Applying Metrology to the Limitations of Breath

Transcription

SESSION 301
Applying Metrology to the Limitations of
Breath Testing – Using the Government
Mule to Plow Your Field
Daniel J. Koewler
Charles A. Ramsay
Ramsay Law Office
Roseville
The 2016 Criminal Justice Institute – August 22 & 23, 2016
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Applying Metrology to the Limitations of Breath Testing –
Using the Government Mule to Plow Your Field
Daniel J. Koewler & Charles A. Ramsay
Table of Contents
Fredrickson Order re Kevin Hunt
Gullberg Summary
Starr Order re Mahoney McCarthy & McMahon
BT-023 - Estimation of Measurement Uncertainty for DataMaster DMT-G (DMT)
Breath Test Results
Measurement Uncertainty Computed for the
Forensic Breath Alcohol Test Program in Minnesota
Our objective here is to develop and illustrate the calculation of measurement uncertainty in forensic
breath alcohol analysis for the forensic breath alcohol test program in Minnesota. We will follow the
approach outlined in the Guide to the Expression of Uncertainty in Measurement (GUM) document. [1] This
document is internationally recognized as an approach to estimating, interpreting and reporting
measurement uncertainty. We begin by identifying the principle components contributing to measurement
uncertainty. For the program in Minnesota these three components include: (1) breath sampling, (2)
reference standard traceability and (3) measurement bias. The standard deviation (standard uncertainty)
was estimated for each of these components from data received from the Minnesota Breath Alcohol Test
Program. A spreadsheet was developed in Microsoft Excel V 8.0 (Microsoft, Inc., Redmond, WA) which
allows for the entry of data for a particular breath alcohol test result and then computes the measurement
uncertainty as a 99% confidence interval.
Computing the Uncertainty Function
The state of Minnesota employs the Datamaster DMT (Intoximeters, Inc., St.Louis, MO) breath alcohol
test instrument in which the alcohol is quantified by infrared absorption. Duplicate breath test data from
actual arrested and tested subjects was received from the Minnesota program in April 2016. These included
n=35,793 sets of duplicate test results all reported to four digits. The means of duplicates ranged from 0 to
0.4261 g/210L with an overall mean result of 0.1569 g/210L. The data were from drunk driving subjects
arrested during the years 2014 and 2015. The uncertainty function was computed using the statistical
program R Ver. 3.2.1. The R code is found in the Appendix. The standard deviation was determined for all
values within each 0.010 g/210L interval. Three digit breath test data was used (truncating the fourth digit)
because that is how breath test results are reported on the test document. The standard deviation was
computed from:
k
S
d
i 1
2k
2
i
Eq .1
where: d = the difference between duplicate test results
k = the number of individuals within the specific 0.010 g/210L interval
These estimates for the standard deviation are then plotted against the midpoint for each concentration
interval (0.010 g/210L) seen in figure 1. A linear regression model is developed using all duplicates including
1
those with differences greater than 0.020 g/210L. Only duplicate data having mean results ≥ 0.020 g/210L
were used in this first computation (figure 1) to ensure that each interval had at least n=30 duplicates from
which to estimate the standard deviation. The linear uncertainty function is then incorporated into the
Excel spreadsheet for computing the combined uncertainty. The value C in the uncertainty function
represents the mean breath alcohol results for the individual’s test. All duplicate test results which did not
agree within 0.020 g/210L were then removed and the uncertainty function was computed for this reduced
set of data as well. A total of 1.3% (n=468) of the full data set did not meet the 0.020 g/210L agreement
standard and were removed for the re-analysis. The results of this uncertainty function using only those
results with differences less than or equal to 0.020 g/210L is seen in figure 2. This computation of the
uncertainty function based on duplicate breath test results is very important and demonstrates the
increasing variation with concentration. [2,3] It will include most of the components contributing to total
uncertainty. Some of these components include: (1) breath sampling (possibility of low level mouth alcohol
or interfering substances, breath temperature, partition ratio, etc.), (2) analytical component, (3) operators
