1

THE AGRIFOOD SECTOR -

LINKAGES AND DRIVING EFFECTS IN NATIONAL ECONOMY

Filon TODEROIU1

Abstract

In the national economy system, the subsystems of agricultural production (ASPEFV) and of

food production (PABT) are "anchored" to other sectors by a series of "backward linkages"

and "forward linkages". Representing, in fact, the intermediary consumption intensity in

final production, the backward linkages coefficients per total national economy had a strong

descending trend in the period 1989 – 1998. One may notice the presence of strong

backward linkages in a number of four branches of the six branches considered, out of which

food industry can be easily explained, if we consider that agriculture is the main upstream

supplier of food industry. Also, one may observe the presence of strong linkages in only two

of the six branches, out of which agriculture can be easily explained if we consider that the

main beneficiary in the downstream sector of agriculture is food industry. While agriculture

(ASPEFV) is found in the type III of linkages (weak backward linkages but strong forward

linkages) in eight of the ten years of the investigated period and in the type IV of linkages in

the remaining two years, food industry is found in type II of linkages (strong backward but

weak forward). Agriculture would induce from 1.935 to 2.353 economic activity units in its

upstream sector and from 2.464 to 2.903 units in its downstream sector. It means that,

summing up the two driving effects, agriculture would induce more than 4.8 economic

activity units, and food industry more than 4.7 units. At the same time, agriculture may be

characterized by a low driving backward power, but quite a strong driving forward power; by

contrast, the trade features by a low driving forward power.

Key words: agrifood, linkages coefficients, driving effects, transition economy, Romania.

JEL Classification: Q18, P28, C49

1. Backward and Forward Linkages

1.1. Methodological benchmarks

Relevant information regarding the structural changes produced in Romania’s economy,

mainly after 1989 – as a premise to the identification of adjustment potential to the market

economy rules and EU rigors – are provided by the input – output analysis of the data

synthesized in the national accounts.

Starting from the synthetic input – output table (TIO), elaborated by the National

Commission for Statistics on the basis of national accounts, after aggregating the activities

by six branches (ASPEFV = agriculture, forestry and hunting, pisciculture and forest

operation; PABT = food products, beverages and tobacco; TEXC = textiles and ready-made

clothes; COM = trade; HRAT = hotels, restaurants and tourism agencies; RRAM = remaining

branches of the economy; TRAM = total branches), the matrix of structural coefficients of

intermediary inputs was elaborated in relation to final production, on one hand, and the

matrix of intermediary deliveries in relation to final demand, on the other hand (Artis et. al.,

1994, Enciso et. al., 1995, Toderoiu, 1996).

1 Institute of Agricultural economics, The Romanian Academy.

2

The main relations existing between the agrifood branches are revealed by

determining those considered as “key” branches, for which the evolution and relative

position are investigated in the context of the economic activity as a whole. The Chenery –

Watanabe and Rasmussen coefficients make it possible to analyze the most important

relations that are established between the agrifood branches and the remaining production

system in the national economy.

The analysis of dependence relations that are established between the agrifood

sector and the other sectors of the economy, as well as the determination of branches that

are considered as ‘engines’ to development can be made starting from the Input – Output

Table (TIO), that contains the inter-sectoral relations in the economy relevant linkages

existing between the indices and coefficients with which the direct and indirect relations

existing between the production sectors of the economy are relatively optimally quantified.

Several quantification modalities of these inter-sectoral relations are identified:

a) by measuring the main aggregate dimensions of the primary sector and of the agrifood

industries;

b) by the analysis of the dependence relations between the sectors composing the agrifood

system, starting from the study of linkages between the production branches, the

results being under the form of internal intermediary consumption (demand) matrix and

of total intermediary consumption;

c) by the analysis of structural sensitiveness, while determining the relative importance of

each of the TIO technical coefficients;

d) by the analysis of agrifood system external dependence.

In the national economy system, the subsystems of agricultural production (ASPEFV) and of

food production (PABT) are ‘anchored’ by a series of backward linkages - that are produced

when a production branch uses intermediary inputs coming from other branches – and

forward linkages – when the products of a certain branch are used for other branches, as

intermediary inputs to produce their products.

The inter-sectoral relations at national economy level can be investigated by

quantifying the direct effects (Chenery – Watanabe coefficients) and the total effects

(Rasmussen coefficients).

The first econometric attempt to measure the relations existing between the

different economic activities was made by Hirschman (1958); for the first time, Chenery and

Watanabe (1958) made a classification of the economic activities in relation to the forward

and backward linkages.

The backward linkages coefficients (μj) are defined as:

µj = Σ (xij / Xj) (1)

where:

xij = the uses given by the branch ‘j’ to the products of branch ‘I’ (i.e. the share of

intermediary inputs in the final production of branch ‘j’);

Xj = value of final (effective) production of branch ‘j’.

If µj is higher than are average of all branches, this means that the specific weight of

intermediary inputs in the final production of branch ‘j’ is high and, as a result, the activity

has strong backward linkages.

The coefficients of forward linkages ( ωI) are similarly defined:

ωi = Σ (xij / Zi) (2)

where:

xij = products of branch ‘i’ used as inputs for other branches ‘j’;

Zi = total uses of branch ‘i’;

The coefficient ωI represents the specific weight of the intermediary demand in total

uses of branch ‘I’. If this is higher than the average of all branches, it means that the share of

3

intermediary demand of branch ‘I’ in relation to toal uses is high and, as a result, the

respective activity presents strong forward linkages.

