ASTM E456-96
(Terminology)Standard Terminology for Relating to Quality and Statistics
Standard Terminology for Relating to Quality and Statistics
SCOPE
1.1 This terminology includes those quality and statistical terms in wide use in ASTM for which standard definitions appear desirable.
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Designation: E 456 – 96
Standard Terminology for
Relating to Quality and Statistics
This standard is issued under the fixed designation E 456; 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.
systematic error or bias component.
1. Scope
1.1 This terminology includes those quality and statistical
aliases, n—in a fractional factorial design, two or more effects
terms in wide use in ASTM for which standard definitions
which are estimated by the same contrast and which,
appear desirable.
therefore, cannot be estimated separately. E 1325
assignable cause, n—a factor that contributes to variation, and
2. Referenced Documents
which is feasible to detect and identify.
2.1 ASTM Standards:
NOTE 2—Many factors will contribute to variation but it may not be
E 177 Practice for the Use of the Terms Precision and Bias
feasible (economically or otherwise) to identify some of them.
in ASTM Test Methods
E 1325 Terminology Relating to Design of Experiments attribute data, n—observed values or determinations which
indicate the presence or absence of specific characteristics.
E 1402 Terminology Relating to Sampling
DISCUSSION—Items or units of material may be evaluated by counting
3. Significance and Use
or measurement. Attributes are counted whereas variables are mea-
3.1 This terminology is the general terminology standard for
sured. Attribute distributions are discrete. See variables data.
terms defined by Committee E-11.
attributes, method of, n—measurement of quality by the
3.2 Citation is made to other E-11 standards which contain
method of attributes consists of noting the presence (or
more extensive information regarding the particular term and
absence) of some characteristic or attribute in each of the
its usage. These references may be to other practices and
units in the group under consideration, and counting how
guides or to more specific terminology standards, such as
many units do (or do not) possess the quality attribute, or
Terminology E 1325.
how many such events occur in the unit, group, or area.
4. Terminology average run length (ARL)—(1) sample sense, n—the aver-
age number of times that a process will have been sampled
acceptance (control chart or acceptance control chart
and evaluated before a shift in process level is signaled, and
usage, n), n—a decision that the process is operating in a
(2) unit sense, n—the average number of units that will have
satisfactory manner with respect to the statistical measures
been produced before a shift in level is signaled.
being plotted: action limits: control limits.
DISCUSSION—A long ARL is desirable for a process located at its
accepted reference value, n—a value that serves as an
specified level (so as to minimize calling for unneeded investigation or
agreed-upon reference for comparison, and which is derived
corrective action) and a short ARL is desirable for a process shifted to
as: (1) a theoretical or established value, based on scientific
some undesirable level (so that corrective action will be called for
principles, (2) an assigned or certified value, based on
promptly). ARL curves are used to describe the relative quickness in
experimental work of some national or international organi-
detecting level shifts of various control chart systems.
zation, or (3) a consensus or certified value, based on
balanced incomplete block design (BIB), n—an incomplete
collaborative experimental work under the auspices of a
block design in which each block contains the same number
scientific or engineering group.
k of different versions from the t versions of a single
accuracy, n—the closeness of agreement between a test result
principal factor arranged so that every pair of versions
and an accepted reference value.
occurs together in the same number, l, of blocks from the b
NOTE 1—The term accuracy, when applied to a set of test results,
blocks. E 1325
involves a combination of a random component and of a common
batch, n—a definite quantity of some product or material
produced under conditions that are considered uniform.
This terminology is under the jurisdiction of ASTM Committee E-11 on Quality
NOTE 3—A batch is usually smaller than a lot.
and Statistics and is the direct responsibility of Subcommittee E11.60 on Terminol-
ogy.
bias, n—the difference between the expectation of the test
Current edition approved June 10, 1996. Published September 1996. Originally
results and an accepted reference value.
published as E 456 – 72. Last previous edition E 456 – 92.
Annual Book of ASTM Standards, Vol 14.02.
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NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 456
NOTE 4—Bias is the total systematic error as contrasted to random
linear combinations of the treatments (contrasts).
error. There may be one or more systematic error components contributing
NOTE 8—Contrast analysis involves a systematic tabulation and analy-
to the bias. A larger systematic difference from the accepted reference
sis format usable for both simple and complex designs. When any set of
value is reflected by a larger bias value.
orthogonal contrasts is used, the procedure, as in the example, is
characteristic, n—a property of items in a sample or popula-
straightforward. When terms are not orthogonal, the orthogonalization
process to adjust for the common element in nonorthogonal contrast is
tion which, when measured, counted or otherwise observed,
also systematic and can be programmed. E 1325
helps to distinguish between the items.
cluster sampling, n—when the primary sampling unit com-
control—(evaluation), n—an evaluation to check, test, or
prises a bundle of elementary units or a group of subunits,
verify; (authority): the act of guiding, directing, or manag-
the term cluster sampling may be applied.
ing; (stability): a state of process in which the variability is
DISCUSSION—Examples of cluster sampling are: selection of city attributable to a constant system of chance causes.
