incertidumbre metodos analiticos

7/30/2019 Incertidumbre metodos analiticos

http://slidepdf.com/reader/full/incertidumbre-metodos-analiticos 1/50



©SPEX CertiPrep 2011

Housekeeping

Everyone in attendance will receive a copy of the slides

The webinar is being recorded and will be available foreveryone to view on demand

– The recording will be posted about one week after the

event

Questions will be answered at the end of the presentation

– Type any questions you may have into the question box

and we will answer them during the Q & A portion

Stay tuned after the Q&A session – we’re giving away afree gift!




Topics Covered

Precision & Accuracy

Precision & Accuracy

Confidence Limits

Confidence Limits

Errors in Measurements

Errors in Measurements

Uncertainty in Measurements

Uncertainty in Measurements




True Value (TV)

MethodMethod

InstrumentInstrument

Skill of the OperatorSkill of the Operator




Central tendency

Not an absolute value

Estimate of true value

Average (0)

Sum of the results of each measurement

number of measurementsAverage (0) = 0 =

…

True value is described by average

and standard deviation

or

Average is:




Standard Deviation (s)

0 ±1.96 s at 95% Confidence Interval

0±2.94 s at 99% Confidence Interval

Standard Deviation (s)

You can narrow your estimate of True Value using standard deviation

Can also be described as sigma,

True Value can be expressed as:

0 1




Accuracy & Precision

PrecisionPrecision

• Reproducibility of the method

• Evaluated by Average Deviation,Variance and Standard Deviation

AccuracyAccuracy

• Correctness of the measurementin relation to the true value

• (TV=0 ± E) or Measured value ±E

True Value ( ) = 8.50

7

8

9

10

1 2 3 4 5 6 7 8

V a

l u e s

Measurement #

Good Accuracy (0 = 8.55)

7

8

9

10

1 2 3 4 5 6 7 8

V a l u e s

Measurement #

Poor Accuracy (0 = 7.39)

7

8

9

10

1 2 3 4 5 6 7 8

V a l u e s

Measurement #

Good Precision (0 = 8.55)

7

8

9

10

1 2 3 4 5 6 7 8

V a l u e s

Measurement #

Bad Precision (0 = 8.55)




Evaluation of Precision

Key Word Symbol Equation Description

Average

DeviationAD

The smaller the AD, the

more precise the

measurements

Not an accurate measure

of precision

Variance V Indicates the spread of

measurements around the

data

Better measure of

precision

Standard

Deviations The amount of variation or

spread from the True Value

AD

s 0 1

0

0 2 1




Glossary Review

Key Word Symbol Equation

Average 0

Standard Deviation s

0 …

s 0

1




Uncertainty

Uncertainty is a parameter associated with the result of

measurement, that characterizes the dispersion of the valuesthat could be reasonably attributed to measured value

Error vs. Uncertainty:

– Error: Usually can’t be estimated

– Uncertainty: Can be estimated




Uncertainty Estimation

Determine what is to be measuredDetermine what is to be measured

Outline the various processesOutline the various processes

Identify sources of uncertaintyIdentify sources of uncertainty

Estimate uncertainties from eachsourceEstimate uncertainties from eachsource

Combine and expand all uncertaintyCombine and expand all uncertainty




Types of Uncertainty

Type A Type A• Usually associated with

repeated measurements

• Type A uncertainty isexpressed as:

Type B Type B• Based on scientific judgment

made from previousexperience, manufactures’specifications, etc.

• Three common models are:

Where s is standard deviation

and n is the number of replicates

o Rectangular

o Triangular

o Normal




Type B: Rectangular Distribution

Use this when a certificate or other specification gives limitswithout specifying a level of confidence

Normalizing factor for converting to Standard Uncertainty is

X

3




Type B: Triangular Distribution

This is used when distribution is symmetric and when values closeto the target value are more likely than near the boundaries

Example: Uncertainty associated with volumetric glassware


6

X




Type B: Normal Distribution

This is used when an estimate is made from repeated observations of a randomlyvarying process and an uncertainty is associated with a certain confidenceinterval.