Starting from the coefficients defined above, the activity branches can be classified

into four types, depending upon the linkages that are present:

a) branches with forward and backward linkages (and-and);

b) branches with backward linkages but no forward linkages (and – no);

c) branches with no backward linkages but with forward linkages (no – and);

d) branches with no forward linkages and no backward linkages (no – no).

In relation to the average of coefficients per total branches, the four types of linkages

can be grouped into strong linkages and weak linkages. The Cheneray – Watanabe

coefficients do not include the indirect linkages and hence they give a partial picture to the

multitude of intersectoral interdependecies. A first approximation of the interdependency

level of productive branches is given by the sum of elements in the Leontieff inverse matrix

columns. The diffusion effect (Edj) is expressed as:

Edj = Σ Aij (3) where:

Aij = column vectors of the Leontieff invers matrix.

The diffusion effect reveals the productive effort of the ‘n’ branches, when the final

demand of branches ‘j’ increases by one unit, thus quantifying the backward linkages of each

branch in total economy.

The absorption effect (Eai) is defined as:

Eaj = Σ Aij (4)

where:

Aij = line vectors of Leontieff inverse matrix.

The absorption effect is equal to the sum of elements in row ‘I’ of Leontieff inverse

matrix and reveals to what extend the production of branch ‘I’ will be modified if an increase

by one unit is wanted in each element of final demand; thus the intensity by which one

sector absorbs the variations of final demand of other sectors (forward effects) is quantified.

The diffusion and absorption effects presented above can be reformulated in order

to make intersectoral comparisons, relating each sectoral value to total average. Thus,

Rasmusen (1956) defines the diffusion power (Rd) as:

Rdj = [(ΣAij / n) / (ΣΣ Aij / n2)] (5)

While the absorption power (Ra) as:

Rai = [(ΣAij / n) / (ΣΣ Aij / n2)] (6)

1.2. Coefficients of backward and forward linkages in the agrifood sector

Using the method of Chenery – Watanabe coefficients it is determined the degree in which

the investigated branches have more or less backward and or forward linkages, in relation to

the value of coefficients compared to the aggregate average of intermediary input share in

final production per total national economy.

The analysis of backward linkages coefficients by the six ‘blocks’ of the national

economy makes it possible to identify and quantify the intensity and tendency of

destructuring and disarticulation processes between each branch and the other branches

supplying intermediary inputs.

Representing, in fact, the intensity of intermediary consumptions in final production,

the coefficients of backward linkages per total national economy had a strong decreasing

trend in the period 1989-1998, ranging from 0.653 (maximum level 1989) to 0.537

(minimum level 1998).

It is quite striking that, in the economy, there are not always linear

interdependencies between the economic growth and the structural modernization of

4

national economy. Hence the lack of concordance between the minitendencies of these

parameters with economic increase (decrease) intervals in the transition period. Thus, the

three year interval of systematic economic decline (1990-1992) was converted into five

years of decreasing backward linkages coefficients, from 0.653 (1989) to 0.541 (1994). After

1995, it seems that things begin to “settle down” in the economic sector, in the sense that

years of economic growth 1995-1996 of economic features progressive coefficients of

backward linkages, while the years of economic decline 1997/1998 features regressive

coefficients.

In relation to the average per total economy, 34 of the 54 coefficients of backward

linkages afferent to transition years 1990-1998 (62.9%) are larger than unit, referring to four

branches: food industry (PABT) and remaining branches (RRAM) 9 coefficients each, on one

hand, and the textiles and ready – made clothes (TEXC) and hotel economy (HRAT) 8

coefficients each, on the other hand (Figure 1.1).

Source: own calculations according to Chenery – Watanabe method, on the basis of data from

national Accounts, 1989-1998, NIS.

Figure 1.1. Coefficients of backward linkages in Romania’s agrifood sector, 1989 – 98

At the same time, only 16 coefficients of the forward linkages out of the 54 calculated for

the transition years 1990-1998 (29.63%) are larger than unit and refer to two branches:

agriculture (ASPEFV) – 7 coefficients and the remaining branches (RRAM) – 9 coefficients

(Figure 1.2).

Source: own calculations according to Chenery – Watanabe method, on the basis of data from

national Accounts, 1989-1998, NIS.

Figure 1.2. Coefficients of forward linkages in Romania’s agrifood sector, 1989-98

0,600

0,700

0,800

0,900

1,000

1,100

1,200

1,300

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

(Wh

ole

econ

om

y =

1)

ASPEF PABT TEXC RRAMFIT-IEA-02

0,600

0,700

0,800

0,900

1,000

1,100

1,200

1,300

1,400

1,500

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

(Wh

ole

econ

om

y =

1)

ASPE F PA B T T E X C R R AMF IT-IE A -02

5

Several essential aspects are worth mentioning:

• Presence of strong backward linkages in four of the six branches considered, among

which food industry (fact that can be easily explained, if we consider that agriculture is

the main upstream supplier of food industry);

• Presence of strong forward linkages in only two of the six branches, among which

agriculture (explainable fact, if we consider that food industry is the main downstream

supplier of agriculture).

Simultaneously analysed, in ‘tandem’ the coefficients of backward and forward linkages in

relation to total economy permit the placing of each of the six branches in one of the four

types, depending upon the present linkages (Table 1.1).

Table 1.1. Distribution of the four branches of national economy into the four types of inter

– branch linkages in the period 1989-1998

Types of linkages : ASPEF PABT TEXC COM HRAT RRAM Total

correlations

I. Strong backward and

forward linkages

(μj > μ; ωi > ω )

10 10

II. Strong backward

linkages and weak

forward linkages

(μj > μ; ωi < ω )

10 9 19

III. Weak backward

linkages and strong

forward linkages

(μj < μ; ωi > ω )

8 8

IV. Weak backward and

forward linkages

(μj < μ; ωi < ω )

2 10 10 1 23

Total correlations 10 10 10 10 10 10 60

Source: own calculations, on the basis of Chenery – Watanabe coefficients, calculated for the period

1989-1998.

