화학시험에서의 측정 불확도 한 국 화 학 시 험 연 구 원 전 성 주 전 성 주 Korea Laboratory Accreditation Scheme

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

EURACHEM/CITAC Guide Korea Laboratory Accreditation Scheme

The number after the ± 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

The particular quantity that is subject to the measurement 측정량(Measurand) 이란 ? The particular quantity that is subject to the measurement 측정하고자 하는 특정 대상에 대한 량 5.5 5.3 5.6 5.5 5.8 5.2 5.3 Korea Laboratory Accreditation Scheme

측정불확도의 도식적 표현 9 11 10 ± 1 ± 0.5 ± 0.5 8.5 9.5 10.5 11.5 Korea Laboratory Accreditation Scheme

GUM에 의한 측정불확도 추정 1. 모델식(측정량의 함수) 표현: y = f ( x1, x2, . . . 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

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

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

y = f(xi, xj, xk, .) 측정불확도 모델 (Model) x x x y u(y) + + i j k This view of input effect uncertainties leading to uncertainty in the output is fundamental to the ISO method for estimation of measurement uncertainty. To use this method, we must have a mathematical model - that is, an equation - that describes the relationship between input and output. In practice, the ‘model’ we have is simply the equation we use to calculate the result from the input measurements. It is rarely comprehensive, because it deliberately leaves out effects that are either controlled by specification in the method, and because it does not include a precision term. In estimating uncertainty, therefore, we usually have to include an allowance for observed variability (precision), and may have to examine the ‘controlled effects’ (such as specified operating temperature) separately. u(y) Korea Laboratory Accreditation Scheme

측정불확도 요인 (Influence Factors) Nominal range Values + x i j k u(y) Analyst 1 Analyst 2 Analyst 3 Analyst 4 Combined distribution sR y1 y2 y3 y4 Korea Laboratory Accreditation Scheme

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

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

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

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

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

Internal Standard weight Cause & Effect Diagram Internal Standard weight Experiment: Recovery for representative matrices, levels (replicated) Sample weight Balance GC Analytical result GC ratio Ratio IS area Sample peak Response factor IS Concentration Weight used Standard volume Repeatability Flask Calibration Temperature Purity IS Volume Pipette calibration linearity Buoyancy correction “Recovery”   The diagram shows how a list of this kind can support experimental planning. In principle, the overall uncertainty could be obtained by varying every factor separately to the extent of its uncertainty and combining the effects on the result. In practice, this would result in a large number of experiments, and for minor contributions would in any case give poor answers. However, we can take advantage of the fact that whenever a particular experiment does vary factors representatively, any standard deviation from that experiment will include the relevant contributions. In the ‘experiment’ above, the recovery for a GC determination has been estimated for a range of analyte levels and matrices. Though only recovery has been determined, the variation must also have included a range of other factors - chiefly those contributing to the precision of the method. The factors which would be expected to vary naturally and representatively in the experiment have been ‘ticked off’ the list. Notice that most of the remainder are ‘calibration’ contributions. This is quite common - experimental variation rarely covers a representative range of recalibrations. Korea Laboratory Accreditation Scheme

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

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

A Type 표준 불확도 Korea Laboratory Accreditation Scheme

A Type 표준 불확도 Log 10 변환 Korea Laboratory Accreditation Scheme

A Type 표준 불확도 Korea Laboratory Accreditation Scheme

Pooled Estimate Stdev : 합동표준편차 A Type 표준 불확도 (Sp) Pooled Estimate Stdev : 합동표준편차 m 측정횟수 2/1 3/1 4/1 1 회 0.028 0.029 2 회 0.084 0.083 0.081 3 회 0.135 0.131 0.133 Vi 2 SI 0.053 0.051 0.052 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

B Type 표준 불확도 A type 표준 불확도가 아닌 불확도 수학적인 방법에 의해 구한 불확도 2로 나누는 경우 3으로 나누는 경우 6으로 나누는 경우 Korea Laboratory Accreditation Scheme