Example: A calibration certificate with stated level of confidence.


X

2




Combined Uncertainty (uc)

We will be using the following model to combine overall uncertaintiesfrom all of the processes:

We will use the following model for calculating interim uc within aprocess:



Slide 19

m1 should one of these be X bar?msnyder, 10/25/2011




Glossary Review

Key Word Symbol Equation

Average 0

Standard Deviation s

Combined Uncertainty

Expanded Uncertainty

0 …

s

0

1




Uncertainty in the

measurement of a gold

solution, analyzed by ICP




Review of the Steps

Determine what is to be measuredDetermine what is to be measured

Outline the various processesOutline the various processes

Identify sources of uncertaintyIdentify sources of uncertainty

Estimate uncertainties for each

source

Estimate uncertainties for each

source

Combine all the components andexpandCombine all the components andexpand




Process Outline for Analysis of Au

Components: Symbol Value

NIST SRM conc• Weighing

• Flask

• SRM value

Stdp 100.225 mg/L

Sample Dilution• Pipette

• Flask

Crmf 100 fold

SRM Measured conc Stdm

100.985 mg/L

CRM Measured conc Crmm 100.797 mg/L




Determination of concentration

CCrm Std Crm

Std

Where:

Cau = Concentration of Au in sample

Crmm = ICP measured concentration of sample

Crmf = Dilution factor for sample

Stdp = Prepared concentration of SRM

Stdm = ICP measured concentration of standard

C 100.797100.225100100.985

10,004mg/L

Component Symbol Value

NIST SRM conc• Weighing

• Flask

• SRM value

Stdp 100.225mg/L

Sample Dilution

• Pipette

• Flask

Crmf 100 fold

SRM Measured conc StdM 100.985 mg/L

CRM Measured conc CrmM 100.797 mg/L




ICP-Sample

measurement

(Crmm)

ICP-SRM

measurement

(Srmm)

Tolerance Temp

Vol

COA

Prep. SRM (Stdp)

Mass

Uncertainty Sources

The aim is to identify all major uncertainty sources and to understand their

effect on the analyte and its uncertainty

Uc(Cau)

Pipette

Flask

Sample dil (Crmf )

Tolerance Temp

Tolerance Temp




Uncertainty from SRM - U(Stdp)

Weighing onthe balanceWeighing onthe balance

500 mLFlask

SRMCertification

Used NIST SRM 3121 for calibration

To prepare the SRM:

– Weighed 5.067 g

– Diluted to 500 mL in a volumetric flask

There are 3 uncertainties associated with this process:




U(Stdp) – From the Balance


500 mL FlaskSRM

Certification

1

√3

Device Value (V) Standard uCombined u

(uc)

Relative u

( )

Balance 5.0670 g 8.165 x 10-5 8.165 x 10-5 1.611 x 10-5 2.597 x 10-10

Uncertaintyfrombalancecalibration Listed

NormalizationFactorforRectangularDistribution

0.00013

5.774 10

StandardUncertainty TareWeight GrossWeight

5.774 10 5.774 10

8.165 10




U(Stdp) – From the Flask


SRMCertification

500 mLFlask

There are 2 uncertainties associated with the dilution:

u ListedTolerance6

0.26

.

.

u ThermalCoefficientofWater TempVariation Volume

NormalizationFactorforRectangularDistribution 2.1x10oC/mL 3oC 500mL

3

,triangular




U(Stdp) – From the Flask (cont.)

DeviceValue

(V)uvolume utemp

Combined u

(uc)

Relative u

( )

Flask 500 mL 0.08165 0.1819 0.19935 0.0003987 1.5897 x 10-7


SRMCertification

500 mLFlask

CombinedUncertaintyu

0.08165 0.1819

0.19935 Relative

0.19935

500 0.0003987




U(Stdp) – From the SRM Cert.


