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  • 1

    O OJ

    ,

    Guide to Expression of Uncertainty in Measurement . , , . () . . . . 1.

    19. 20. . , , . . . , , . , . , . , . , , , , 1978.

    . 1980. . , 1993. , , 1. , . . , . . , , , , . . . , , . , dr hc (1897 1976), , : .

    1 , , , , , .

    1

  • 2

    : . . , , . .

    2. ()

    . .

    3.1

    , u (. Uncertainty), s, u = s. . , ,

    , ( ), 68,2 % ( 4.1.3).

    ux s sx

    . . ,

    ni xxxx ,...,...,, 21

    = n ixnx 1s1

    ,

    , uc, . , , , .

    1

    )( 2s

    =

    n

    xxs

    n

    ii

    . (1)

    , ,

    sx

    sxs 2

    , U, , k, , 3 3. , 99 %. , .

    nss

    sx= . (2)

    , ( ) . . ix su = , u .

    sxss=

    . ( . ). , , (, .).

    3.

    , . ( ) , . , . , 1 C. , 20,0 C, 19,0 C 21,0 C. 20,1 C, 0,1 C.

    . C10

    , n . ,

    ss

    )1(2s = n

    ss , (1.)

    (1.) n. , ,

    ss

    =ns /s

    8s

    2 , , 1.3.

    2

  • 3

    27 %. . 3.3

    3.2 , . . . , P I U,

    IUP = . , uI uU. uP . () r . .

    , . , , . . . , , , .

    , , , . , , , . , , . , , .

    4.

    . . , . , . .

    . , , . , . , , . . . , . , . , , . , , .

    , . n . n , . , , . . . . , , , + 200 V. ,

    3

  • 4

    . , ( ). V. . . , (drift) . . , . . 1 N . N N + . , , () , , 4.1.1. 2 U = 1,000000 V. 30 V. 0,999970 V 1,000030 V. ) , ) ) . , .

    4.1

    : (), . .

    4.1.1

    .1. a.

    x x ( -a, +a), . , 1.

    , p(

    . 1

    1d)(p =

    xx )x

    2xx

  • 5

    , .2, , 65%. , .

    .

    , ( ).

    ( , , .) (xmin, xmax).

    ,2/)( maxmin xx += .minmax xxa ==

    . 3 , .

    4.1.2

    4.1.3 ()

    .2.

    , .3, . . .

    . . 2

    p(x)

    xx1 x2

    3 (za = 99,7 %) P 2

    2,58 (za = 99 %) P

    ekvi val entpol u{ i r i nest andardnoodst upawe

    sr edwavr ednost

    P=68,2 %

    1

    p(x)

    xx1 x2

    a

    pol u{ i r i nast andardnoodst upawe

    sr edwavr ednost

    a6

    s=

    P=65,0%

    1a

    .2 . a . . . .2 1, , a/1)(p = , .

    (6) 2xx

    x

    22

    12

    1

    ,/)(p,/)(p

    axxxaxx

    ==

    )()(

    xx

    .3 () .

    ),,(,e2

    1)(p

    2

    21

    =

    xx

    x

    (8) , . 2/1)(p = . , x , . , )3( 99,73%. ,

    p(x) = 0, , , , (6) (4),

    tt us =

    5

    6/tt aus == (7) 3 1.11

    .

  • 6

    , . , , = 3 . 99% . = 2,56 . : 3=k

    , .

    56,2=k

    1s = nn

    sn

    , . 68,2 %, ( .3) .1 .2. , , . .4

    n

    ,

    4 .

    . , ,

    ( 10 == s ) . . 4 , .

    .4 sn 20 40 . ,

    minn20min n

    %2,68P

    40min n , . %99P

    n

    11 2,2

    2N/m

    , . .

    P , .

    , . 2 4.2.

    4.2

    , . . . - 5. , . 4.1. 1, . 1 N/m100,2( )1011 2. .