(instructions to subject, etc.), (4) over 30,000 subjects, (5) two years of time, (6) 280 instruments, (7)
environmental elements, (8) ambient conditions, (9) health conditions etc. All of these contribute to the
variation observed in duplicate test differences and are captured with the computation and resulting linear
function observed in figures 1 and 2.
2
Figure 1 – The uncertainty function using all duplicate data where the instrument accepted
the results and differences may have exceeded 0.020 g/210L
SD = 0.0222C + 0.0010
n = 35,398
3
Figure 2 – The uncertainty function using only duplicate results that complied with the
0.020 g/210L agreement criteria
SD = 0.0166C + 0.0014
n = 34,962
From figures 1 and 2 we see that using all of the data (figure 1) yields a slightly larger estimate for the
standard deviation. At a concentration of 0.085 g/210L the model in figure 1 would yield a standard
deviation of 0.00287 g/210L while the model in figure 2 would yield a standard deviation of 0.00282 g/210L.
The difference is negligible. However, the more conservative estimate from figure 1 will be used in the
Excel spreadsheet computation of combined uncertainty.
Excel Spreadsheet and Computations
We begin by entering the duplicate breath test results for a specific individual on lines 1 and 2. The mean is
computed (line 3) and then entered into the uncertainty function on line 4. The coefficient of variation
squared (CV2) for this breath sampling term is then computed from the standard deviation, n and the mean
of the individual results. The reference value (line 5) is the value of the gas standard used in the field and
measured with each subject test. These standards are purchased from a vendor and their reference value is
4
assigned based on a barometric pressure correction (0.077 g/210L in our example). The uncertainty
estimate from the certificate of analysis (assumed here to be 0.001 g/210L on line 5) will then be divided by
the square root of the number of measurements performed by the vendor on the reference material (if
known) or divided by at least the square root of two. This is finally divided by the reference value (0.077
g/210L on line 5) and squared to yield the CV2 for the standard reference material. The third term found on
line 6 is for the bias component. We recommend that the maximum observed bias be the fixed value of
0.005 g/210L. This is the maximum absolute bias observed for 98.8% of the gas standard measurements in
the field for the two years of 2014 and 2015. Using the field gas standard measurements for the bias
estimates is preferred to those control standard measurements performed in the laboratory during annual
calibration procedures because they are more representative of the large variation in environmental and
analytical conditions experienced in the field throughout the year. This maximum absolute bias is assumed
to follow a uniform distribution. The standard deviation for this distribution is determined from half the
interval width (the maximum observed bias) divided by the square root of three. This is then divided by the
control value or mean gas standard measurement associated with the duplicate test results (assumed here
to be 0.076 g/210L on line 6) and squared to yield the CV2 value. These three CV2 values are then added
(line 7) and the square root taken which is multiplied by the mean of the individual’s test results (line 8).
This finally yields the combined uncertainty on line 8 which in our example is 0.00389 g/210L. This
combined uncertainty is then used to compute the 95% (line 9) and 99% (line 10) confidence intervals. For
the 95% confidence interval we have used a coverage factor of 1.96 which yields an exact 95% confidence
interval. For the 99% confidence interval we have used a coverage factor of 2.575 which provides an exact
99% confidence interval. The far right column indicating Percent shows the percent that each of the three
terms contributes to the combined uncertainty. Where one of the terms contributes less than one-third of
the largest term, this term can be reasonably eliminated. [4] This would be the reference standard control
value. However, given the forensic context it is advisable to retain all three terms in the calculations. The
values that will need to be added for each uncertainty estimation are highlighted in yellow on the Excel
spreadsheet.
The computations described above for computing the combined uncertainty are found in the equation 2
below:
uc  Y
2
 uRe f
 u Sampling 



