Evolution Pre 1978 80 Randomsystematic error Error propagation

측정불확도의 변천 (Evolution) Pre 1978 -80 Random/systematic error; Error propagation in chemistry (Eckschlager 1961); Collaborative study • 1982 BIPM INC-1 (1980) – Type A / Type B – Combine as variances 1986 1993 1995 1997 2000 • • • AOAC Stats manual (Development/validation) ISO 5725: 1986 (Collab trial) ISO Guide • ISO 5725: 1994 (Adds Trueness) EURACHEM Guide 1 st ed 2 nd EURACHEM workshop l New EURACHEM guide Korea Laboratory Accreditation Scheme

EURACHEM/CITAC Guide Korea Laboratory Accreditation Scheme

측정의 불확도 란 ? “A parameter, associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand” (ISO Guide) “충분히 타당성 있는 이유에 의해 측정량에 영향을 미칠 수 있는 값들의 분포를 특성화한 패러미터. “ The number after the ± Korea Laboratory Accreditation Scheme

측정량(Measurand) 이란 ? The particular quantity that is subject to the measurement 측정하고자 하는 특정 대상에 대한 량 5. 5 5. 3 5. 6 Korea Laboratory Accreditation Scheme 5. 5 5. 8 5. 2 5. 3

측정불확도의 도식적 표현 9 11 10 ± 1 ± 0. 5 8. 5 ± 0. 5 9. 5 Korea Laboratory Accreditation Scheme 10. 5 11. 5

GUM에 의한 측정불확도 추정 1. 모델식(측정량의 함수) 표현: y = f ( x 1, x 2, . . . xn ) 2. 입력량의 표준불확도( standard uncertainty, u(xi))의 계산 – A형 평가 – B형 평가 3. 합성표준불확도(combined standard uncertainty, uc(y))의 계산 4. 확장불확도(expanded uncertainty : U = k· uc(y) )의 계산 Korea Laboratory Accreditation Scheme

Eurachem에 의한 측정불확도 추정 Korea Laboratory Accreditation Scheme

Eurachem에 의한 측정불확도 추정 Korea Laboratory Accreditation Scheme

측정불확도 모델 (Model) xi y = f(xi, xj xk x j, xk, . ) Korea Laboratory Accreditation Scheme y

측정불확도 모델 (Model) xi xj xk y = f(xi, xj, xk, . ) Korea Laboratory Accreditation Scheme y u(y)

측정불확도 모델 (Model) xj xi + xk + y = f(xi, xj, xk, . ) Korea Laboratory Accreditation Scheme y u(y)

측정불확도 요인 (Influence Factors) xi xj + xk + Analyst 1 y 2 y 3 y 4 Analyst 2 Analyst 3 Analyst 4 Combined distribution Nominal range Korea Laboratory Accreditation Scheme s. R u(y) Values

현실적 접근 (Real World Problems) “Well characterised” quantified effects, differentiable, continuous, traceable WELL POORLY Poorly characterised; Unpredictable effects; Input parameters unclear Measurement model applies Whole method study applies Korea Laboratory Accreditation Scheme POORLY WELL

요인 분석도 (Cause & Effect Diagram) 적정(Titration)을 통한 HCl solution의 농도 V(Titration) c(Na. OH) c(HCl) V(HCl) Korea Laboratory Accreditation Scheme

요인 분석도 (Cause & Effect Diagram) V(Titration) c(Na. OH) Temperature Calibration Dosing Repeatability Bias Repeatability End-point c(HCl) Calibration Repeatability Temperature V(HCl) Korea Laboratory Accreditation Scheme

Grouping Sources V(Titration) c(Na. OH) Temperature Calibration Dosing Repeatability Bias Repeatability End-point c(HCl) Calibration Repeatability Temperature Repeatability Korea Laboratory Accreditation Scheme V(HCl)

Grouping Sources V(Titration) c(Na. OH) Temperature Calibration Dosing Bias End-point c(HCl) Dosing Calibration End-point Temperature V(HCl) Repeatability Korea Laboratory Accreditation Scheme V(HCl)

Cause & Effect Diagram GC ratio IS area GC Ratio Sample peak area GC Response factor Repeatability Calibration IS Concentration Repeatability Standard volume Repeatability Flask Calibration Purity Pipette volume Balance calibration Balance linearity Buoyancy correction Weight used Sample weight “Recovery” Temperature Calibration IS Volume Temperature Analytical result Internal Standard weight Korea Laboratory Accreditation Scheme Experiment: Recovery for representative matrices, levels (replicated)

Forensic alcohol standard titration Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

Uncertainty in Analysis Process Korea Laboratory Accreditation Scheme

A Type 표준 불확도 • 반복측정에 의한 구한 Raw Data를 통계적인 방법에 의해 구한 불확도 • Std. dev. of n repeated measured readings: n Standard uncertainty : Korea Laboratory Accreditation Scheme

A Type 표준불확도의 자유도 v=n-1 자유도 : Degree of Freedom Korea Laboratory Accreditation Scheme

A Type 표준 불확도 Korea Laboratory Accreditation Scheme

A Type 표준 불확도 Log Korea Laboratory Accreditation Scheme 10 변환

A Type 표준 불확도 Korea Laboratory Accreditation Scheme

A Type 표준 불확도 (Sp) Pooled Estimate Stdev : 합동표준편차 m 2/1 3/1 4/1 1회 0. 028 0. 029 2회 0. 084 0. 083 0. 081 3회 0. 135 0. 131 0. 133 Vi 2 2 2 SI 0. 053 0. 051 0. 052 측정횟수 Korea Laboratory Accreditation Scheme