    , . ( , .

    11101,2 =,N/m10 2111=a

    ) .

    5 , 1.13 4 . , 1.14

    6

  • 7

    , (5), .N/m10577,03/ 211== au

    ) (7),

    .N/m10408,06/ 211== au ) (, - .) . 99 %, , (1),

    99,7 %, u

    .N/m10388,058,2/ 211== au

    03/ == a .N/m10333, 211 2 10 , , 1 g 2. 2 . 1 2 3 4 5 (kg)

    1,002 0,995 1,000 1,008 1,005

    . 6 7 8 9 10 (kg)

    1,011 1,003 1,012 1,006 1,001

    . . . (1), ( )

    g3,1004s =m

    g.2,5== su ,

    g)29,03/5,0( = , 1 4 (5). . U . : g0,93 == uU ; T : g7,126 == uU ; g4,1358,2 == uU , ( %),99=P U . %)7,99(,g6, =P153 == u , a . U . %

    .91s == nn%99=P

    ,99=P

    sn

    9.16 g25,3 == u73

    g2,2109,4 == uU

    100

    . .

    n

    1 , . , , , , . . - 6 . . 1 , .

    .

    , (99 % 99,7 %) (2,58, 3).

    ( %99=P ) .

    .

    5.

    , . , , . .

    n . .

    , . . .

    6 , 1.15.

    7

  • 8

    . ,

    . .

    ixix

    1

    ..

    (P = 100 %)

    0,577 a 57,7 % a5,0

    1,73

    (P = 100 %)

    0,408 a 65,0 % a1

    2,45

    P = 99 %

    0,388 a

    68,2 %

    a03,1

    2,58

    P = 99,7 %

    0,333 a

    a20,1

    3

    5.1

    ,

    , . , . , .

    ),...,...,( 21 ni xxxxfy =ix

    7

    = 2

    2

    ixi

    y sxys (9)

    .

    (9),

    ixs

    ,( 1xfixix ),...,...2 nxxy =

    ix

    = 2

    2

    ixi

    y uxyu (10)

    . (10)

    . ,

    ixu ix

    ix

    V , m

    Vm /= . ( ), . , , . , .

    ,( 1 xxfy =

    y

    , 5.3.

    5.2

    .

    ),...,...,( 21 ni xxxxfy =y 8

    = ii xxyy . (11)

    ),...,...2 ni xx ,

    (11),

    ix

    = ixi uxyu (12)

    ( ) . (11) , yu

    7 , 1.7. 8 , 1.7

    8

  • 9

    u .

    ix

    x1

    1x

    21uxx

    9 ,

    ),( 21 xxr11 r .

    r . 1x 2x

    1),( 21 =xxr bax += 2 , ( a ), . . , 5.3.

    b

    .0),( 1 xxr 2

    , , , 1,(0

  • 10

    IRV nn =

    ItRtV )()( = , nVn /)()( tVRtR = . ,

    . ,

    nR)t

    1nV (V

    )),(( n VtVr ,

    .1=

    i

    e

    RR

    iR

    0)

    ,

    , ,

    . (10) ,( ji RRr

    . , , , .

    18, 010R =R e = uu eR

    %)99(,58,2 == Pk ,

    , . 46= ,0eRu=e kU R )46,01000= (eR .

    nF500=eCnF100=C

    .nF1,0C =

    eC

    =Ce iC

    1),( ji CCrCu

    eC

    nF5,05 C =U

    C 5e =

    Ce =UeC

    nF)5,0500(e =C

    )(tR nR

    0/ nn RuR )(t

    Vn =ItRt )()( =

    IRn

    I)(tR

    .

    nn /)()( VR

    tVtR =

    2nnn

    /)()( VtVRV

    tR = (12)

    n2

    n)(

    nn)(

    )(1VtVtR u

    VtVu

    VR =u . (14) 3,

    . (14)

    )(tR

    . ( ) U . U .

    n

    VtVtR

    Vu

    tVu

    tRu

    n

    )()()()( = (15)

    , , . (15) .

    nR )(tRVVtV uuu == n)(

    )()()()(

    tVu

    tRu tVtR

  • 11

    V , ( ). , (10) ,

    )(t nV

    nn /)()( VtVRtR =

    2

    n

    n

    RuR

    (tV

    Vu

    )

    )

    Ru

    )(tR

    C05,0 o

    mW.

