ASTM D5280-96(2001)
(Practice)Standard Practice for Evaluation of Performance Characteristics of Air Quality Measurement Methods with Linear Calibration Functions
Standard Practice for Evaluation of Performance Characteristics of Air Quality Measurement Methods with Linear Calibration Functions
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.
1.5 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.
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Designation: D 5280 – 96 ( Reapproved 2001)
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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
2 bility of regulatory limitations prior to use.
1.1 This practice covers procedures for evaluating the
following performance characteristics of air quality measure-
2. Referenced Documents
ment methods: bias (in part only), calibration function and
2.1 ASTM Standards:
linearity,instability,lowerdetectionlimit,periodofunattended
D1356 Terminology Relating to Sampling andAnalysis of
operation, selectivity, sensitivity, and upper limit of measure-
Atmospheres
ment.
E177 Practice for Use of the Terms Precision and Bias in
1.2 The procedures presented in this practice are applicable
ASTM Test Methods
only to air quality measurement methods with linear continu-
E456 Terminology Relating to Quality and Statistics
ous calibration functions, and the output variable of which is a
2.2 ISO Standard:
defined time average.The linearity may be due to postprocess-
ISO 6879: 1983, Air Quality—Performance Characteristics
ing of the primary output variable. Additionally, replicate
and Related Concepts for Air Quality Measuring Meth-
values belonging to the same input state are assumed to be
ods
normally distributed. Components required to transform the
primary measurement method output into the time averages
3. Terminology
desired are regarded as an integral part of this measurement
3.1 Definitions:
method.
3.1.1 For definitions of terms used in this practice, refer to
1.3 For surveillance of measurement method stability under
Terminology D1356.
routine measurement conditions, it may suffice to check the
3.2 Definitions of Terms Specific to This Standard:
essential performance characteristics using simplified tests, the
degree of simplification acceptable being dependent on the
NOTE 1—The statistical performance characteristics used throughout
this practice are estimated, by convention, at the confidence level
knowledge on the invariance properties of the performance
1− a=0.95.
characteristics previously gained by the procedures presented
here.
3.2.1 averaging time— predefined time interval length for
1.4 There is no fundamental difference between the instru-
which the air quality characteristic is made representative and
mental (automatic) and the manual (for example, wet-
Du the averaging time.
chemical) procedures, as long as the measured value is an
3.2.1.1 Discussion—Every measured value obtained is rep-
average representative for a predefined time interval. There-
resentative for a defined interval of time, t, the value of which
fore, the procedures presented are applicable to both. Further-
always lies above a certain minimum due to the intrinsic
more, they are applicable to measurement methods for ambi-
properties of the measuring procedure applied. In order to
ent, workplace, and indoor atmospheres, as well as emissions.
attain mutual comparability of data pertaining to comparable
1.5 This standard does not purport to address all of the
objects, a normalization to a common, predefined interval of
safety concerns, if any, associated with its use. It is the
time is necessary.
responsibility of the user of this standard to establish appro-
3.2.1.2 Discussion—By convention, this normalization is
achieved by transformation by means of a simple, linear, and
unweighted averaging process.
This practice is under the jurisdiction of ASTM Committee D22 on Sampling
and Analysis of Atmospheres and is the direct responsibility of Subcommittee
D22.03 on Ambient Atmospheres and Source Emissions. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Oct. 10, 1996. Published December 1996. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
published as D5280–94. Last previous edition D5280–94. 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.
D 5280 – 96 ( Reapproved 2001)
(a) Series of Discrete Samples: 3.2.10 warm-up time— the minimum waiting time for an
instrument to meet predefined values of its performance
K
cˆ u?Du 5 cˆ u 1 k 21 t?t (1)
~ ! ~ ~ ! characteristics after activating an instrument stabilized in a
( 0
K
k51
nonoperating condition.
where: 3.2.10.1 Discussion—In practice, the warm-up time can be
u = u− Du, and
determined by using the performance characteristic that is
Kt = Du, t << Du
expected to require the longest interval of time.
(b) Continuous Time Series:
3.2.10.2 Discussion—In the case of the manual procedures,
run-up time is used correspondingly.