A Type 표준 불확도 (Sp) Korea Laboratory Accreditation Scheme

A Type 표준 불확도 (Sp) Korea Laboratory Accreditation Scheme

A Type 표준 불확도 (Sp) Korea Laboratory Accreditation Scheme

Microbiological Test에서의 불확도 Korea Laboratory Accreditation Scheme

Microbiological Test에서의 불확도 Korea Laboratory Accreditation Scheme

Korea Laboratory Accreditation Scheme

정규분포 (NORMAL DISTRIBUTION) 6 8 % 95 % -4 U = k u c -3 -2 -1 0 1 2 3 4 불확도 : 0. 2 (단, 약 95 % 신뢰구간에서 k = 2) Korea Laboratory Accreditation Scheme

직사각형 분포 (Rectangular Distribution) 1 Standard Uncertainty = a/ 3 a a 1/2 a -a 58% ut Korea Laboratory Accreditation Scheme +a

삼각형 분포 (Triangular Distribution) 1 Standard Uncertainty = a/ 6 a a 1/a 65% -a ut Korea Laboratory Accreditation Scheme +a

합성 표준불확도(Combined Standard Uncertainty) • 함수 f (x)를 이용한 불확도 전파의 법칙 에 의해 산출. • 이중 제곱근 합 : Root-Sum-square (RSS) - Addition of individual uncertainty contributions in the system “The expanded Taylor Series” Korea Laboratory Accreditation Scheme

이중제곱근 합 : Root-Sum-Square (RSS) u 2 • Standard deviations u 1 • Established error propagation theory • Addition of individual uncertainty contributions in the system Korea Laboratory Accreditation Scheme

감도 계수 (Sensitive Coefficient) W = 10 m ± 2 m 감도계수 (Sensitive Coefficient) : 각 불확도 인자가 전체 불확도에 미치는 영향 감도계수 = c A = 100 m 2 W = 10 m ± 2 m Korea Laboratory Accreditation Scheme

상대표준불확도의 활용 Y = A [a(x) X b(x) X c(x)] Ur = Relative Standard Uncertainty Korea Laboratory Accreditation Scheme

합성 표준불확도의 활용 사례 1 사례 2 사례 3 Korea Laboratory Accreditation Scheme

상대표준불확도의 활용 Korea Laboratory Accreditation Scheme

상대표준불확도의 활용 Korea Laboratory Accreditation Scheme

화학분석 불확도 • • • Balance Calibration Mass of Reference Material Uncertainty of RM Purity Reference Material Purity Precision as SD Typical Test Result Homogeneity (2 ug/g ± 4. 9 %) Recovery Precision as SD Recovery Korea Laboratory Accreditation Scheme ± 0. 08 mg 2. 0 mg ± 2. 89 % 95 % ± 0. 1 ug/g 2. 0 ug/g ± 0. 098 ug/g ± 3% 85 %

화학분석 불확도 Korea Laboratory Accreditation Scheme

Resp’se 검량선(Calibration Curve) 불확도 Conc. Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 여기서, p는 y값의 측정횟수 Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 Concentration [mg 1 -1] 1 2 3 0. 1 0. 028 0. 029 0. 3 0. 084 0. 083 0. 081 0. 5 0. 131 0. 133 Value STDEV B 1 0. 2410 0. 0050 0. 7 0. 180 0. 181 0. 183 B 0 0. 0087 0. 0029 0. 215 0. 230 0. 216 Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 B 1 P n C 0 : Slope , Bo : Intercept : Number of measurements to determine conc. : Number of measurements for the calibration : Determined concentration : Mean value of the different calibration standards I : Index for the number of calibration standards to obtain the calibration Curve J : Index for the number of measurements Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 2 Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 EURACHEM Page 75 Korea Laboratory Accreditation Scheme

확장불확도 (Expanded Uncertainty) U = k uc ◆ k = 포 함 인 자 (Coverage Factor) ▶ t 분포도에서 보정계수 선정 - 희망 신뢰수준 (Confidence Level) - 유 효 자 유 도 의 계 산 (Welsh - Satterthwaite Equation) ▶ 포함인자 “ k ” = Student Factor "t"이다. - (Veff, F%), F % 신뢰구간 Korea Laboratory Accreditation Scheme

T’s Distribution’s Table (t 분포표) Korea Laboratory Accreditation Scheme

유효자유도의 계산 Welch-Satterthwaite formula Korea Laboratory Accreditation Scheme

유효자유도의 계산 Welch-Satterthwaite formula Korea Laboratory Accreditation Scheme

확장불확도 (Expanded Uncertainty) 1. 신뢰수준의 결정 ( 95%, 99% etc. ) 2. 유효자유도의 결정 3. t 값의 결정 4. 확장불확도의 계산 U = k · uc(y) CL 99. 5 50 Korea Laboratory Accreditation Scheme 99. 8 80 90 95 98 99

T’s Distribution’s Table (t 분포표) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (1/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (2/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (3/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (4/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (5/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (6/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (7/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (8/9) Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (9/9) Korea Laboratory Accreditation Scheme

Questions & Answers 감사합니다! Thank You ! Korea Laboratory Accreditation Scheme