    - . - 1 . 710- ( C.)123 o2

    n

    )(

    )()( +

    =Vu

    ttRu VVtR (16) - < %.60

    . V , ,

    ) n ( ), . , , , , . , , . , .

    n

    n(

    ( Ru

    tRtR . (17)

    (17) , .4, .

    4 5.3.3. , , .5. .

    6. E M

    . . , , . , , .

    - , . VR- ,

    . 4321 ,,, RRRR- , . )(tI-

    .

    )(tT),( tTR

    - , . Tu

    , . 1% 5% . , .

    ( ,

    T

    T c

    onst

    .~ ~

    Rn

    R( )T V( )T

    Vn

    I

    1.288453 V

    vi sokoomskivol t met ar

    et al onskiot por ni k

    pl at i nskit er momet ar

    stru

    jni

    gene

    rato

    r

    t er most at

    dvopol o` ajnipr eki da~

    , ,

    . , , . .

    610

    - 100 . .5 .4,

    . - , , . - () . C23 o

    , ).

    - . , .

    - 10

    11

  • 12

    , , , .

    , , ( , , , , , , ).

    , , . , , . , , . .

    . . , . , , , . .

    6.

    3 . 3 . , .

    I1x

    3

    -

    -

    I 1 x1

    II n, n>>1 (.6, )

    nsu /A =

    As ukx

    ( I)

    III 1

    Bu

    Bs ukx ( I)

    IV 1

    BuC

    Bukx Cs

    () ( II

    III)

    V n -

    CABu

    CABs ukx

    VI n (. 6 )

    o, . .

    CUu

    CUukx s

    - (, -)

    12

  • 13

    13

    : .

    U

    ()

    ) )

    )

    ucBucAB

    ucu k.

    = k u cu.Uc

    = =sxs uAsn

    (xi s-x )2

    n - 1=s

    ?

    6 ) ; ) ; ) VI, 3.

  • . . . , , , .6 , ( 3.1). , , , .6 . 3, , . 1 2 4.

    II

    III

    IV

    V

    V

    VI

    V

    II III IV V

    ( ). , 5 5.3. , . , ( ) ( ). , 1 5.3. . 3 ( 6). . , , . ( ) . 6 . , , ,

    Guide to Expression of Uncertainty i Measurement, BIPM, IEC, IFC, ISO, IUPAC, IUPAP, OIML, Geneva 1993. ., , , 1997. B.Taylor, C.Kuyatt Guidelines of Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, Gaithersburg, 1994 Edition. K.Sommer, M.Kochsiek, Role of Measurement Uncertainty in Deciding Conformance in Legal Metrology,OIML Bulletin Vol.XLII, Number 2, April 2002. Expression of Uncertainty of Measurement in Calibration, EAL-R2, Edition 1, 1997. Abstract The aim of this contribution is to present in a short and concise manner the essence of the book Guide to the Expression of Uncertainty in Measurements that is today the international reference in the field of the Uncertainty of obtained experimental results. The majority of readers have not the necessary knowledge of random processes and basic error theory that is indispensable for practical use of the mentioned book. This contribution has to be the basis for future use as one of the textbook chapters for the undergraduate study. That is the reason why many rigid mathematical proofs are omitted. Many examples taken from the different subjects in electrical engineering have been supplied to make the better and easier understanding of the essence of related field.

    14

    14

    n, n>>1 (??.6, ? ? ?)n (??. 6 ?)