One can draw the clear conclusion that, while agriculture (ASPEFV) is placed in the

type III of linkages (weak backward but strong forward) in 8 years of the ten years of the

investigated period and in the type IV of linkages in the remaining two years, food industry is

totally placed in the type II of linkages (strong backward but weak forward).

2. Driving Effects of the agrifood sector in total economy

2.1. Preliminary methodological approach

The backward and forward linkages coefficients (known as Chenery – Watanabe coefficients)

do not incorporate the indirect linkages, thus giving a partial picture of inter-sectoral

interdependencies. A first attempt to calculate the interdependency level of production

branches is represented by the sum of elements in the Leontieff reciprocal matrix. Summing

up by columns the diffusion effect (Edj) is determined, that measures the productive effect

of the six branches (in reality the input – output table, elaborated by NIS, on the basis of

national accounts, includes 105 branches) when the final demand of one branch increases by

6

one unit, thus quantifying the backward effects of each branch in the context of total

economy.

Summarizing up by rows the elements of Leontieff reciprocal matrix, it is determined

to what extend the production of a certain branch is modified if each element of final

demand increases by one unit, thus quantifying the intensity by which one sector absorbs

the final demand variations of other sectors, named forward effects.

2.2. Quantification of backward and forward driving effects in the agrifood sector

Obtained on the basis Leontieff reciprocal matrix of the structural coefficients of backward

and forward linkages, the Rasmussen coefficients of backward driving (diffusion) effects and

forward (absorption) effects quantify the direct relations that are established in national

economy, starting from the inter-sectorally induced demand. The use of algorithms

elaborated2 for each of the six branches and for the whole economy, for each year of the

investigated period, led to the determination of 140 diffusion coefficients (backward driving

effects) and absorption coefficients (forward driving effects).

When analyzing the coefficients for the period 1990-1998 compared to the year

1989, one can draw a series of conclusions referring to the extend to which the transition

from centrally – planned to market economy meant an important improvement of the

driving capacity of different branches.

In the first place, in total national economy, the average value of backward driving

coefficients (which is similar to that of forward coefficients) for the period 1990-1998 was

2.355, which is means that, in this period, an economic activity unit induced by about 22%

less economic activity compared to 1989.

In the second place, among the six investigated branches, only the textile and ready-

made clothes industry (TEXC) has average backward and forward driving effects for the years

1990-1998 which are higher than those in the year 1989; the other two branches (trade – CO

and hotels economy – HRAT) have averages superior th the year 1989 only in the forward

driving effects.

In the third place, the decline rates of the driving effects induced by the remaining

branches (RRAM) are among the highest (27.4% in the absorption effects and 23.5% in the

diffusion effects).

In the fourth place, both main components of the agrifood sector (agriculture –

ASPEFV and food industry – PABT) present considerable decline of the driving effects, their

averages in the transition period being by 10.9% and 19.7% respectively lower than their

levels in 1989 in agriculture and by 11.6% and 12.0% in the food industry.

Thus, as we should know what are the economic driving effects in the future, one

can state that agriculture would induce in the remaining economic branches from 1.935 to

2.353 economic activity units in its upstream (backward) sector its downstream (forward)

sector. This means that by summing up the two driving effects, agriculture might induce

more than 4.8 economic activity units, while food industry more than 4.7 units.

2 Algorithms include econometric relations to determining the backward and forward linkages

(structural coefficients), the backward and forward driving effect (Chenery – Watanabe coefficients),

the backward and forward driving power (Rasmusen coefficients), as well as the sensitivity

coefficients, that measure the maximum percentage modification of technical coefficients that is

accepted, with no error produced by this variation in sectoral production larger than 1% (Annexes 2.2

–2.5).

7

2.3. Backward and forward driving power in the agrifood sector

The most pregnant picture of diffusion effects (Edj) and of absorption effects (Eai) was

obtained by relating each value given to the two effects with their average per total national

economy (Rasmusen coefficients), thus measuring the diffusion power (Rdj) and the

absroption power (Rai) respectively these coefficients allow for relevant intersectoral

comparisons (Table 2.1).

Table 2.1. Backward driving power (diffusion = Ed) and forward driving power (absorbtion =

Ea) in Romania’s economy, 1989 – 98 (Total economy= 1).

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

Rd 0,868 0,780 0,883 0,899 0,907 0,914 0,868 0,865 0,881 0,937 ASPEF

Ra 1,274 1,119 1,081 1,085 1,322 1,364 1,208 1,091 1,091 1,160

Rd 1,074 1,031 1,081 1,099 1,077 1,096 1,065 1,070 1,103 1,111 PABT

Ra 0,934 0,975 0,800 0,846 0,939 1,023 0,937 0,991 1,007 0,939

Rd 0,930 1,008 1,161 1,170 1,123 1,057 1,058 1,083 1,078 1,085 TEXC

Ra 0,640 0,684 0,733 0,752 0,748 0,780 0,817 0,816 0,851 0,905

Rd 0,707 0,745 0,618 0,615 0,686 0,718 0,746 0,796 0,808 0,777 COM

Ra 0,373 0,397 0,375 0,389 0,437 0,472 0,452 0,430 0,443 0,460

Rd 1,294 1,258 1,135 1,098 1,111 1,124 1,165 1,073 1,023 1,048 HRAT

Ra 0,382 0,404 0,381 0,401 0,452 0,489 0,491 0,483 0,494 0,507

Rd 1,127 1,178 1,123 1,119 1,097 1,092 1,098 1,113 1,107 1,041 RRAM

Ra 2,396 2,421 2,630 2,527 2,103 1,873 2,094 2,189 2,113 2,029

Source: own calculations, on the basis of data from National Accounts, Rasmunsen method. The parameters from table 2.1 can be analyzed in several ways:

• By separate, comparative analysis of tendencies in backward driving powers in the main

branches taken into consideration (Figure 2.1);

• By separate, comparative analysis, of the tendencies in the forward driving powers in

the main branches taken into consideration (Figure 2.2);

• By determining the variation coefficients of the backward and forward driving powers,

by which can find out their relative stability value, as a premise to their taking into

consideration in the elaboration of certain sectoral development strategies (Annex 2.1).