1 u
cˆ~u?Du! 5 ducˆ~u?t! (2)
*
3.3 Abbreviations:Symbols and Abbreviations:
Du
u
3.3.1 a ,a ,a —coefficientsofthevariancefunctionmodel.
0 1 2
In both cases (a and b), the original sample, described by cˆ(
3.3.2 b , b —parameters of the estimate function for the
0 1
t), is linked to a representative interval of time of length t
calibration function.
whereas cˆ(Du), the result after application of the averaging
3.3.3 C—air quality characteristic.
process,ismaderepresentativefortheintervaloftime Du(just
3.3.4 c—value of C.
preceding u), the averaging time.
3.3.5 cˆ—measured value at c.
3.2.1.3 Discussion—The averaging time, Du, is therefore
3.3.6 c— value of C in the i-th sample; this sample may be
i
the predefined and, by convention, common time interval
generated from reference material.
length for which the measured variable cˆ is made representa-
3.3.7 c —normalization factor for air quality characteris-
tive in a sense that the square deviation of the original values,
tics; in this case | c |=1.
attributed to time interval lengths t << Du from cˆ over Du is a
3.3.8 Dc —inaccuracy of C at c .
minimum. 1 i
3.3.9 c¯ —weighted mean, with set of weights v .
v k
3.2.1.4 Discussion—The averaging process can alterna-
3.3.10 D(b )—drift (see ISO 6879) of the intercept of the
tively be realized by means of a special sampling technique
linear calibration function.
(averaging by sampling).
3.3.11 D(b )—drift of the slope of the linear calibration
3.2.2 continuously measuring system—a system returning a
function.
continuous output signal upon continuous interaction with the
3.3.12 D(cˆ)—drift of the measured value, cˆ,at c.
air quality characteristic.
3.3.13 DEP(b ) —first order measure of dependence of
0 IVi
3.2.3 influence variable—a variable affecting the interrela-
the intercept on the influence variable labeled by i.
tionship between the (true) values of the air quality character-
3.3.14 DEP(b ) —first order measure of dependence of
istic observed and the corresponding measured values; for 1 IVi
the slope on the influence variable labeled by i.
example, variable affecting the slope or the intercept of or the
3.3.15 DEP(cˆ) —first order measure of dependence of the
scatter around the calibration function. IVi
measured value on the influence variable labeled by i at c.
3.2.4 noncontinuously measuring system—a system return-
3.3.16 DEP(x) —first order measure of dependence of the
ing a series of discrete output signals. IVi
output signal on the influence variable labeled by i.
3.2.4.1 Discussion—The discretization of the output vari-
3.3.17 F—statistic (cf F-test).
able can be due to sampling in discrete portions or to inner
3.3.18 F —x-quantile of the F-distribution.
function characteristics of the system components. x
3.3.19 I — selectivity with respect to the influence vari-
3.2.5 period of unattended operation—the maximum ad- IVi
able labeled by i.
missible interval of time for which the performance character-
3.3.20 IV— influence variable labeled by i.
istics will remain within a predefined range without external i
3.3.21 iv— value of IV.
servicing, for example, refill, calibration, adjustment.
i i
3.3.22 D iv—difference of values of IV.
3.2.6 random variable—avariablethatmaytakeanyofthe
i i
3.3.23 L—total number of time intervals of the instability
valuesofaspecifiedsetofvaluesandwithwhichisassociated
test.
a probability distribution.
3.3.24 LDL—lower detection limit.
3.2.7 randomization— if, from a population consisting of
3.3.25 M—total number of samples generated by reference
the natural numbers 1 to n, these are drawn at random one by
material within one calibration experiment.
one successively without replacement until the population is
exhausted, the numbers are said to be drawn in random order. 3.3.26 N— number of values of the output variable at c.
i i
3.3.27 P , p —estimate of the slope of the regression
3.2.7.1 Discussion—If these numbers have been associated
|ll u
in advance with n distinct objects or n distinct operations that function of the output variable on time at c = c , c = c ,
|ll u
respectively.
are then rearranged in the order in which the numbers are
drawn, the order of the objects or operations is said to be 3.3.28 R—reproducibility.
randomized. 3.3.29 r—repeatability.
