ASTM D5280-96(2007)

Standard Practice for Evaluation of Performance Characteristics of Air Quality Measurement Methods with Linear Calibration Functions

ABSTRACT
This practice covers procedures for evaluating the performance characteristics of air quality measurement methods with linear calibration functions. The steps involved in the measurement method used shall be described, and the performance characteristics to be evaluated shall be specified and tested under explicitly specified conditions. The performance characteristics for evaluation include bias, calibration function and linearity, instability, lower detection limit, period of unattended operation, selectivity, sensitivity, and upper limit of measurement.
SCOPE
1.1 This practice covers procedures for evaluating the following performance characteristics of air quality measurement methods: bias (in part only), calibration function and linearity, instability, lower detection limit, period of unattended operation, selectivity, sensitivity, and upper limit of measurement.
1.2 The procedures presented in this practice are applicable only to air quality measurement methods with linear continuous calibration functions, and the output variable of which is a defined time average. The linearity may be due to postprocessing of the primary output variable. Additionally, replicate values belonging to the same input state are assumed to be normally distributed. Components required to transform the primary measurement method output into the time averages desired are regarded as an integral part of this measurement method.
1.3 For surveillance of measurement method stability under routine measurement conditions, it may suffice to check the essential performance characteristics using simplified tests, the degree of simplification acceptable being dependent on the knowledge on the invariance properties of the performance characteristics previously gained by the procedures presented here.
1.4 There is no fundamental difference between the instrumental (automatic) and the manual (for example, wet-chemical) procedures, as long as the measured value is an average representative for a predefined time interval. Therefore, the procedures presented are applicable to both. Furthermore, they are applicable to measurement methods for ambient, workplace, and indoor atmospheres, as well as emissions.
This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 31-Mar-2007
• ICS: 13.040.20 - Ambient atmospheres
• Technical Committee: D22 - Air Quality
• Drafting Committee: D22.03 - Ambient Atmospheres and Source Emissions

Relations

• Replaces: ASTM D5280-96(2001) - Standard Practice for Evaluation of Performance Characteristics of Air Quality Measurement Methods with Linear Calibration Functions
• Effective Date: 01-Apr-2007

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D5280 − 96(Reapproved 2007)
Standard Practice for
Evaluation of Performance Characteristics of Air Quality
Measurement Methods with Linear Calibration Functions
This standard is issued under the fixed designation D5280; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.5 This standard does not purport to address all of the
2 safety concerns, if any, associated with its use. It is the
1.1 This practice covers procedures for evaluating the
responsibility of the user of this standard to establish appro-
following performance characteristics of air quality measure-
priate safety and health practices and determine the applica-
ment methods: bias (in part only), calibration function and
bility of regulatory limitations prior to use.
linearity,instability,lowerdetectionlimit,periodofunattended
operation, selectivity, sensitivity, and upper limit of measure-
2. Referenced Documents
ment.
2.1 ASTM Standards:
1.2 The procedures presented in this practice are applicable
D1356Terminology Relating to Sampling and Analysis of
only to air quality measurement methods with linear continu-
Atmospheres
ous calibration functions, and the output variable of which is a
E177Practice for Use of the Terms Precision and Bias in
definedtimeaverage.Thelinearitymaybeduetopostprocess-
ASTM Test Methods
ing of the primary output variable. Additionally, replicate
E456Terminology Relating to Quality and Statistics
values belonging to the same input state are assumed to be
2.2 ISO Standard:
normally distributed. Components required to transform the
ISO 6879:1983, Air Quality—Performance Characteristics
primary measurement method output into the time averages
and Related Concepts for Air Quality Measuring Meth-
desired are regarded as an integral part of this measurement 4
ods
method.