From the perspective of the last mentioned analysis modality, it was determined that, in the

period 1990-98, the driving power (Rasmussen coefficients) in the backward sector had

variation coefficients ranging from 20.5% (PABT) to 8.85% (COM), agriculture being the third

branch out of the six branches with 4.54%.

Source: own calculations according to Rasmusen method, on the basis of National Accounts data,

1989-1998.

Figure 2.1. Backward driving power of the agrifood sector, 1989 - 98

0,7

0 ,75

0,8

0 ,85

0,9

0 ,95

1

1 ,05

1,1

1 ,15

1,2

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

(Wh

ole

econ

om

y =

1)

A S P E F P A B T T E X C R R A MF IT -IE A -02

8

Source: own calculations according to Rasmusen method, on the basis of National Accounts data,

1989-1998.

Figure 2.2. Forward driving power of the agrifood sector, 1989 – 98

The much larger variation coefficients however placed in the proximity of the higher

confidence limit (10%), describe the forward driving powers, i.e. from 7.04% (PABT) to

10.78% (HRAT), agriculture being placed on the second place in the hierarchy of the six

branches.

The simultaneously interpretation of the two categories of driving powers

(backward – Rd and forward – Ra) for each year, make it possible to distribute the six

branches into the four driving power (Table 2.2).

Table 2.2. Distribution of national economy branches into the four driving types,

1989 - 1998

Driving typese: ASPEF PABT TEXC COM HRAT RRAM Total

correlations

I. Strong backwards and

strong forwards

(Rd > 1; Ra > 1 )

2 10 12

II. Strong backwards and

weak forwards

(Rd > 1; Ra < 1)

8 9 10 27

III. Weak backwards and

strong forwards

(Rd < 1; Ra > 1)

10 10

IV. Weak backwards and

weak forwards

(Rd < 1; Ra < 1)

1 10 11

Total correlations 10 10 10 10 10 10 60

Source: own calculations, based upon Chenery-Watanabe coefficients matrix, calculated for the period

1989-1998.

It results that, in the period 1989-1998, our economy mainly featured (39 of 60

correlations, i.e. 65%) a strong backward driving power, out of which in 12 cases this was

accompanied by a strong driving power in the forwards sector, too (food industry – 2 cases

and the remaining branches – 10 cases); in the other 27 cases, weak forward driving power

(food industry – 8, textiles and ready-made clothes –9 and hotels and restaurants – 10).

0,600

1,100

1,600

2,100

2,600

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

(Wh

ole

econ

om

y =

1)

ASPEF PABT TEXC RRAMFIT-IEA-02

9

At the same time, agriculture was characterized by weak backward driving power

but strong forward driving power; at the same time, trade featured weak forward driving

power.

REFERENCES.

Artis, M., Surinach, J., Pons, J., (1994): El sistema agroalimentario catalan en la tabla Input-

Output de 1987, in “Investigation Agraria-Economia” (IAE), INITAA, Vol. 9, nr.1.

Dumitru,D., Ionescu, L., Popescu, M.,Toderoiu, F.,(1997): Agricultura României – tendinţe pe

termen mediu şi lung, Ed. Expert, Bucureşti.

Enciso,J.P.,Sabate,P.,(1995): Una vision del complejo de producccion agroalimentario

espanol en la decada de los ochenta, în ”Investigation Agraria-Economia’(IAE), INITAA,

Vol.10, No. 3, Madrid.

Gavrilescu, D., Giurcă, D. (coord.) (2000): Economia Agroalientară, Ed. Expert,Bucureşti.

Greig Smith,W.,(1984): Economics and Management of Food Processing, AVI Publ.Co.Inc.

Westport.

Hartmann, M. ,(1993): Überlegungen zur Wettbewerbsfähigkeit des deutschen

Ernährungsgewerbes, în “Agrarwirtschaft”(AW), Jg. 42, Heft 6.

Eiteljoerge,U., Hartmann,M. (1999): Central and Eastern European Food Chains

Competitivness, în:‘The European Agro-food System and the Challenge of Global

Competition‘, ISMEA,Rome.

Popescu, M. (2001): Concentrarea producţiei agricole - tendinţe convergente şi divergente cu

UE, în: Evoluţia sectorului agroalimentar în România – convergenţe multicriteriale cu UE, Vol.

17 ESEN, Ed. Expert, Bucureşti.

Schmitt, G.(1997): Unvollkommene Arbeitsmärkte, Produktivität und Effizienz des

Faktoreinzatzes in der Landwirtschaft. în ’Agrarwirtschaft‘, Jg. 46, H. 10.

Toderoiu,F.,(2002): Sectorul agroalimentar în România - mutaţii structurale multicriteriale Comparative , în: Evoluţia sectorului agroalimentar în România – convergenţe multicriteriale

cu UE, Vol. 17 ESEN, Ed. Expert, Bucureşti.