n
Breath

   nRe f
 Re f
 Y







2
2
2

 Bias 

 3 





Re f 





2
 0.005 
 0.00289 
 0.0010 





3 
2  
2  
uc  0.085 
 0.0760 
 0.085 
 0.077 






Eq . 2
2
 0.00390
5
The first term under the square root in equation 2 comes from the uncertainty function (line 4), the second
term from the reference value (line 5) and the third term from the bias component (line 6).
Plot of Differences
Figure 3 shows the plot of absolute differences against their mean. This includes all data, including those
where the 0.020 g/210L agreement was not met. From this we see that most of the results not complying
with the 0.020 g/210L agreement are above 0.10 g/210L. This indicates, as do the uncertainty functions in
figures 1 and 2, that the variation is increasing with concentration. This is indicative of a multiplicative error
model and is very common in the analytical sciences.
Figure 3 – Plot of the absolute duplicate test differences against their mean. The agreement
criteria of 0.020 g/210L is shown by the horizontal line
Absolute Duplicate Test Differences (g/210L)
0.08
0.06
n = 35,792
0.04
0.02
0.00
0.0
0.1
0.2
0.3
0.4
Mean of Duplicate Results (g/210L)
6
Figure 4 shows the plot of differences against their mean which is known as a Bland-Altman plot. [5] The
difference is determined from BrAC1-BrAC2. We look for trends in this plot and for systematic differences
as measured by the mean difference. The data look very uniform throughout the range with no indication
of a trend. The mean difference of 0.0012 g/210L does not suggest that one result is systematically
different from the other. From this plot we also see the increasing variation with concentration.
Figure 4 – Plot of duplicate test differences (BrAC1-BrAC2) against their mean
Duplicate Test Difference (BrAC1-BrAC2) g/210L
0.08
0.06
0.04
0.02
mean + 2SD = 0.0142 g/210L
mean = 0.0012 g/210L
0.00
mean - 2SD = -0.0118 g/210L
-0.02
-0.04
n = 35,792
-0.06
-0.08
0.0
0.1
0.2
0.3
0.4
0.5
Mean BrAC Result (g/210L)
Figure 5 shows the frequency distribution of the bias estimates from the full data set received. The bias
estimates ranged from -0.0078 (-10.3%) to 0.0075 (+9.9%) g/210L. The distribution is quite normal in
appearance.
7
Figure 5 – Frequency distribution of the bias values observed for all data during 2014-2015
12000
10000
mean = -0.0007 g/210L
SD = 0.0018 g/210L
n = 35,793
Frequency
8000
6000
4000
2000
0
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
Duplicate Test Difference (g/210L)
When The Confidence Interval Brackets a Critical Per Se Level
Assume that an individual arrested for DUI provides two breath samples resulting in 0.083 and 0.087
g/210L. The combined standard uncertainty associated with breath alcohol measurement at this
concentration is σ = 0.00389 g/210L determined from the example illustrated in the Excel spreadsheet. We
use the large sample Z statistic to compute the 99% confidence interval and determine the probability that
the individual’s true mean breath alcohol concentration exceeds 0.080 g/210L.
We compute the 99% confidence interval as follows:
8
Y  Z 0.995 SY
0.0850  2.575 0.00389  0.0850  0.0100  0.0750 to 0.0950

0.0750
0.0950
0.080
The probability that the individual is over 0.080 g/210L is found by first considering the following form for
expressing the confidence interval showing the probability that µ is bracketed by upper and lower limits:


P Y - Z (1-/2) SY    Y + Z (1-/2) SY = 
The value π simply represents the probability that we are interested in determining and Y represents the
mean breath alcohol results for the subject. Since we are interested in determining the probability that µ
exceeds the lower limit we rewrite the equation as follows:


P Y  Z (1 -/2) SY   = 
We now set the lower limit equal to 0.080 g/210L and solve for Z (1-α/2):
Y  Z (1 -/2) SY = 0.080  0.0850  Z (1 -/2) 0.00390 = 0.080  Z (1 -/2) = 1.28
Next, we rearrange our probability statement and introduce the value for Z(1-α/2):
9
Y - 