정규분포 (NORMAL DISTRIBUTION) -4 -3 -2 -1 1 2 3 4 U = k uc 95 % 68 % 불확도 : 0.2 (단, 약 95 % 신뢰구간에서 k = 2) Korea Laboratory Accreditation Scheme

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

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

v = ½(100/R)2 B Type 표준불확도의 자유도 자유도 : Degree of Freedom 사람의 신뢰성을 나타냄 만약, R = 25 % 이면, R = 50 % 이면, R = 0 % (확신하는 경우) Korea Laboratory Accreditation Scheme

“The expanded Taylor Series” 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) Standard deviations Established error propagation theory Addition of individual uncertainty contributions in the system Korea Laboratory Accreditation Scheme

감도계수 (Sensitive Coefficient) : 각 불확도 인자가 전체 불확도에 미치는 영향 A = 100 m2 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 ± 0.08 mg Mass of Reference Material 2.0 mg Uncertainty of RM Purity ± 2.89 % Reference Material Purity 95 % Precision as SD ± 0.1 ug/g Typical Test Result 2.0 ug/g Homogeneity (2 ug/g ±4.9 %) ± 0.098 ug/g Recovery Precision as SD ± 3 % Recovery 85 % Korea Laboratory Accreditation Scheme

화학분석 불확도 Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 Conc. Resp’se 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 0.135 0.131 0.133 0.7 0.180 0.181 0.183 0.9 0.215 0.230 0.216 Value STDEV B1 0.2410 0.0050 B0 0.0087 0.0029 Korea Laboratory Accreditation Scheme

검량선(Calibration Curve) 불확도 B1 : Slope , Bo : Intercept P : Number of measurements to determine conc. n : Number of measurements for the calibration C0 : 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

U = k  uc 확장불확도 (Expanded Uncertainty) ◆ k = 포 함 인 자 (Coverage Factor)    ▶  t 분포도에서 보정계수 선정        - 희망 신뢰수준 (Confidence Level)        - 유효자유도의 계산 (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

포함인자 k의 결정 도수, 확률 값 가상의 결과(∞) 실제의 결과 Korea Laboratory Accreditation Scheme

Welch-Satterthwaite formula 유효자유도의 계산 Welch-Satterthwaite formula Korea Laboratory Accreditation Scheme

Welch-Satterthwaite formula 유효자유도의 계산 Welch-Satterthwaite formula Korea Laboratory Accreditation Scheme

확장불확도 (Expanded Uncertainty) CL 50 80 90 95 98 99 99.5 99.8 신뢰수준의 결정 ( 95%, 99% etc.) 유효자유도의 결정 t 값의 결정 4. 확장불확도의 계산 U = k · uc(y) Korea Laboratory Accreditation Scheme

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

측정불확도의 표현 ◆ 측정값 ± 불확도 (희망신뢰수준) 예시 1) Ms = (1 000,021 47 ± 0,000 70) g   ◆ 측정값 ± 불확도 (희망신뢰수준)    예시 1) Ms = (1 000,021 47 ± 0,000 70) g  (단, 약 95% 신뢰구간, k = 2) 예시 2)         Ms = 1 000,021 47 (단, 95 %의 신뢰구간에서 불확도는 ± 0,000 70 g)    예시 3)          Ms = 1 000,021 47g (70) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (1/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (2/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (3/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (4/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (5/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (6/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (7/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (8/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

예제 : Preparation of Calib STD (9/9) This was included in the ITS CAS OPM appendix so it should look familiar. Its from ECMA-181. The darker bar represents the maximum allowable measurement uncertainty. The lighter bar represents the actual measurement uncertainty which should always be smaller than the allowable. This means, for determination of compliance purposes the dark bar is irrelevant, so let’s eliminate it (next slide). Korea Laboratory Accreditation Scheme

감 사 합 니 다 ! Thank You ! Questions & Answers Korea Laboratory Accreditation Scheme