Toderoiu,F.,(2002): Agricultura - Resurse şi Eficienţă. (O retrospectivă semiseculară), Ed.

Expert, Bucureşti.

Toderoiu,F., Ştefănescu, C. (2002): Agri - Food Sector in Romania - Loss on Internal and

External Competitivness, în: 'Romanian Journal of Economic Forecasting', Nr. 1, CEID - NIER,

Bucharest.

Toderoiu, F. (2003): Evoluţia sectorului agroalimentar al României - decalaje faţă de Uniunea

Europeană, în: Zahiu, L.(coord) (2003) 'Structurile agrare şi viitorul politicilor agricole', Ed.

Economică, Bucureşti.

10

ANNEX 3.1r ..0 5 c ..0 9

Variation coefficients of the difusion and absorbtion power in Romania's economy, 1989 - 98

89 90 91 92 93 94 95 96 97 98

0 1 2 3 4 5 6 7

8 9

0 ASPEF

1 PABT

2 TEXCRda

0.868

1.074

0.929

0.707

1.294

1.127

0.780

1.031

1.008

0.745

1.258

1.178

0.882

1.080

1.161

0.618

1.135

1.123

0.899

1.099

1.170

0.615

1.098

1.119

0.907

1.076

1.123

0.686

1.111

1.096

0.914

1.096

1.057

0.718

1.124

1.091

0.868

1.065

1.057

0.746

1.165

1.099

0.866

1.070

1.083

0.796

1.073

1.113

0.880

1.103

1.078

0.808

1.023

1.107

0.937

1.111

1.085

0.777

1.048

1.041

3 COM

4 HRAT

5 RRAM

89 90 91 92 93 94 95 96 97 98

0 1 2 3 4 5 6 7 8 9

0 ASPEF

1 PABT

2 TEXCRaa

1.274

0.935

0.640

0.373

0.382

2.396

1.119

0.976

0.684

0.397

0.404

2.421

1.081

0.800

0.733

0.375

0.381

2.630

1.085

0.846

0.755

0.389

0.401

2.525

1.322

0.939

0.748

0.437

0.452

2.103

1.364

1.023

0.780

0.472

0.489

1.873

1.208

0.938

0.817

0.452

0.491

2.094

1.091

0.991

0.816

0.430

0.483

2.189

1.091

1.007

0.852

0.443

0.494

2.113

1.160

0.940

0.905

0.460

0.507

2.028

3 COM

4 HRAT

5 RRAM

Rda0c

Rda,5 c

=mean( )Rda0 1.1094 Raa0c

Raa,5 c

=mean( )Raa0 2.2372

=stdev ( )Rda0 0.0326 =stdev ( )Raa0 0.23

=.stdev ( )Rda0

mean( )Rda0100 2.94 =.stdev ( )Raa0

mean( )Raa0100 10.28CVda

r

4.54

2.05

6.26

8.85

7.24

2.94

CVaar

8.58

7.04

9.65

8.16

10.78

10.28

0 ASPEF 0 ASPEF

1 PABT 1 PABT

2 TEXC 2 TEXC

3 COM 3 COM

4 HRAT 4 HRAT

5 RRAM 5 RRAM

10.78

2.05

CVdar

CVaar

10

50 r

11

i ..0 6 j ..0 6 r ..0 5 c ..0 5 ANNEX 3.2

CI-aspefv CI-pibt CI-texc CI-com CI-hrat CI-rram CI-tram APPLICATION 1989p89

0 1 2 3 4 5 6

0 CI-aspefv

1 CI-pabt

2 CI-texc

M89

48.223

20.130

0.376

0.001

0.028

42.927

111.684

125.239

27.110

0.223

0.001

0.015

10.707

163.294

8.380

0.064

40.761

0.001

0.026

17.578

66.809

0.004

6.770

1.148

0.001

0.006

8.606

16.534

4.694

45.635

0.066

0.001

0.747

4.154

55.296

5.861

5.656

18.789

0.003

2.414

908.060

940.780

192.401

105.365

61.363

0.008

3.236

992.032

1354.397

3 CI-com

4 CI-hrat

5 CI-rram

6 CI-TRAM

X89 ( )226.902 214.226 116.992 54.039 63.826 1399.501 2075.486 PF-TRAM

TUTIL

0 ASPEFV

1 PABT

2 TEXC

Y89

230.656

267.561

134.388

4.030

69.397

1593.632

2299.663

3 COMU89

,i j

M89,i j

X89,0 j

W89,i j

M89,i j

Y89,i 04 HRAT

5 RRAM

6 TRAM

0 ASPEFV

1 PABT

2 TEXC

=U89

0.213

0.089

0.002

4.407 106

1.234 104

0.189

0.492

0.585

0.127

0.001

4.668 106

7.002 105

0.05

0.762

0.072

5.47 104

0.348

8.548 106

2.222 104

0.15

0.571

7.402 105

0.125

0.021

1.851 105

1.11 104

0.159

0.306

0.074

0.715

0.001

1.567 105

0.012

0.065

0.866

0.004

0.004

0.013

2.144 106

0.002

0.649

0.672

0.093

0.051

0.03

3.855 106

0.002

0.478

0.653

3 COM

4 HRAT

5 RRAM

6 TRAM

0 ASPEFV

1 PABT

2 TEXC

=W89

0.209

0.075

0.003

2.481 104