P Y  Z 1-/2 SY   = P 
 Z1 / 2  = P Z  Z 1-/2  = P Z  1.28 = 0.8997
 SY



The probability that the true mean breath alcohol results exceeds 0.080 g/210L is 0.8997. Whether this is
evidence beyond a reasonable doubt is for the jury to decide.
Based on the analyses presented above it is recommended that the uncertainty function, the maximum
observed bias, the vendor’s estimate for the uncertainty of the gas standard and the gas standard target
value be reviewed annually. Any changes in these values should be incorporated in the Excel computation
spreadsheet. In addition, it is recommended that the program policy manual define which set of
spreadsheet computations will apply to a particular individual’s test results. In addition, it is recommended
that the program policy manual explain the meaning of the values found in the Excel spreadsheet.
Appendix – R Code for developing the Uncertainty Function
Routine for importing duplicate breath alcohol data and then separating into bins of 0.01 based on
duplicate means and then computingestimates of the standard deviation and plotting against the bin
mid-points
data=read.table("c:/Minnesota Breath Test/dat8.csv", header=TRUE, sep=",")
attach(data)
mn=(brac1+brac2)/2
d=brac1-brac2
ds=d^2
10
conc=c(seq(.005,.325,.01))
factor=(mn<.01)+(mn<.02)+(mn<.03)+(mn<.04)+(mn<.05)+(mn<.06)+(mn<.07)+(mn<.08)+(mn<.09)+(mn<.10)
+(mn<.11)+(mn<.12)+(mn<.13)+(mn<.14)+(mn<.15)+(mn<.16)+(mn<.17)+(mn<.18)+(mn<.19)+(mn<.20)+(mn
<.21)+(mn<.22)+(mn<.23)+(mn<.24)+(mn<.25)+(mn<.26)+(mn<.27)+(mn<.28)+(mn<.29)+(mn<.30)+(mn<.31)
+(mn<.32)+(mn<.33)+(mn<.34)
table(factor)
sum(ds[factor==2])
s33=sqrt(sum(ds[factor==2])/(2*(length(mn[factor==2]))))
sum(ds[factor==3])
sum(ds[factor==3])
sum(ds[factor==5])
sum(ds[factor==6])
sum(ds[factor==7])
sum(ds[factor==8])
sum(ds[factor==9])
sum(ds[factor==10])
sum(ds[factor==11])
sum(ds[factor==12])
sum(ds[factor==13])
sum(ds[factor==14])
sum(ds[factor==15])
sum(ds[factor==16])
sum(ds[factor==17])
sum(ds[factor==18])
sum(ds[factor==19])
sum(ds[factor==20])
sum(ds[factor==21])
11
sum(ds[factor==22])
sum(ds[factor==23])
sum(ds[factor==24])
sum(ds[factor==25])
sum(ds[factor==26])
sum(ds[factor==27])
sum(ds[factor==28])
sum(ds[factor==29])
sum(ds[factor==30])
sum(ds[factor==31])
sum(ds[factor==32])
sum(ds[factor==33])
sum(ds[factor==34])
sd=c(s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,s15,s16,s17,s18,s19,s20,s21,s22,s23,s24,s25,s26,s27,s28,s
29,s30,s31,s32,s33)
v=sd^2
mod1=lm(sd~conc)
summary(mod1)
plot(conc,sd,pch=16,xlab="Breath Alcohol Concentration",ylab="Standard
Deviation",xlim=c(0,.4),ylim=c(0,.015))
abline(lsfit(conc,sd))
sd
conc
SCRIPT2 C:\Minnesota Breath Test\
References
12
1. International Organization for Standardization, Guide to the Expression of Uncertainty in
Measurement, ISO, Geneva, 2008. Available at:
http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf
2. Thompson, M. and Wood, R., Using uncertainty functions to predict and specify the performance of
analytical methods, Accred Qual Assur, Vol.10, 2006, pp. 471-478.
3. EURACHEM/CITAC Guide, Quantifying Uncertainty in Analytical Measurement, 3rd Ed., 2012, pp. 117-119
Available at http://www.eurachem.org/images/stories/Guides/pdf//QUAM2012_P1.pdf
4. EURACHEM/CITAC Guide, Quantifying Uncertainty in Analytical Measurement, 3rd Ed., 2012, p. 16
Available at http://www.eurachem.org/images/stories/Guides/pdf//QUAM2012_P1.pdf
5. Altman DG, Bland JM, Measurement in medicine: the analysis of method comparison studies,
The Statistician Vol.32, 1983, pp. 307–317
This work was completed under contract with the State of Minnesota, SWIFT contract number 107618
Rod G. Gullberg, MS, PStat
Clearview Statistical Consulting
20119 61st Avenue SE
Snohomish, WA 98296
[email protected]
6/1/2016
13
BT-023
Page 1 of 8 Pages
Title:
Authorization: Catherine M. Knutson
Version:
Issue Date: 07/13/2016
Estimation of Measurement Uncertainty for DataMaster DMT-G (DMT)
Breath Test Results
Scope:
This document provides instruction for the estimation of measurement uncertainty for DMT
breath test results.
Background Information:
Estimation of measurement uncertainty is an element of measurement traceability. Traceability
ensures consistency and comparability of test results reported by DMTs in the State of Minnesota
and between other traceable breath test results. Traceability of the measurement result is