3. Terminology
1.3 For surveillance of measurement method stability under
3.1 Definitions:
routine measurement conditions, it may suffice to check the
essentialperformancecharacteristicsusingsimplifiedtests,the 3.1.1 For definitions of terms used in this practice, refer to
degree of simplification acceptable being dependent on the Terminology D1356.
knowledge on the invariance properties of the performance
3.2 Definitions of Terms Specific to This Standard:
characteristics previously gained by the procedures presented
NOTE 1—The statistical performance characteristics used throughout
here.
this practice are estimated, by convention, at the confidence level
1.4 There is no fundamental difference between the instru-
1− α=0.95.
mental (automatic) and the manual (for example, wet-
3.2.1 averaging time— predefined time interval length for
chemical) procedures, as long as the measured value is an
which the air quality characteristic is made representative and
average representative for a predefined time interval.
∆θ the averaging time.
Therefore, the procedures presented are applicable to both.
3.2.1.1 Discussion—Every measured value obtained is rep-
Furthermore, they are applicable to measurement methods for
resentative for a defined interval of time, τ, the value of which
ambient, workplace, and indoor atmospheres, as well as
always lies above a certain minimum due to the intrinsic
emissions.
properties of the measuring procedure applied. In order to
attain mutual comparability of data pertaining to comparable
objects, a normalization to a common, predefined interval of
ThispracticeisunderthejurisdictionofASTMCommitteeD22onAirQuality
time is necessary.
and is the direct responsibility of Subcommittee D22.03 on Ambient Atmospheres
and Source Emissions.
Current edition approved April 1, 2007. Published June 2007. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1994. Last previous edition approved in 2001 as D5280-96(2001). contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
DOI: 10.1520/D5280-96R07. Standards volume information, refer to the standard’s Document Summary page on
This practice was adapted from International Standard ISO/DP9169, prepared the ASTM website.
byISO/TC146/SC4/WG4,bythekindpermissionoftheChairmanofISO/TC146 AvailablefromInternationalOrganizationforStandardization,CasePastale56,
and the Secretariat of ISO/TC 146/SC 4. CH-1211, Geneva 20, Switzerland.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5280 − 96 (2007)
3.2.1.2 Discussion—By convention, this normalization is 3.2.8 referenceconditions—aspecifiedsetofvalues(includ-
achieved by transformation by means of a simple, linear, and ing tolerances) of influence variables delivering representative
unweighted averaging process. values of performance characteristics.
3.2.9 variance function—avarianceoftheoutputvariableas
(a) Series of Discrete Samples:
a function of the air quality characteristic observed.
K
3.2.10 warm-up time— the minimum waiting time for an
cˆ~θ ∆θ! 5 cˆ ~θ 1~k 21!τ τ (1)
? ( 0 ?
K
k51
instrument to meet predefined values of its performance
where: characteristics after activating an instrument stabilized in a
nonoperating condition.
θ = θ− ∆θ, and
3.2.10.1 Discussion—In practice, the warm-up time can be
Kτ = ∆θ, τ << ∆θ
determined by using the performance characteristic that is
(b) Continuous Time Series:
expected to require the longest interval of time.
θ
3.2.10.2 Discussion—In the case of the manual procedures,
cˆ θ ∆θ 5 dθcˆ θ τ (2)
~ ! * ~ !
? ?
∆θ θ
run-up time is used correspondingly.
3.3 Symbols and Abbreviations:
In both cases (a and b), the original sample, described by
3.3.1 a ,a ,a —coefficientsofthevariancefunctionmodel.
cˆ(t), is linked to a representative interval of time of length τ
0 1 2
whereas cˆ(∆θ), the result after application of the averaging
3.3.2 b,b —parameters of the estimate function for the
0 1
process,ismaderepresentativefortheintervaloftime ∆θ(just
calibration function.
preceding θ), the averaging time.
3.3.3 C—air quality characteristic.
3.2.1.3 Discussion—The averaging time, ∆θ, is therefore
3.3.4 c—value of C.
the predefined and, by convention, common time interval
length for which the measured variable cˆ is made representa- 3.3.5 cˆ—measured value at c.
tive in a sense that the square deviation of the original values,
3.3.6 c— value of C in the i-th sample; this sample may be
i
attributed to time interval lengths τ << ∆θ from cˆ over ∆θ is a
generated from reference material.
minimum.