4.035 104

0.027

0.049

0.543

0.101

0.002

2.481 104

2.161 104

0.007

0.071

0.036

2.392 104

0.303

2.481 104

3.747 104

0.011

0.029

1.734 105

0.025

0.009

2.481 104

8.646 105

0.005

0.007

0.02

0.171

4.911 104

2.481 104

0.011

0.003

0.024

0.025

0.021

0.14

7.444 104

0.035

0.57

0.409

0.834

0.394

0.457

0.002

0.047

0.622

0.589

3 COM

4 HRAT

5 RRAM

6 TRAM

TRAM

µc

r

U89,r c

ωr

c

W89,r c

=µ

0.492

0.762

0.571

0.306

0.866

0.672

=ω

0.834

0.394

0.457

0.002

0.047

0.622

r ..0 5 c ..0 5

I

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

U,r c

U89,r c

12

sr,0 c

1

.U,0 c

.0.01 L,c 0

.L,0 0

X89( ),0 0

Y89,0 0

sr,3 c

1

.U,3 c

.0.01 L,c 3

.L,3 3

X89,0 3

Y89,3 0

sr,1 c

1

.U,1 c

.0.01 L,c 1

.L,1 1

X89,0 1

Y89,1 0

sr,4 c

1

.U,4 c

.0.01 L,c 4

.L,4 4

X89,0 4

Y89,4 0

sr,2 c

1

.U,2 c

.0.01 L,c 2

.L,2 2

X89,0 2

Y89,2 0

sr,5 c

1

.U,5 c

.0.01 L,c 5

.L,5 5

X89,0 5

Y89,5 0

semnif. : sr < 10

0 ASPEFV (3 +)

1 PABT (3 +)

2 TEXC (1 +)=sr

3.421

11.216

446.487

1.692 104

8.623 103

2.077

1.255

7.839

711.499

1.597 104

1.518 104

7.863

10.253

1.836 103

2.102

8.724 103

4.827 103

2.615

9.924 103

8.017

34.869

4.027 103

9.664 103

2.468

9.988

1.405

716.353

4.76 103

90.695

6.039

174.404

246.817

54.869

3.477 104

617.132

0.599

3 COM (0 +)

4 HRAT (0 +)

5 RRAM (6 +)

sc,r 0

1

.U,r 0

.0.01 L,0 r

.L,0 0

X89,0 0

Y89,0 0

sc,r 3

1

.U,r 3

.0.01 L,3 r

.L,3 3

X89,0 3

Y89,3 0

sc,r 1

1

.U,r 1

.0.01 L,1 r

.L,1 1

X89,0 1

Y89,1 0

sc,r 4

1

.U,r 4

.0.01 L,4 r

.L,4 4

X89,0 4

Y89,4 0

sc,r 2

1

.U,r 2

.0.01 L,2 r

.L,2 2

X89,0 2

Y89,2 0

sc,r 5

1

.U,r 5

.0.01 L,5 r

.L,5 5

X89,0 5

Y89,5 0

semnif. : sc < 100

0 ASPEFV (5 +)

1 PABT (5 +)

2 TEXC (3 +)=sc

3.421

8.224

442.746

1.665 105

5.919 103

3.882

1.715

7.839

964.63

2.148 105

1.421 104

20.091

10.34

1.354 103

2.102

8.663 104

3.333 103

4.928

1.007 103

0.595

3.51

4.027 103

671.652

0.468

14.59

1.501

1.038 103

6.848 104

90.695

16.486

93.56

96.985

29.187

1.829 105

227.183

0.599

3 COM (0 +)

4 HRAT (1 +)

5 RRAM (6 +)

13

i ..0 6 j ..0 6 r ..0 5 c ..0 5 ANNEX 3.3

CI-aspefv CI-pibt CI-texc CI-com CI-hrat CI-rram CI-tram APPLICATION 1992p92

0 1 2 3 4 5 6

0 CI-aspefv

1 CI-pabt

2 CI-texc

M92

468.596

153.297

3.187

0.215

0.405

516.763

1142.463

775.820

209.895

3.075

0.390

0.223

136.900

1126.303

23.767

0.158

250.197

0.064

0.219

124.092

398.497

0.027

79.718

10.097

0.006

0.137

97.529

187.514

6.607

209.345

0.347

0.082

5.537

20.268

242.186

28.360

40.014

127.881

3.103

25.632

6063.381

6288.371

1303.177

692.427

394.784

3.860

32.153

6958.933

9385.334

3 CI-com

4 CI-hrat

5 CI-rram

6 CI-TRAM

X92 ( )2290.391 1526.299 579.299 916.245 372.996 9615.297 15300.527 PF-TRAM

TUTIL

0 ASPEFV

1 PABT

2 TEXC

Y92

2478.533

1910.071

878.767

25.793

435.809

11867.997

17596.969

3 COMU92

,i j

M92,i j

X92,0 j

W92,i j

M92,i j

Y92,i 04 HRAT

5 RRAM

6 TRAM

=U92

0.205

0.067

0.001

9.387 105

1.768 104

0.226

0.499

0.508

0.138

0.002

2.555 104

1.461 104

0.09

0.738

0.041

2.727 104

0.432

1.105 104

3.78 104

0.214

0.688

2.947 105

0.087

0.011

6.548 106

1.495 104

0.106

0.205

0.018

0.561

9.303 104

2.198 104

0.015

0.054

0.649

0.003

0.004

0.013

3.227 104

0.003

0.631

0.654

0.085

0.045

0.026

2.523 104

0.002

0.455

0.613 6 TRAM

=W92

