VDI 3492 Measurement Uncertainty Chapter 9...evaluated filter area and n = actually counted number of fibres λ u and λ o define the lower and upper limit of the 95% confidence intervall

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Seminar for Asbestos Laboratories Israel 2014

APC GmbH 2014

VDI 3492 Measurement Uncertainty

Chapter 9

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Measurement Uncertainty

General

Deviations have

Random sample related instrumental and

subjective

causes

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General

Random sample related deviations are given within a certain measurement plan and cannot be influenced

The two other causes can be minimized

by training and other organisational measures (Seminars)

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General

The measured numerical fibre concentration usually deviates from the actual value.

Deviations arise during all steps of the method:

• sampling (time of sampling, simulation of usage, volume

measurement) • sample preparation (cold ashing)

• analysis (apparatus adjustment. fibre counting, measurement and identification)

Random variations of the measuring results can be estimated using

the Poisson statistical method

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Total error of the method

The total error T of the measuring method is understood here as the root of the sum of the squares of the

standard deviations for sampling P, evaluation A and the Poisson variability S of the count result. Pro

vided that these errors are independent the total error is:

²T = ²P + ²A + ²Poisson

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Total error of the method

²T = ²P + ²A + ²Poisson

In real numbers: as relative error for E = 5 (amphiboles):

0,2081 = 0,0056 + 0,0025 + 0,2

and for chrysotile:

0,311 = 0,0056 + 0,1056 + 0,2

E= expectation value = number of fibres wich are expected in the filter area evaluated (mean value)

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The random sample related deviation is mostly dominant for

concentrations below 1000 f/m³ (N = 10 fibres)

The analytical deviation is smaller for longer fibres with parallel edges(i.e MMVF, amphibole asbestos) compared to curved fibres

with smaller length to width ratios (L/D)

The uncertainty due to sampling results in indoor measurements mostly from the simulation of usage and is in this case larger than

the value given in the standard (calculated from parallel measurements with no simulation)

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random sample related deviation

The random sample related deviation is considered in the following, based on small numerical fibre concentrations. The

probability W of detecting n fibres of a defined fibre class by scanning N image fields can be described using the Poisson

distribution:

The variable <n> corresponds to the expected value n of the number of fibres to be detected when evaluating

N image fields.

W( n ,n) = nnn

nexp

!

1

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random sample related deviation

The 95 % confidence intervall is described by:

0,95 =

where <n> = expectation value of the number of fibres within the evaluated filter area and n = actually counted number of fibres

λu and λo define the lower and upper limit of the 95% confidence

intervall

0

exp

exp

ndnn

ndnn

n

nO

U

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Poisson-distribution(=probability of a count) for the expectation-value (mean-value)

of:

0

0,05

0,1

0,15

0,2

0,25

0 1 2 3 4 5 6 7 8 9 10 11 12

Count

pro

bab

ilit

y

4

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probability-density distribution of the expectation (mean) value for the count:

0

0,05

0,1

0,15

0,2

0,25

0 1 2 3 4 5 6 7 8 9 10 11 12

expectation value (mean value)

pro

bab

ilit

y-d

en

sit

y

4

u o

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Count LambdaU LambdaO

0 0,025 3,689

1 0,242 5,572

2 0,619 7,225

3 1,090 8,767

4 1,623 10,242

5 2,202 11,668

6 2,814 13,059

7 3,454 14,423

8 4,115 15,763

9 4,795 17,085

10 5,491 18,390

Calculation of the 95% confidence intervall for the count 4

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Estimation of the analytical error A of one laboratory: Comparison of the results from four laboratories (example) We have the following relation, if the four labs have evaluated a series of n filters (same filter loading for each laboratory in one round);

A = Where xi are the individual counts of the laboratories and = meanvalue of the results of the four labs

n

x

n

x

xx n

i

n

i

ii

11

2

1

3

4

ix

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Example, calculation of the measurement uncertainty for the random related part and then together with the analytical

deviation of a Lab (for chrysotile) eff. Filter area 380 mm², air volume: 3.80 m³, analyzed filter area: 1 mm² countable fibres chrysotile : n = 5 analyzed sample volume: 3,8 m³/380 = 0,01 m³ Chrysotile fibre concentration 5/0,01 m³ = 500 f/m³ Calculation of the upper limit of the 95% confidence interval OL for the random related part only: OL = D/2 mit D = value of χ² with 2*(n+1) degrees of freedom (dgf) in Microsoft Excel = CHIINV(0.025;12)/2= 11.67 11.67/0.01 m³ = 1167 f/m³ with an analytical error of 20% relative (1 σ): n’ = 5+ 5*0,2*2 = 7 OL = value of χ ² with 2*(7+1) dgf / 2 in Microsoft Excel = CHIINV(0.025;16)/2= 14.42 14.42/0.01 m³ = 1442 f/m³

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Subjective errors

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Subjective errors in sampling

Observed mostly:

Leakage of the sampling head due to not tight fitted filter

Leakage of the sampling train (not discovered)

wrong volume calculated

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Subjective errors SEM evaluation

Observed mostly:

Incorrect calibration of the magnification

No plasma ashing (VDI 3492 mandatory)

Evaluation (counting) too quickly:

Thin fibres (< 0.4 µm not reported) curved structures with non-parallel edges not detected as fibre

VDI 3492 Measurement Uncertainty Chapter 9...evaluated filter area and n = actually counted number of fibres λ u and λ o define the lower and upper limit of the 95% confidence intervall

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