ASTM D5280-96
(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 An American National Standard
Standard Practice for
Evaluation of Performance Characteristics of Air Quality
Measurement Methods with Linear Calibration Functions
This standard is issued under the fixed designation D 5280; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 This practice covers procedures for evaluating the 2.1 ASTM Standards:
following performance characteristics of air quality measure- D 1356 Terminology Relating to Sampling and Analysis of
ment methods: bias (in part only), calibration function and Atmospheres
linearity, instability, lower detection limit, period of unattended E 177 Practice for Use of the Terms Precision and Bias in
operation, selectivity, sensitivity, and upper limit of measure- ASTM Test Methods
ment. E 456 Terminology Relating to Quality and Statistics
1.2 The procedures presented in this practice are applicable 2.2 ISO Standard:
only to air quality measurement methods with linear continu- ISO 6879: 1983, Air Quality—Performance Characteristics
ous calibration functions, and the output variable of which is a and Related Concepts for Air Quality Measuring Meth-
defined time average. The linearity may be due to postprocess- ods
ing of the primary output variable. Additionally, replicate
3. Terminology
values belonging to the same input state are assumed to be
normally distributed. Components required to transform the 3.1 Definitions:
3.1.1 For definitions of terms used in this practice, refer to
primary measurement method output into the time averages
desired are regarded as an integral part of this measurement Terminology D 1356.
3.2 Definitions of Terms Specific to This Standard:
method.
1.3 For surveillance of measurement method stability under
NOTE 1—The statistical performance characteristics used throughout
routine measurement conditions, it may suffice to check the
this practice are estimated, by convention, at the confidence level
essential performance characteristics using simplified tests, the
1−a5 0.95.
degree of simplification acceptable being dependent on the
3.2.1 averaging time—predefined time interval length for
knowledge on the invariance properties of the performance
which the air quality characteristic is made representative and
characteristics previously gained by the procedures presented
Du the averaging time.
here.
3.2.1.1 Discussion—Every measured value obtained is rep-
1.4 There is no fundamental difference between the instru-
resentative for a defined interval of time, t, the value of which
mental (automatic) and the manual (for example, wet-
always lies above a certain minimum due to the intrinsic
chemical) procedures, as long as the measured value is an
properties of the measuring procedure applied. In order to
average representative for a predefined time interval. There-
attain mutual comparability of data pertaining to comparable
fore, the procedures presented are applicable to both. Further-
objects, a normalization to a common, predefined interval of
more, they are applicable to measurement methods for ambi-
time is necessary.
ent, workplace, and indoor atmospheres, as well as emissions.
3.2.1.2 Discussion—By convention, this normalization is
1.5 This standard does not purport to address all of the
achieved by transformation by means of a simple, linear, and
safety concerns, if any, associated with its use. It is the
unweighted averaging process.
responsibility of the user of this standard to establish appro-
(a) Series of Discrete Samples:
priate safety and health practices and determine the applica-
K
bility of regulatory limitations prior to use.
cˆ~u?Du! 5 cˆ~u 1 ~k 2 1!t ? t (1)
(
K
k51
where:
This practice is under the jurisdiction of ASTM Committee D-22 on Sampling
and Analysis of Atmospheres and is the direct responsibility of Subcommittee
D22.03 on Ambient Atmospheres and Source Emissions.
Current edition approved Oct. 10, 1996. Published December 1996. Originally
published as D 5280 – 94. Last previous edition D 5280 – 94. Annual Book of ASTM Standards, Vol 11.03.
2 4
This practice was adapted from International Standard ISO/DP 9169, prepared Annual Book of ASTM Standards, Vol 14.02.
by ISO/TC 146/SC 4/WG 4, by the kind permission of the Chairman of ISO/TC 146 Available from International Organization for Standardization, Case Pastale 56,
and the Secretariat of ISO/TC 146/SC 4. CH-1211, Geneva 20, Switzerland.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
D 5280
determined by using the performance characteristic that is
u 5u − Du, and
expected to require the longest interval of time.
Kt5Du, t << Du
3.2.10.2 Discussion—In the case of the manual procedures,
(b) Continuous Time Series:
run-up time is used correspondingly.
1 u
cˆ~u?Du! 5 ducˆ~u ? t! (2)
3.3 Symbols and Abbreviations:
*
Du
u
3.3.1 a , a , a —coefficients of the variance function model.
0 1 2
In both cases (a and b), the original sample, described by
3.3.2 b , b —parameters of the estimate function for the
0 1
cˆ(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, is made representative for the interval of time 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 | 5 1.
attributed to time interval lengths t << Du from cˆ over Du is a
3.3.8 Dc —inaccuracy of C at c .
1 i
minimum.
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
1 IVi
istic observed and the corresponding measured values; for
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
IVi
scatter around the calibration function.
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
IVi
ing a series of discrete output signals.