established by using a properly certified DMT, which has calibration results that are traceable to
NIST and by establishing an Uncertainty of Measurement associated with the breath test results.
Measurement uncertainty defines a confidence interval symmetric about the average of multiple
measurement results. This uncertainty applies to the average value of the breath results obtained
from a DMT test. The uncertainty is an estimate; it is not a specific or exact number.
The measurand is the concentration of ethanol in the breath of the subject of a DMT test.
Both Type A and Type B uncertainty components must be considered:
•
Type A uncertainty components can be evaluated statistically through a series of
observations. For a well-characterized measurement under statistical control, a combined
or pooled experimental standard deviation that characterizes the measurement may be
used to evaluate Type A standard uncertainty (GUM 4.2.4).
•
Type B uncertainty components are evaluated by means other than statistical analysis of a
series of observations. The information used in the evaluation of Type B uncertainty may
be taken from sources including, but not limited to, manufacturer's specifications and
data provided on calibration or other certificates (GUM 4.3.1).
The approach utilized here for the estimation of measurement uncertainty for DMT subject test
results is outlined in the Guide to the Expression of Uncertainty in Measurement (GUM). [1]
This approach was applied to the Minnesota Breath Alcohol program by Rod Gullberg, MS,
PStat. [2]
UNCONTROLLED COPY WHEN PRINTED
MN BCA Forensic Science Service
BT-023
Page 2 of 8 Pages
Version:
References:
1. International Organization for Standardization, Guide to the Expression of Uncertainty in
Measurement, ISO, Geneva, 2008. Available at:
http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf
2. Gullberg, R.G., Measurement Uncertainty Computed for the Forensic Breath Alcohol
Test Program in Minnesota, June 1, 2016
3. ASCLD/LAB Policy on Measurement Traceability AL-PD 3057 Ver 1.3, ASCLD/LABInternational (2013).
4. ASCLD/LAB Guidance on Measurement Traceability AL-PD-3058 Ver 1.0,
ASCLD/LAB-International (2013).
5. ASCLD/LAB Guidance on Measurement Traceability-Measurement Assurance AL-PD3059 Ver 1.0 ASCLD/LAB-International (2013).
6. ASCLD/LAB Policy on Measurement Uncertainty AL-PD-3060 Ver 1.1, ASCLD/LABInternational (2013).
7. ASCLD/LAB Guidance on the Estimation of Measurement Uncertainty- Overview ALPD-3061 Ver 1.0 ASCLD/LAB-International (2013).
Operation:
1. Breath sample values are saved to four digits in the Breath Alcohol Database (BrAD).
Since the DMT test record printout shows breath sample results to only three digits, all
values in the duplicate breath sample data set will be truncated to three digits prior to data
analysis.
2. To prevent loss of information, rounding and/or truncation of numbers is avoided during
all calculations performed prior to the final result. At minimum all significant figures are
conserved and additional digits may be conserved during calculations.
3. When calculating the combined standard uncertainty, the uncertainty components must
all be in the same units.
BT-023
Page 3 of 8 Pages
Version:
4. A list of the major uncertainty components to be considered and characterization of the
method of evaluation of the components are maintained in the Calibration Laboratory.
5. The evaluation of the data contributing to the Type A uncertainty components has been
performed using a custom computer script written by Rod Gullberg for the R program.
6. An Excel spreadsheet will be used to facilitate calculation of combined standard
uncertainties and to produce a confidence interval table.
7. Dry gas certified reference material (CRM) is considered to have valid measurement
traceability when supplied by an accredited Reference Material Producer that is
accredited to ISO Guide 34:2009 by an accrediting body that is a signatory to a mutual or
multilateral recognition arrangement in an ILAC recognized regional accreditation
cooperation or the ILAC Mutual Recognition Arrangement, with a scope of accreditation
covering the CRM.
There are three terms that contribute to the combined uncertainty. They are:
1.
2.
3.
CV − Coefficientofvariationforduplicatebreathsamples