3.3.7 c —normalizationfactorforairqualitycharacteristics;
3.2.1.4 Discussion—The averaging process can alterna-
in this case | c |=1.
tively be realized by means of a special sampling technique
3.3.8 ∆c —inaccuracy of C at c .
1 i
(averaging by sampling).
3.3.9 c¯ —weighted mean, with set of weights ω .
ω k
3.2.2 continuously measuring system—a system returning a
3.3.10 D(b )—drift (see ISO 6879) of the intercept of the
continuous output signal upon continuous interaction with the
linear calibration function.
air quality characteristic.
3.2.3 influence variable—a variable affecting the interrela- 3.3.11 D(b )—drift of the slope of the linear calibration
tionship between the (true) values of the air quality character- function.
istic observed and the corresponding measured values; for
3.3.12 D(cˆ)—drift of the measured value, cˆ,at c.
example, variable affecting the slope or the intercept of or the
3.3.13 DEP(b ) —firstordermeasureofdependenceofthe
0 IVi
scatter around the calibration function.
intercept on the influence variable labeled by i.
3.2.4 noncontinuously measuring system—a system return-
3.3.14 DEP(b ) —firstordermeasureofdependenceofthe
1 IVi
ing a series of discrete output signals.
slope on the influence variable labeled by i.
3.2.4.1 Discussion—The discretization of the output vari-
3.3.15 DEP(cˆ) —first order measure of dependence of the
able can be due to sampling in discrete portions or to inner IVi
measured value on the influence variable labeled by i at c.
function characteristics of the system components.
3.2.5 period of unattended operation—themaximumadmis- 3.3.16 DEP(x) —first order measure of dependence of the
IVi
sibleintervaloftimeforwhichtheperformancecharacteristics output signal on the influence variable labeled by i.
will remain within a predefined range without external
3.3.17 F—statistic (cf F-test).
servicing, for example, refill, calibration, adjustment.
3.3.18 F —x-quantile of the F-distribution.
x
3.2.6 random variable—avariablethatmaytakeanyofthe
3.3.19 I —selectivitywithrespecttotheinfluencevariable
IVi
valuesofaspecifiedsetofvaluesandwithwhichisassociated
labeled by i.
a probability distribution.
3.3.20 IV— influence variable labeled by i.
3.2.7 randomization— if, from a population consisting of i
the natural numbers 1 to n, these are drawn at random one by
3.3.21 iv— value of IV.
i i
one successively without replacement until the population is
3.3.22 ∆ iv—difference of values of IV.
i i
exhausted, the numbers are said to be drawn in random order.
3.3.23 L—total number of time intervals of the instability
3.2.7.1 Discussion—If these numbers have been associated
test.
in advance with n distinct objects or n distinct operations that
3.3.24 LDL—lower detection limit.
are then rearranged in the order in which the numbers are
drawn, the order of the objects or operations is said to be 3.3.25 M—total number of samples generated by reference
randomized. material within one calibration experiment.
D5280 − 96 (2007)
3.3.26 N— number of values of the output variable at c. 3.3.56 υ , υ —number of degrees of freedom for the nu-
i i 1 2
merator and denominator of the F-distribution, respectively.
3.3.27 P ,p —estimate of the slope of the regression
|ll u
function of the output variable on time at c = c , c = c , 3.3.57 ω = ω(c)—continuous weighing factor gained by
|ll u
respectively. modeling s.
i
3.3.28 R—reproducibility. 3.3.58 ω —weighing factor at c .
1 1
3.3.29 r—repeatability.
4. Requirements and Provisions
3.3.30 RES — resolution at C = c.
c
4.1 Description of the Steps of the Measurement Methods
3.3.31 sˆ—estimate of the smoothed standard deviation of X
Under Test—Describe all steps of the measurement method
at c.
used, such as sampling, analysis, postprocessing, and calibra-
3.3.32 sˆ —smoothedestimateofthevarianceof X(repeated tion. Fig. 1 illustrates schematically the steps to be followed in
making a measurement or performing a series of calibration
measurements) at c.
experiments in order to determine the performance character-
3.3.33 s —normalization factor for the standard deviation;
istics.
the magnitude of s equals to 1.
