ratio of the sets of allj Ô i;j 2 ạjº, for which condition (2.5) is fulfilled by the given.Cr/RUTS system, to the set of allj Ôi;j 2 ạjº, which are possible within
Section 2.1 Classification of RUTS systems 93
the given national system of measurements. Then
".Cr/D ạjºr
C.Cr/ ạjº D 1
C.Cr/ạjºr
ạjº. (2.12a)
In order tocomparethe possibilities of various RUTS system types it is sufficient to analyze the relative efficiency of the RUTS systems (for example,C1andC2):
"rel
C1 C2
".C1/
".C2/ D C.C2/ C.C1/ạjº1
ạjº2
, (2.13)
since the setạjºis common with respect to them.
First of all let us consider the RUTS systems of the CC type, for whichạjºr D ạjº evidently takes place, and then discuss their relative efficiency from the point of view of the difference between RUTS system structures. For such systems the efficiency will be determined only by expenditures connected with the creation and operation of the system, which consist of both the costs for creating and operating a national system of measurements and the costs for developing and realizing a transfer method (TM) for the unit size:
"1.Ccc/DX
i
Ci.MMI/CX
i
Ci.TM/.
Consequently, the task of finding the most efficient structure of a CC type RUTS systems is reduced to minimizing the joint costs connected with creation and operation of such a system. From the metrological point of view it is evident that in a general case any complication of the RUTS system structure (increase of a number of transfer steps and, in the long run, the number of MMI) leads to an increase in the general cost (a decrease in efficiency), since the increase in the number of MMIs is followed by an increase in the number of transfer methods (the number of elements connections) as well as an increase in the number of the common staff of specialists in metrology.
On the other hand, the decrease in the number of MMI in the RUTS system structure is connected with a rise in price of each metrological measuring instrument due to the need to provide them with a required productivity.
Actually, the productivity of a given metrological measuring instrument (i.e., a max- imum number of subordinate measuring instruments verified or calibrated with its help) is determined by the expression
P0D T1
N t1
,
whereTj is the average verification (calibration) interval for measuring instruments
ạSiº0, subordinated to a given metrological measuring instrument (S0), andtN1is the average time duration of the subordinate MI verification or calibration procedures.
Then the “transfer capability” of the RUTS systems at n steps of verification (n-levels of MMI) is
P .Ccc/D T1
N
t1 T2t10 N
t2 Tnt0n1
N
tn Š Yn jD1
Tj N
tj , (2.14)
wheretj0 is the average time of the MMI disuse (Sj), that includes the time of its ver- ification and transportation (for the verification); usually we havetj0 Tj, therefore here a transition has been made to an approximate equality.
It should be noted that, as a rule,T0> T1> T2> > Tnandt1> t2> > tn. Moreover, usually the calibration (verification) interval of a given metrological mea- suring instrument is less, the greater its productivity is, i.e., in the first approximation:
Tj 1
P D tNjC1
TjC1
or TjT :j C1 N
tjC1 Š const . Therefore,
P .Ccc/Š Yn jD1
Tj tj D
8ˆ ˆ<
ˆˆ :
.const/n2
ti atneven,
.const/n12
t2 Ttnn atnodd.
(2.15)
The maximum productivity value is achieved atT0 D const (an intercertification period of an RMMI):
Pmax.Ccc/D .T0/n=2 t1 .
Comparing theC1system withn-levels and theC2with one level of the MMI (an ideal, extreme case of the RUTS), one obtains that the equal productivityP .C1/ D P .C2/(i.e., the same degree of fulfilling condition (2.5) on condition that the verifi- cation time of a WMI is the same in both cases) can be achieved only when
.T01/n=2DT02.
This means that the RMMI of a one-level system should have a greater metrological reliability (ton=2 power) than that in a system withn levels. It is known that the increase in the system reliability by a factor ofkleads to an increase in its price on average by a factor ofk2 (i.e., in the case considered by a factor of 4). Moreover, there is a limit, i.e., a minimal time of verification of a subordinate MMI. To get more accurate estimates, special investigation and corresponding initial data are required.
It is possible to show that at a sufficient detailed elaboration of the measurement comparability condition (2.5), the RUTS system of the MC type can be reduced to systems of the CC type (from the point of view of the metrological effect, i.e., the
Section 2.1 Classification of RUTS systems 95 degree of fulfilment of this condition), since, at ak-multiple system,
ạjº DXk
rD1
ạjºr.
As regards the RUTS systems of the LC and DC types, their metrological effect, as a rule, is significantly less than that of the systems of the CC or MC type, since the powers of the sets greatly differ:jạjºrj jạjºj D j‰j.
The fulfillment of the RUTS systems functions in full volume (i.e., the condition of comparability of measurements) is possible, strictly speaking, only when “constant”
physical quantities are available which allow'2uD'1uto be realized in equation (2.5) and, consequently, provide the possibility of an indirect comparison of unit sizes in the presence of many RMMI. However the costs for creation and operation of RUTS systems of the LC and DC types are much less that those for systems of the CC and MC types. In connection with this, their technical and economical efficiency can be compared, and the creation of systems of the LC and DC is justified.
The use of other classification signs for comparing the technical and economical efficiency of the RUTS systems unlikely makes sense since this efficiency weakly depends on them.
In conclusion let us formulate the necessary and sufficient conditions (signs of grounding) which are common for creating centralized RUTS systems of one or an- other type (i.e., and for creating RMMI).
Necessaryconditions (i.e., in the aggregate the obligatory ones) are:
the availability of WMI in the SSM which are intended for direct measurements of a given PQ;
the technical possibility of realizing comparisons of various types of MI for a given PQ (i.e., the availability of corresponding methods of the unit size transfer) within the framework of a chosen degree of centralization;
the availability of a unified system of units, accepted in the SSM;
the availability of a necessary resource of accuracy between an RMMI and WMI.
Thesufficientconditions (fulfillment of at least one of which in meeting all necessary conditions serves as the basis for creating a system) are:
the unit of a given PQ belonging to the basic units of an accepted system of units (the adequacy condition for CC type systems);
dependence of the accuracy of reproducing a derivative unit mainly on properties of a given RMMI (as a measuring setup) further than on the accuracy of direct measurements of other PQs determining the given one;
availability of a primary RMMI, which at the same time cannot provide the accuracy required for transferring the unit size of a given PQ for the considered measurement conditions (the adequacy condition for the MC type systems);
localization (for example, within the limits of one industry branch or economical region of the country) of a significant park of WMI of a given PQ in SSM (the adequacy condition for the LC type systems);
maximum economical efficiency of a given type of RUTS systems for a given PQ.