CV − Coefficientofvariationforthereference
CV − Coefficientofvariationforthebias
These terms are calculated and then combined as a root sum squared to estimate the combined
uncertainty.
1. Coefficient of variation for duplicate breath samples ( )
An uncertainty function will be used to estimate the standard deviation associated with the
average of two accepted breath samples in a DMT test. This standard deviation will be used
to calculate the coefficient of variation for the sampling term of the combined uncertainty
function. This is a type A uncertainty component.
Duplicate breath data is compiled and the average of each set of duplicates is calculated. The
duplicate samples are assigned to a bin corresponding to their average result. Each bin has a
width of 0.01. Bins containing fewer than 30 sets of duplicate data are disregarded. The
standard deviation of the remaining bins is calculated and then plotted against the midpoints
of the respective bins. A linear regression is then developed to model the data. This linear
regression will serve as the uncertainty function for duplicate breath samples and will
BT-023
Page 4 of 8 Pages
Version:
provide an estimation of the standard deviation for the average of two breath samples
provided in a single breath test.
A. Data collection (perform steps in list order):
i.
Using the sql query “Test Uncertainty Data w 02 agreement not met”, collect at
least 30,000 sets of duplicate breath sample data, with corresponding control data.
Transfer of appropriate data is verified and documented in the uncertainty folder
on the L drive.
ii.
Copy and paste the data, with headers, to an Excel spreadsheet.
iii. Cut and paste Target and Control columns to a second spreadsheet. The original
sheet should now contain just the columns “brac1”, “brac2” and “mean”.
iv.
Save the original sheet as a CSV file
v.
Calculate the average control target and average control value on the second
sheet.
B. Evaluate the data using R
i.
Open R code in a text file and edit first line of code to point to the CSV file
created in part A.iv.
ii.
Copy/paste the code to the R workspace.
iii. R will run the code automatically.
C. Assemble the uncertainty function for duplicate breath samples in the following format:
= ! "#$% + '!
where: = ()*+,*-,,./0*)01+.()02*).31-,45607*).8-.*)ℎ(*256.(
! = 615.1360+.*--.:-.((01+3-12;
"#$% = */.-*:.13,45607*).8-.*)ℎ(*256.(
'! = '0+).-7.5)1360+.*--.:-.((01+3-12;
Calculate the coefficient of variation for duplicate breath samples using the following
equation.
BT-023
Page 5 of 8 Pages
Version:
>+
<= =
"#$%
where: <= = 71.33070.+)13/*-0*)01+31-,45607*).8-.*)ℎ(*256.(
= ()*+,*-,,./0*)01+.()02*).31-,45607*).8-.*)ℎ(*256.(
+ = +428.-13(*256.()*?.+,4-0+:8-.*)ℎ).()@2B
"#$% = */.-*:.13,45607*).8-.*)ℎ(*256.(
2. Coefficient of variation for the reference (C )
Each complete DMT test includes a control sample drawn from a dry gas cylinder of known
alcohol concentration. The certificate of analysis for each dry gas control lists a measurement
uncertainty for the concentration of the cylinder. The uncertainty of the known cylinder
concentration is included in the combined uncertainty estimation as a type B component.
The uncertainty of the cylinder should be reduced to a single standard deviation before
calculating the coefficient of variation for the reference.
Calculate the coefficient of variation for the reference using the following equation.
D
√+D
<=D =
F#$%
where: <=D = 71.33070.+)13/*-0*)01+31-,45607*).8-.*)ℎ(*256.(
D = ()*+,*-,,./0*)01+.()02*).31--.3.-.+7.
+D = +1. 137H60+,.-(*256.(*+*6HI.,8H2*+43*7)4-.-@min 2B
F#$% = */.-*:.71+)-16)*-:.)3-12,*)*(.)
3. Coefficient of variation for the bias (J )
Measurement bias is accounted for in the combined standard uncertainty. The absolute
observed bias is fixed at 0.005, which is the maximum bias observed in 98.8% of tests run
2014 – 2015. The absolute observed bias will be evaluated as described in part 6. It is
included in the uncertainty calculation as a type A component.
BT-023
Page 6 of 8 Pages
Version:
The bias is assumed to have a uniform distribution and therefore should be divided by √3
when calculating the coefficient of variation for the bias.
Calculate the coefficient of variation for the reference using the following equation.
0.005
√3
<=L =
<#$%
where: <=L = 71.33070.+)13/*-0*)01+31-80*(
<#$% = */.-*:.71+)-16-.(46)3-12,*)*(.)