NOTE 2—Under certain conditions it may be suitable to test only one
3.3.34 s ,s —estimate of the standard deviation of insta-
b b
0 1
step or a selected group of steps of the measurement method. Under other
bility(seeISO6879)oftheinterceptandtheslopeofthelinear
conditions it may not be possible to include all the steps of the
calibration function.
measurement method. However, include as many steps as possible.
3.3.35 sc—estimate of the standard deviation of instability
4.2 Specification of Performance Characteristics to Be
at c.
Tested—Specify the performance characteristics of the mea-
3.3.36 s— estimate of the standard deviation of repeated x
surement method in order of their relevance for the final
i
at c ; j repetition index.
assessment of accuracy. The descriptors of the calibration
ij i
function, for example, intercept, β , and slope, β , as well as
3.3.37 sˆ —smoothed estimate of the standard deviation of 0 1
i
their qualifying performance characteristics are vital. Those
“repeated” x at c; j repetition index.
ij i
performance characteristics for which prior knowledge is
3.3.38 s — estimate of the repeatability standard deviation.
r
available, and those pertaining to influence variables covered
3.3.39 s —estimateofthestandarddeviationoftheexperi-
cˆx by randomization are of lesser importance and need not be
mentally determined calibration function (in units of the air
determined.
quality characteristic).
3.3.40 s — estimate of the standard deviation of the
xc
experimentally determined calibration function (in units of the
output variable).
3.3.41 t —q-quantileofthet-distributionwithυdegreesof
υ;q
freedom.
3.3.42 TC—test characteristic of Grubbs’ outlier test.
3.3.43 X—output variable.
3.3.44 x—value of X.
3.3.45 x—estimate of x.
3.3.46 x— estimate of output signal at c .
i i
3.3.47 x¯ —mean of the set of output signals at c.
i i
3.3.48 x —output signal at c with the highest absolute
i,extr i
distance from x¯ .
i
3.3.49 x —j-th output signal at c.
ij i
3.3.50 x ,x —output signal after i time intervals at the
l;i` u;i
lower and upper value of the air quality characteristic of
reference material.
3.3.51 x¯ —weightedmeanofthewholesetofoutputsignals
ω
within the calibration experiment.
3.3.52 β , β —intercept and slope of the linear calibration
0 1
function, respectively.
3.3.53 θ—time.
NOTE 1— ____Measurement Branch.
3.3.54 ∆θ—averaging time.
NOTE2—___ Calibration Branch.
3.3.55 υ—number of degrees of freedom in the calibration
FIG. 1 Schematic of the Procedures of Measurement and of
experiment. Evaluation for Performance Characteristics
D5280 − 96 (2007)
4.3 Test Conditions— Perform the tests under explicitly 5.2.2 Determine a linear calibration function by its slope
stated conditions representative of the operational measure- (sensitivity) and its intercept. Describe instability and the
ments. When testing for performance characteristics, describ- effects of influence variables by their impacts on the slope
ing functional dependencies, keep all influence variables con- (sensitivity) and intercept.
stant except the one under consideration. 5.2.3 Obtain all output signals evaluated throughout these
tests after the measuring system has reached stabilized condi-
5. Test Procedures
tions.
5.1 Averaging Time (see 3.2.1)—The range of allowable
5.3 Calibration:
averaging times is constrained by the requirement that the
5.3.1 Acalibration experiment for the evaluation of perfor-
differences of subsequent output signals be mutually statisti-
mancecharacteristicsconsistsofatleasttenrepeatedmeasure-
cally independent.The corresponding minimum of the averag-
ments at a minimum of five different values (two each) of the
ing time is determined by a specific performance (time)
air quality characteristic.
characteristic, that is, continuously measuring systems; the
5.3.2 In case of dr
...