Невизначеність вимірювання в метрологічній практиці. Повторні вимірювання та ієрархічні експерименти

1 2 4

1 2 З? 4 4.1 4.2 4.3 4.4 5 5.1 5.2 5.3 5.4 5.5 6 7 7.1 7.2 7.3 8 8.1 8.2 8.3 8.4 8.5 8.6 —? —? —? —? —?

MEASUREMENT UNCERTAINTYFOR METROLOGICAL APPLICATIONS Repeated measurements and nested experiments
1

2 ISO 3534-1:1993 Statistics — Vocabulary and symbols — Part 1: Probability and general statistical terms
ISO 3534-3:1999 Statistics — Vocabulary and symbols — Part 3: Design of experiments
ISO 5725-1 Accuracy (trueness and precision) of measurement methods and results — Part 1: General principles and definitions
ISO 5725-2 Accuracy (trueness and precision) of measurement methods and results — Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method
ISO 5725-3 Accuracy (trueness and precision) of measurement methods and results — Part 3: Intermediate measures of the precision of a standard measurement method
ISO 5725-4 Accuracy (trueness and precision) of measurement methods and results — Part 4: Basic method for the determination of the trueness of a standard measurement method
ISO 5725-5 Accuracy (trueness and precision) of measurement methods and results — Part 5: Alternative methods for the determination of the precision of a standard measurement method
ISO 5725-6 Accuracy (trueness and precision) of measurement methods and results — Part 6: Use in practice of accuracy values
Guide to the expression of uncertainty in measurement (GUM), BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, 1993, corrected and reprinted in 1995.
ISO 3534-1:1993 ISO 3534-3:1999 ISO 5725-1 ISO 5725-2 ISO 5725-3 ISO 5725-4 ISO 5725-5 ISO 5725-6 3.1 3.2

3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 [ 3.11 [ 3.12 [ISO 3534-3, 3.13 4 4.1

а?) Ь?) с?) d) е?) GUM 4.2 а?) Ь?) с?) d) —? —? 4.3.1 —? —? —? 4.3.2 а?) 1) —? —? —? 2) Y=f(X, 3) Ь?) с?) d) 4.4 5 5.1 5.1.1 —? —? —? —? —? 5.1.2 —? —? 5.2.1 5.2.2 5.2.2.1 а?) Ь?) с?) —? —? —? Yikj =

5.2,2.2

а?) Ь?) с?) d) е?) f) д?) h) і?) j) /=1 >1

LK(J-V

— 1 J
I 5.2.3 5.2.3.1 —? —? 5.2.3.2 Ykj = 5.2.3.3 —? —? 5.2.3.4 а?) Ь?) с?) d) е?) f) h) і?) j)

,

- _ MS D -MS E

g d ~ ~ 5.3 5.3.1 — —? —? —? —? —? —? 5.3.2 5.3.3 1 Q 5.3.4 5.4 5.4.1 а?) Ь?) 5.4.2 5.4.3 Vl, 2 Ms item -MS E
"^inh d =— J /- MS item — S'Y — u inh = max (S inh . 0).
5.4.4

5.4.5

5.5 5.5.1

* ( а?) Ь?) с?) d) —? —? —? —? Yi = Y - 0 = ( Y =0+ b + . Y to = 5.5.2 5.5.2.1 Y ki (k=l Y ki = 9 + b k + Y.i = 0 + / . bk = Y - Y - h ' S- ( 5.5.2.2
5£?4/
—? —? —?

5.5.3 5.5.3.1 5.5.3.2
X — Y — 1,..., 5 —
Sb2!i3 -
11 [0,0001879-(-0,0001841)]
5.5.4 5.5.4.1 5.5.4.2 29
6 = ^1—= -0,00383.
29
= 0,00096 0,01
-0,02 - 0 5 10 15 20 25 Y
X — 1 5 — 6 6.1 —? —? —? —? —? 6.2 —? —? —? 6.3 а?)

Ь?)