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.
x
function characteristics of the system components.
3.3.19 I —selectivity with respect to the influence variable
IVi
3.2.5 period of unattended operation—the maximum ad-
labeled by i.
missible interval of time for which the performance character-
3.3.20 IV —influence variable labeled by i.
i
istics will remain within a predefined range without external
3.3.21 iv —value of IV .
servicing, for example, refill, calibration, adjustment. i i
3.3.22 Div —difference of values of IV .
3.2.6 random variable—a variable that may take any of the i i
3.3.23 L—total number of time intervals of the instability
values of a specified set of values and with which is associated
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
3.3.26 N —number of values of the output variable at c .
exhausted, the numbers are said to be drawn in random order.
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
function of the output variable on time at c 5 c , c 5 c ,
in advance with n distinct objects or n distinct operations that
|ll u
respectively.
are then rearranged in the order in which the numbers are
3.3.28 R—reproducibility.
drawn, the order of the objects or operations is said to be
3.3.29 r—repeatability.
randomized.
3.2.8 reference conditions—a specified set of values (in- 3.3.30 RES —resolution at C 5 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 —smoothed estimate of the variance of X (repeated
as a function of the air quality characteristic observed. measurements) at c.
3.2.10 warm-up time—the minimum waiting time for an 3.3.33 s —normalization factor for the standard deviation;
instrument to meet predefined values of its performance the magnitude of s equals to 1.
characteristics after activating an instrument stabilized in a 3.3.34 s , s —estimate of the standard deviation of insta-
b b
0 1
nonoperating condition. bility (see ISO 6879) of the intercept and the slope of the linear
3.2.10.1 Discussion—In practice, the warm-up time can be calibration function.
D 5280
3.3.35 sc—estimate of the standard deviation of instability
at c.
3.3.36 s —estimate of the standard deviation of repeated 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 —estimate of the standard deviation of the experi-
cˆx
mentally determined calibration function (in units of the air
quality characteristic).
3.3.40 s —estimate of the standard deviation of the ex-
xc
perimentally determined calibration function (in units of the
output variable).
3.3.41 t —q-quantile of the t-distribution with y degrees of
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
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;i8 u;i
lower and upper value of the air quality characteristic of
NOTE 1— ____Measurement Branch.
reference material.
NOTE 2—___ Calibration Branch.
3.3.51 x¯ —weighted mean of the whole set of output
v
FIG. 1 Schematic of the Procedures of Measurement and of
signals within the calibration experiment.
Evaluation for Performance Characteristics
3.3.52 b , b —intercept and slope of the linear calibration
0 1
function, respectively. performance characteristics for which prior knowledge is
3.3.53 u—time.
available, and those pertaining to influence variables covered
3.3.54 Du—averaging time. by randomization are of lesser importance and need not be
3.3.55 y—number of degrees of freedom in the calibration
determined.
experiment. 4.3 Test Conditions—Perform the tests under explicitly
3.3.56 y , y —number of degrees of freedom for the nu-
stated conditions representative of the operational measure-
1 2
merator and denominator of the F-distribution, respectively. ments. When testing for performance characteristics, describ-
3.3.57 v5v(c)—continuous weighing factor gained by
ing functional dependencies, keep all influence variables con-
modeling s . stant except the one under consideration.
i
3.3.58 v —weighing factor at c .
1 1
5. Test Procedures
4. Requirements and Provisions
5.1 Averaging Time (see 3.2.1)—The range of allowable
4.1 Description of the Steps of the Measurement Methods
averaging times is constrained by the requirement that the
Under Test—Describe all steps of the measurement method
differences of subsequent output signals be mutually statisti-
used, such as sampling, analysis, postprocessing, and calibra-
cally independent. The corresponding minimum of the averag-
tion. Fig. 1 illustrates schematically the steps to be followed in
ing time is determined by a specific performance (time)
making a measurement or performing a series of calibration
characteristic, that is, continuously measuring systems; the
experiments in order to determine the performance character-
response time and noncontinuously measuring systems; the
istics.
sample time (filling time, accumulation time, etc.).
5.1.1 Continuously Measuring Systems—In order to estab-
NOTE 2—Under certain conditions it may be suitable to test only one
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
function of the air quality characteristic to the continuously
measurement method. However, include as many steps as possible.
measuring system. This may be done by abruptly changing the
4.2 Specification of Performance Characteristics to Be value of the air quality characteristic from, for example, 20 to
Tested—Specify the performance characteristics of the mea- 80 % of the upper limit of measurement (cf Fig. 2). Confirm
surement method in order of their relevance for the final these performance characteristics by an appropriate number of
assessment of accuracy. The descriptors of the calibration repetitions. If rise time and fall time differ, take the longer one
function, for example, intercept, b , and slope, b , as well as for the computation of the response time. By convention the
0 1
their qualifying performance characteristics are
...
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