3.2.8 reference conditions—a specified set of values (in- 3.3.30 RES — resolution at C = c.
c
cluding tolerances) of influence variables delivering represen- 3.3.31 sˆ—estimate of the smoothed standard deviation of X
tative values of performance characteristics. at c.
3.2.9 variance function—a variance of the output variable 3.3.32 sˆ —smoothedestimateofthevarianceof X(repeated
as a function of the air quality characteristic observed. measurements) at c.
D 5280 – 96 ( Reapproved 2001)
3.3.33 s —normalization factor for the standard deviation;
the magnitude of s equals to 1.
3.3.34 s , s —estimate of the standard deviation of insta-
b b
0 1
bility(seeISO6879)oftheinterceptandtheslopeofthelinear
calibration function.
3.3.35 sc—estimate of the standard deviation of instability
at c.
3.3.36 s—estimateofthestandarddeviationofrepeated x
i ij
at c ; j repetition index.
i
3.3.37 sˆ—smoothed estimate of the standard deviation of
i
“repeated” x at c; j repetition index.
ij i
3.3.38 s — estimate of the repeatability standard deviation.
r
3.3.39 s —estimateofthestandarddeviationoftheexperi-
cˆx
mentally determined calibration function (in units of the air
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-distributionwith ydegreesof
y;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
NOTE 1— ____Measurement Branch.
3.3.48 x —output signal at c with the highest absolute
i,extr i
NOTE 2—___ Calibration Branch.
distance from x¯ .
i FIG. 1 Schematic of the Procedures of Measurement and of
3.3.49 x —j-th output signal at c. Evaluation for Performance Characteristics
ij i
3.3.50 x , x —output signal after i time intervals at the
l;i8 u;i
lower and upper value of the air quality characteristic of
4.2 Specification of Performance Characteristics to Be
reference material.
Tested—Specify the performance characteristics of the mea-
3.3.51 x¯ —weighted mean of the whole set of output
v
surement method in order of their relevance for the final
signals within the calibration experiment.
assessment of accuracy. The descriptors of the calibration
3.3.52 b , b —intercept and slope of the linear calibration
0 1
function, for example, intercept, b , and slope, b , as well as
0 1
function, respectively.
their qualifying performance characteristics are vital. Those
3.3.53 u—time.
performance characteristics for which prior knowledge is
3.3.54 Du—averaging time.
available, and those pertaining to influence variables covered
3.3.55 y—number of degrees of freedom in the calibration
by randomization are of lesser importance and need not be
experiment.
determined.
3.3.56 y , y —number of degrees of freedom for the nu-
1 2
4.3 Test Conditions— Perform the tests under explicitly
merator and denominator of the F-distribution, respectively.
stated conditions representative of the operational measure-
3.3.57 v = v(c)—continuous weighing factor gained by
ments. When testing for performance characteristics, describ-
modeling s.
i
ing functional dependencies, keep all influence variables con-
3.3.58 v —weighing factor at c .
1 1
stant except the one under consideration.
4. Requirements and Provisions
5. Test Procedures
4.1 Description of the Steps of the Measurement Methods 5.1 Averaging Time (see 3.2.1)—The range of allowable
Under Test—Describe all steps of the measurement method
averaging times is constrained by the requirement that the
used, such as sampling, analysis, postprocessing, and calibra- differences of subsequent output signals be mutually statisti-
tion. Fig. 1 illustrates schematically the steps to be followed in
cally independent.The corresponding minimum of the averag-
making a measurement or performing a series of calibration
ing time is determined by a specific performance (time)
experiments in order to determine the performance character-
characteristic, that is, continuously measuring systems; the
istics.
response time and noncontinuously measuring systems; the
sample time (filling time, accumulation time, etc.).
NOTE 2—Under certain conditions it may be suitable to test only one
5.1.1 Continuously Measuring Systems—In order to estab-
step or a selected group of steps of the measurement method. Under other
lish response time, lag time, and rise and fall time, input a step
conditions it may not be possible to include all the steps of the
measurement method. However, include as many steps as possible. function of the air quality characteristic to the continuously
D 5280 – 96 ( Reapproved 2001)
NOTE 3—Repetitions performed under reproducibility conditions (see
measuring system.This may be done by abruptly changing the
PracticeE177)requirearandomsam
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