„=-4= 7 7.1 7.1.1 7.1.2 —? —? 7.1.3 а?) Ь?) с?) S a ^W 1 Z dXJdZJ S z — Sxz — df/dX — 7.1.5 7.1.4 —? —? —? Y = f(X, Z,...),
b) 3 7.2 7.3 4n ■?JN
II
Nl| X! X Vni) x 2 z 2 xz 8 8.1 а?) Ь?) с?) —? —? 8.2 8.2.1 —? J = 6 —? —? L - 2 ^Ikj = 8.2.2 — —? —? —? —? —? —? 8.3
MS RtRx—MS E v 2 D =S 2 D = = 0,0004866
5
, „ MSp,-MS DlR
d R =S R = — = 0,0001987.
R R 8.4 8.4.1 —? 1 = —? 2 = —? —? 4 = —? 5 = 8.4.2 8.4.3 а?) Ь?) = 0 1 01618 =0 , 005117
8.5 8.5.1 8.5.2 8.5.3 X — 1 5 —

8.6 8.6.1 Ylkj = Y 8.6.2 8.6.3 8.6.4 2 4-MS e , MS DR] MSr c 5 6 30 ^ 2362

U = 2,11 - b k ■?— S 2 — S| — S 2 onfg — Sj -— S 2 un — MS — MS D — MS D ( R )— MS E — MS inh — MS inst — MS item — MS R — SS — SS D(R) — SS e — SS R — 5 — V — — 1 2 Carroll Croarkin and Ruth Varner. Measurement Assurance for Dimensional Measurements on Integrated-circuit Photomasks, NBS Technical Note 1164, U.S. Dept. Commerce, 1982, 44 pp.
3 J. R. Ehrstein and M. C. Croarkin. Standard Reference Materials: The Certification of 100 mm Diameter Silicon Resistivity SRMs 2541 through 2547 Using Dual-Configuration Four-Point Probe Measurement, NIST Special Publication 260—131, 1998, Revised, 84 pp.
4 Churchill Eisenhart. Realistic Evaluation of the Precision and Accuracy of Instrument Calibration Systems J Research National Bureau of Standards-C. Engineering and Instrumentation, 67C (2), 1962, pp. 161—187. *
5 Gerald J. Hahn and William Q. Meeker. Statistical Intervals: A Guide for Practitioners, John Wiley & Sons, Inc., New York, 1991, p. 61.
6 Harry Ku. Notes on the Use of Propagation of uncertainty Formulas. J Research of National Bureau of Standards-C. Engineering and Instrumentation, 70C (4), 1966, pp. 263—273.
7 Samuel Kotz and Norman L. Johnson. Encyclopedia of Statistical Sciences, Vol. 2, John Wiley & Sons, New York, 1982, p. 29.
8 Mary Gibbons Natrella. Experimental Statistics, NBS Handbook 91, US Dept. Commerce. 1963.
9 Stephen Wolfram. Algebraic software, A System of Doing Mathematics by Computer, 2 nd edition, Addison Wesley Publishing Co., New York, 1993.
10 ASTM Method F84-93, Standard Test Method for Measuring Resistivity of Silicon Wafers With an In-line Four-point Probe. Annual Book of ASTM Standards, 10.05, West Conshohocken, PA 19428.
11 Measurement Systems Analysis Reference Manual. Chrysler Corp., Ford Motor Corp., General Motors Corp., 2 nd ed., 1995, 120 pp.
12 Determining and Reporting Measurement Uncertainties, National Conference of Standards Laboratories RP-12, 1994, Suite 305B, 1800 30 th St., Boulder, CO 80301.
13 International vocabulary of basic and general terms in metrology (VIM). BIPM, lEC, IFCC, ISO, IUPAC, IUPAP, OIML, 2 nd ed., 1993, 59 pp.
14 ISO Guide 35 Certification of reference materials — General and statistical principles.
15 ISO/TS 21748 Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation.
1 2 Carrol! Croarkin 4 Churchill Eisenhart. 5 Gerald J. Hahn 6 Harry Ku. 7 Samuel Kotz 8 Mary Gibbons Natrella. 9 Stephen Wolfram. 10 11 12 13 14 ISO Guide 35 15 ISO/TS 21748

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