0.189

0.08

0.004

0.008

9.293 104

0.044

0.065

0.313

0.11

0.003

0.015

5.117 104

0.012

0.064

0.01

8.272 105

0.285

0.002

5.025 104

0.01

0.023

1.089 105

0.042

0.011

2.326 104

3.144 104

0.008

0.011

0.003

0.11

3.949 104

0.003

0.013

0.002

0.014

0.011

0.021

0.146

0.12

0.059

0.511

0.357

0.526

0.363

0.449

0.15

0.074

0.586

0.533

6 TRAM

µc

r

U92,r c

ωr

c

W92,r c

=µ

0.499

0.738

0.688

0.205

0.649

0.654

=ω

0.526

0.363

0.449

0.15

0.074

0.586r ..0 5 c ..0 5

I

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

U,r c

U92,r c

14

sr,0 c

1

.U,0 c

.0.01 L,c 0

.L,0 0

X92( ),0 0

Y92,0 0

sr,3 c

1

.U,3 c

.0.01 L,c 3

.L,3 3

X92,0 3

Y92,3 0

sr,1 c

1

.U,1 c

.0.01 L,c 1

.L,1 1

X92,0 1

Y92,1 0

sr,4 c

1

.U,4 c

.0.01 L,c 4

.L,4 4

X92,0 4

Y92,4 0

sr,2 c

1

.U,2 c

.0.01 L,c 2

.L,2 2

X92,0 2

Y92,2 0

sr,5 c

1

.U,5 c

.0.01 L,c 5

.L,5 5

X92,0 5

Y92,5 0

semnif. : sr < 10

0 ASPEFV (2 +)

1 PABT (2 +)

2 TEXC (1 +)=sr

3.93

15.128

609.688

299.834

6.462 103

1.977

1.598

7.33

421.413

110.149

7.801 103

4.972

19.807

3.741 103

1.937

254.764

3.038 103

2.081

2.758 104

11.731

77.053

4.297 103

7.684 103

4.19

45.884

1.819

912.716

128.029

76.503

8.207

273.666

243.293

63.252

87.207

427.942

0.699

3 COM (0 +)

4 HRAT (0 +)

5 RRAM (6 +)

sc,r 0

1

.U,r 0

.0.01 L,0 r

.L,0 0

X92,0 0

Y92,0 0

sc,r 3

1

.U,r 3

.0.01 L,3 r

.L,3 3

X92,0 3

Y92,3 0

sc,r 1

1

.U,r 1

.0.01 L,1 r

.L,1 1

X92,0 1

Y92,1 0

sc,r 4

1

.U,r 4

.0.01 L,4 r

.L,4 4

X92,0 4

Y92,4 0

sc,r 2

1

.U,r 2

.0.01 L,2 r

.L,2 2

X92,0 2

Y92,2 0

sc,r 5

1

.U,r 5

.0.01 L,5 r

.L,5 5

X92,0 5

Y92,5 0

semnif. : sc < 100

0 ASPEFV (4 +)

1 PABT (4 +)

2 TEXC (3 +)=sc

3.93

12.066

583.605

8.653 103

4.579 103

3.602

2.006

7.33

506.529

3.99 103

6.936 103

11.377

20.693

3.113 103

1.937

7.684 103

2.246 103

3.962

955.138

0.323

2.554

4.297 103

188.239

0.264

64.861

2.047

1.235 103

5.226 103

76.503

21.142

150.639

106.794

33.37

1.38 103

166.844

0.699

3 COM (0 +)

4 HRAT (1 +)

5 RRAM (6 +)

15

i ..0 6 j ..0 6 r ..0 5 c ..0 5 ANNEX 3.4

CI-aspefv CI-pibt CI-texc CI-com CI-hrat CI-rram CI-tram APPLICATION 1996p96

0 1 2 3 4 5 6

0 CI-aspefv

1 CI-pabt

2 CI-texc

M96

9692.9

2372.0

62.9

0.7

21.4

5026.7

17176.6

9886.9

6313.9

97.5

0.6

38.6

2427.8

18765.3

311.3

66.5

3297.0

0.3

22.1

1269.6

4966.8

40.3

1731.6

232.0

0.5

126.8

2884.4

5015.6

15.8

2510.0

63.5

0.3

327.7

1117.5

4034.8

342.3

2477.8

2708.0

6.5

1475.2

81775.7

88785.5

20289.5

15471.8

6460.9

8.9

2011.8

94501.7

138744.6

3 CI-com

4 CI-hrat

5 CI-rram

6 CI-TRAM

X96 ( )38125.7 28372.2 8189.5 14988.2 6784.5 144138.7 240598.8 PF-TRAM

TUTIL

0 ASPEFV

1 PABT

2 TEXC

Y96

38475.7

36465.3

14637.3

365.7

8205.2

189355.9

287495.1

3 COMU96

,i j

M96,i j

X96,0 j

W96,i j

M96,i j

Y96,i 04 HRAT

5 RRAM

6 TRAM

=U96

0.254

0.062

0.002

1.836 105

5.613 104

0.132

0.451

0.348

0.223

0.003

2.115 105

0.001

0.086

0.661

0.038

0.008

0.403

3.663 105

0.003

0.155

0.606

0.003

0.116

0.015

3.336 105

0.008

0.192

0.335

0.002

0.37

0.009

4.422 105

0.048

0.165

0.595

0.002

0.017

0.019

4.51 105

0.01

0.567

0.616

0.084

0.064

0.027

3.699 105

0.008

0.393

0.577 6 TRAM

=W96

0.252

0.065

0.004

0.002

0.003

0.027

0.06

0.257

0.173

0.007

0.002

0.005

0.013

0.065

0.008

0.002

0.225