500 mL Flask

DeviceCertified

SRM Value

(V)

Expanded uCoverage

Factor Standard u Relative u

COA 9.89 mg/g 0.02 2 0.01 1.0111 x 10-3 1.0224 x 10-6

SRMCertification

Standardu ExpandedCoverageFactor 0.022 0.01

Relativeu StandardV 0.019.89 1.011x10




Total Uncertainty Due to Stdp

Add each uncertainty component from the preparation of the standard…

Balance 1.61 x 10-5 2.597 x 10-10

500 mL Flask 0.0003987 1.5897 x 10-7

SRM

Certification0.001011 1.0224 x 10-6

Total: 1.1816 x 10-6

U t i t f S l Dil ti




Uncertainty from Sample Dilution -U(Crmf )

500 mLFlask

Pipette

To prepare the sample:

– A 5 mL of the sample was diluted to 500 mL

There are 2 uncertainties associated with Crmf :




U(Crmf ) – From the Pipette

u ListeduNormalizationFactorforTriangularDistribution

0.016

.

.

Pipette 500 mL Flask

u ThermalCoefficientofWater TempVariation Volume


3




Pipette 500 mL Flask

CombinedUncertainty

0.004082 0.1819x10

0.004469

Relativeu CombinedV

0.0044695

.

U(Crmf ) – From the Pipette (cont.)




Pipette

U(Crmf ) – From the Flask

Flask

u ListeduNormalizationFactor

0.26

0.08165

.

ThermalCoefficientofWater TempVariation Volume


3

TypeB,triangular



ICP Measurement for standard




ICP Measurement for standard-U(Stdm)

Measurement Stdm conc (mg/L)

1 101.260

2 100.853

3 100.985

4 101.542

5 100.914

6 100.685

7 101.251

8 100.720

9 100.654

0 100.985

s 0.29397

0 1

s 0.29397mg/L

0 … 100.985mg/L

St d d C t ti M t




Standard Concentration Measurement-U(Stdm)

0.293979

0.09799

0.09799

100.985

0.00097035

Value

(V) sd # reps uc

Stdm 100.985 0.29397 9 0.09799 0.00097035 9.4158 x 10-7

ICP Measurement for sample-




ICP Measurement for sampleU(Crmm)

Measurement Crmm conc (mg/L)

1 100.200

2 100.781

3 101.054

4 101.108

5 100.775

6 100.854

7 100.578

8 101.075

9 100.752

0 100.797

s 0.3065

0.3065mg/L x 0 n 1

s

0 …

100.797mg/L



Concentration And Uncertainty of




Concentration And Uncertainty of Au Solution By ICP-OES

Symbol Input

Stdp Uncertainty SRM prep 1.1816 x 10-6

Crmf Uncertainty sample prep 9.5793 x 10-7

Stdm

Uncertainty SRMmeasurement

9.4158 x 10-7

Crmm

Uncertainty samplemeasurement

1.0273 x 10-6

Total uc

4.10843 x 10-6

0.002026927

Uc (Cau)0.002027 x (10004) 20.2771




References

Kocherlakota, N, Obenauf, R, “A statistical approach toreporting uncertainty”

Quantifying Uncertainty Measurements,Eurachem/CETAC Guide

Kocherlakota, N, Obenauf, R, “Quantitative Calculation of Uncertainty Associated with Gold Reference Material,” To

be published by NIST

British Standards 1797:1952




Questions?




New in 2011

Visit www.spexcertiprep.com for more information!

2011-2012 Catalog – Now

available on CD!

New Consumer Safety

standards kit for USP 232(Part#USP-TXM1)




Connect with us!

Come visit us on your favorite social networking site!

facebook.com/spexcertiprep

youtube.com/spexcertiprep@spexcertiprep




Was This Presentation Informative?

We want to continue providing you

with useful and informative webinars!

Complete the survey and tell us what you like, what we can

improve, and what you would like to see in future webinars

Anyone who includes contact information will receive a tokenof our appreciation AND be entered into a drawing to receive

a copy of The Elements!




Free Drawing!

The Elements: A

Visual Explorationof Every Known

Atom in the

Universe

By Theodore Gray




Thank You!

Visit us online atwww.spexcertiprep.com

incertidumbre metodos analiticos

Documents