4. Calculating the combined uncertainty and the expanded uncertainty
A. The combined uncertainty will be calculated using the combined uncertainty function
described below:
4O = "#$% P<=Q + <=DQ + <=LQ
where: 4O = 71280+.,4+7.-)*0+)H31-RF8-.*)ℎ).()(
"#$% = */.-*:.13,45607*).8-.*)ℎ(*256.(
<= = 71.33070.+)13/*-0*)01+31-,45607*).8-.*)ℎ(*256.(
<=D = 71.33070.+)13/*-0*)01+31-,-H:*(-.3.-.+7.()*+,*-,
<=L = 71.33070.+)13/*-0*)01+31-80*(
B. The expanded uncertainty is calculated to a 95% confidence interval and a 99%
confidence interval.
i.
The combined uncertainty (4O ) is multiplied by a factor of 1.96 to achieve a 95%
ii.
The combined uncertainty (4O ) is multiplied by a factor of 2.575 to achieve a 99%
5. Reporting measurement uncertainty for a DMT breath test
A confidence interval table will be made available for customer use. The table will include
95% and 99% confidence intervals for all possible average test results and information
regarding the interpretation of the table.
BT-023
Page 7 of 8 Pages
Version:
6. Annual review of measurement uncertainty
The Breath Alcohol Calibration Laboratory will calculate the test measurement uncertainty
estimation annually using a data set containing at least 30,000 sets of duplicate breath sample
data. A new confidence interval table will be created and published each year based on the
most recent uncertainty estimation. The new table will be applied to the following year’s
tests.
7. Updating and Using the Excel Uncertainty Calculator
Save a new copy of the uncertainty calculator spreadsheet in the uncertainty folder on the L
drive and name it with the year the current uncertainty calculation will be implemented. The
following cells in the uncertainty calculator should be reviewed and revised, if necessary,
after the annual review of measurement uncertainty. The combined uncertainty and
confidence interval table will automatically update if any changes are made.
A. Uncertainty Function Coefficients
i. Update the Slope and y-Intercept lines with the appropriate values from the R
result.
B. Reference Value (Line 5)
i. Column “Uncertainty”: input single standard deviation of field dry gas standards.
ii. Column “Mean”: input the mean value of the control targets within the current data
set.
iii. Column “n”: input the number of samples taken by the manufacturer to determine
the stated alcohol concentration of the field dry gas standards. (If unknown, use 2)
C. Bias Term (Line 6)
i. Column “mean”: input the mean value of the control sample readings within the
current data set.
Record requirements from the ASCLD/LAB Policy on Measurement Uncertainty ALPD-3060, May 2013, with the locations listed below:
(a) Statement defining the measurand (the quantity intended to be measured)1
(b) Statement of how traceability is established for the measurement1,
(c) The equipment (e.g., measuring device[s] or instrument[s]) used1, 3
BT-023
Page 8 of 8 Pages
Version:
(d) All uncertainty components considered3
(e) All uncertainty components of significance and how they were evaluated1,3
(f) Data used to estimate repeatability and/or reproducibility2
(g) All calculations performed1,3
(h) The combined standard uncertainty, the coverage factor, the coverage probability and
the resulting expanded uncertainty1,3
(i) The schedule to review and/or recalculate the measurement uncertainty1,3
Locations of Required Items:
1
Breath Alcohol Calibration Laboratory Standard Operating Procedure BT-023
2
Maintained in shared network folder located at L:\Calibration Lab\Uncertainty\Test
Uncertainty
3
Gullberg, R.G., Measurement Uncertainty Computed for the Forensic Breath Alcohol
Test Program in Minnesota, June 1, 2016
**************************************************************************************
Revision and Review History:
Previous version: None (New SOP)
Technical Leader/FS3(s): KK 07/12/16
Supervisor: SAB 07/12/16
Quality Manager/Quality System Coordinator: MS 07/12/16
Assistant Laboratory Director(s) St. Paul: AWH 07/12/2016
Laboratory Director: CMK 07/12/2016
**************************************************************************************
Archived:
Reason for Archiving:
Quality Manager / Quality System Coordinator:
Date:

Applying Metrology to the Limitations of Breath

Transcription

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