8.203 104

0.003

0.007

0.017

0.001

0.047

0.016

0.001

0.015

0.015

0.017

4.106 104

0.069

0.004

8.203 104

0.04

0.006

0.014

0.009

0.068

0.185

0.018

0.18

0.432

0.309

0.527

0.424

0.441

0.024

0.245

0.499

0.483

6 TRAM

µc

r

U96,r c

ωr

c

W96,r c

=µ

0.451

0.661

0.606

0.335

0.595

0.616

=ω

0.527

0.424

0.441

0.024

0.245

0.499r ..0 5 c ..0 5

I

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

1

U,r c

U96,r c

16

sr,0 c

1

.U,0 c

.0.01 L,c 0

.L,0 0

X96( ),0 0

Y96,0 0

sr,3 c

1

.U,3 c

.0.01 L,c 3

.L,3 3

X96,0 3

Y96,3 0

sr,1 c

1

.U,1 c

.0.01 L,c 1

.L,1 1

X96,0 1

Y96,1 0

sr,4 c

1

.U,4 c

.0.01 L,c 4

.L,4 4

X96,0 4

Y96,4 0

sr,2 c

1

.U,2 c

.0.01 L,c 2

.L,2 2

X96,0 2

Y96,2 0

sr,5 c

1

.U,5 c

.0.01 L,c 5

.L,5 5

X96,0 5

Y96,5 0

semnif. : sr < 10

0 ASPEFV (2 +)

1 PABT (3 +)

2 TEXC (1 +)=sr

2.803

15.197

638.311

1.329 103

2.03 103

4.194

2.064

4.22

306.651

1.154 103

834.875

6.461

18.934

117.109

2.573

666.007

423.299

3.566

267.711

8.233

68.113

731.174

135.085

2.874

309.075

2.571

112.631

551.75

23.378

3.357

302.104

55.084

55.733

540.952

110.899

0.962

3 COM (0 +)

4 HRAT (0 +)

5 RRAM (6 +)

sc,r 0

1

.U,r 0

.0.01 L,0 r

.L,0 0

X96,0 0

Y96,0 0

sc,r 3

1

.U,r 3

.0.01 L,3 r

.L,3 3

X96,0 3

Y96,3 0

sc,r 1

1

.U,r 1

.0.01 L,1 r

.L,1 1

X96,0 1

Y96,1 0

sc,r 4

1

.U,r 4

.0.01 L,4 r

.L,4 4

X96,0 4

Y96,4 0

sc,r 2

1

.U,r 2

.0.01 L,2 r

.L,2 2

X96,0 2

Y96,2 0

sc,r 5

1

.U,r 5

.0.01 L,5 r

.L,5 5

X96,0 5

Y96,5 0

semnif. : sc < 100

0 ASPEFV (4 +)

1 PABT (5 +)

2 TEXC (3 +)=sc

2.803

11.517

435.957

3.918 104

1.28 103

5.458

2.726

4.22

276.663

4.49 104

695.576

11.108

27.731

129.806

2.573

2.877 104

390.531

6.795

9.074

0.211

1.576

731.174

2.884

0.127

490.692

3.089

122.085

2.584 104

23.378

6.936

232.297

32.089

29.332

1.223 104

53.86

0.962

3 COM (0 +)

4 HRAT (3 +)

5 RRAM (6 +)

17

sr,0 c

1

.U,0 c

.0.01 L,c 0

.L,0 0

X98( ),0 0

Y98,0 0

sr,3 c

1

.U,3 c

.0.01 L,c 3

.L,3 3

X98,0 3

Y98,3 0

sr,1 c

1

.U,1 c

.0.01 L,c 1

.L,1 1

X98,0 1

Y98,1 0

sr,4 c

1

.U,4 c

.0.01 L,c 4

.L,4 4

X98,0 4

Y98,4 0

sr,2 c

1

.U,2 c

.0.01 L,c 2

.L,2 2

X98,0 2

Y98,2 0

sr,5 c

1

.U,5 c

.0.01 L,c 5

.L,5 5

X98,0 5

Y98,5 0

semnif. : sr < 10

0 ASPEFV (2 +)

1 PABT (3 +)

2 TEXC (1 +)=sr

2.402

23.234

739.105

1.544 103

983.56

4.367

2.077

4.802

674.426

449.601

472.214

7.512

28.846

284.528

3.446

354.138

316.267

4.681

55.575

9.634

52.626

20.399

237.342

4.374

255.262

3.517

45.216

1.412 103

23.999

3.758

243.89

89.013

96.297

618.304

140.924

1.184

3 COM (0 +)

4 HRAT (0 +)

5 RRAM (6 +)

sc,r 0

1

.U,r 0

.0.01 L,0 r

.L,0 0

X98,0 0

Y98,0 0

sc,r 3

1

.U,r 3

.0.01 L,3 r

.L,3 3

X98,0 3

Y98,3 0

sc,r 1

1

.U,r 1

.0.01 L,1 r

.L,1 1

X98,0 1

Y98,1 0

sc,r 4

1

.U,r 4

.0.01 L,4 r

.L,4 4

X98,0 4

Y98,4 0

sc,r 2

1

.U,r 2

.0.01 L,2 r

.L,2 2

X98,0 2

Y98,2 0

sc,r 5

1

.U,r 5

.0.01 L,5 r

.L,5 5

X98,0 5

Y98,5 0

semnif. : sc < 100

0 ASPEFV (4 +)

1 PABT (5 +)

2 TEXC (4 +)=sc

2.402

15.959

355.948

4.983 104

628.05

5.007

3.03

4.802

473.642

2.115 104

439.682

12.563

59.924

405.153

3.446

2.374 104

419.105

11.144

1.721

0.204

0.784

20.399

4.689

0.155

400.09

3.779

34.113

7.148 104

23.999

6.754

212.81

53.31

40.605

1.738 104

78.622

1.184

3 COM (1 +)

4 HRAT (3 +)

5 RRAM (6 +)