blocks as primary sampling units; selection of a household as a cluster
control chart factor, n—a factor, usually varying with sample
of people (of which only one may be interviewed); selection of bundles
size, to convert specified statistics or parameters into a
of rods or pipe from a shipment; and selection, from a shipment, of
central line value or control limit appropriate to the control
cartons that contain boxes or packages within them.
chart.
completely randomized design, n—a design in which the
control chart method, n—the method of using control charts
treatments are assigned at random to the full set of experi-
to determine whether or not processes are in a stable state.
mental units. E 1325
control limits, n—limits on a control chart which are used as
completely randomized factorial design, n—a factorial ex-
criteria for signaling the need for action, or for judging
periment (including all replications) run in a completely
whether a set of data does or does not indicate a state of
randomized design. E 1325
statistical control.
component of variance, n—a part of a total variance identified
conventional true value of a quantity, n—value attributed to
with a specified source of variability.
a particular quantity and accepted, sometimes by conven-
composite design, n—a design developed specifically for
tion, as having an uncertainty appropriate for a given
fitting second order response surfaces to study curvature,
purpose.
constructed by adding further selected treatments to those
NOTE 9—88Conventional true value” is sometimes called 88assigned
n
obtained from a 2 factorial (or its fraction). E 1325
value”, 88best value”, 88conventional value”, or 88reference value”. 88Ref-
confounded factorial design, n—a factorial experiment in
erence value”, in this sense, should not be confused with 88reference
which only a fraction of the treatment combinations are run
value” in the sense of an influence quantity affecting a measuring
in each block and where the selection of the treatment instrument.
NOTE 10—Frequently, a number of results of measurements of a
combinations assigned to each block is arranged so that one
quantity is used to establish a conventional true value.
or more prescribed effects is(are) confounded with the block
DISCUSSION—When warning limits are used, the control limits are
effect(s), while the other effects remain free from confound-
often called “action limits.” Action may be in the form of investigation
ing.
of the source(s) of an “assignable cause”, making a process adjustment,
or terminating a process. Criteria other than control limits are also used
NOTE 5—All factor level combinations are included in the experiment.
frequently.
E 1325
dependent variable, n—See response variable.
confounding, n—combining indistinguishably the main effect
design of experiments, n—the arrangement in which an
of a factor or a differential effect between factors (interac-
experimental program is to be conducted, and the selection
tions) with the effect of other factor(s), block factor(s) or
of the levels (versions) of one or more factors or factor
interactions(s).
combinations to be included in the experiment. Synonyms
NOTE 6—Confounding is a useful technique that permits the effective
include experiment design and experimental design.
use of specified blocks in some experiment designs. This is accomplished
E 1325
by deliberately preselecting certain effects or differential effects as being
deviation, n—the difference between a measurement or quasi-
of little interest, and arranging the design so that they are confounded with
measurement and its stated value or intended level.
block effects or other preselected principal factor or differential effects,
while keeping the other more important effects free from such complica-
DISCUSSION—Deviation should be stated as a difference in terms of
tions. Sometimes, however, confounding results from inadvertent changes
the appropriate data units. Sometimes these units will be original
to a design during the running of an experiment or from incomplete
measurement units; sometimes they will be quasi-measurements; that
planning of the design, and it serves to diminish, or even to invalidate, the
is, a scaled rating of subjective judgments; sometimes they will be
effectiveness of an experiment. E 1325
designated values representing all continuous or discrete measurements
falling in defined cells or classes.
contrast, n—a linear function of the observations for which
error of result, n—the test result minus the accepted reference
the sum of the coefficients is zero.
value (of the characteristic).
NOTE 7—With observations Y , Y ,., Y , the linear function
1 2 n
a Y + a Y + . + a Y is a contrast if, and only if (a = 0, where the a NOTE 11—It is not possible to correct for random error.
1 1 2 2 n n i i
values are called the contrast coefficients. E 1325
experimental design, n—see design of experiments. E 1325
contrast analysis, n—a technique for estimating the param- experiment space, n—the materials, equipment, environmen-
eters of a model and making hypothesis tests on preselected tal conditions and so forth that are available for conducting
NOTICE: This standard has either been superseded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
E 456
within-laboratory control, the intermediate measures of precision are
an experiment. E 1325
likely to vary appreciably from laboratory to laboratory. Thus, intermedi-
experimental unit, n—a portion of the experiment space to
ate precisions may be more characteristic of individual laboratories than of
which a treatment is applied or assigned in the experiment.
the test method.
NOTE 12—The unit may be a patient in a hospital, a group of animals,
intermediate precision conditions, n—conditions under
a production batch, a section of a compartmented tray, etc. E 1325
which test results are obtained with the same test method
evolutionary operation (EVOP), n—a sequential form of
using test units or test specimens (see Practice E 691, 10.3)
experimentation conducted in production facilities during
taken at random from a single quantity of material that is as
regular production.
nearly homogeneous as possible, and with changing condi-
tions such as operator, measuring equipment, location within
NOTE 13—The principal theses of EVOP are that knowledge to improve
the laboratory, and time.
the process should be obtained along with a product, and that designed
experiments using relatively small shifts in factor levels (within produc- item, n—(1) an object or quantity of material on which a set of
tion tolerances) can yield this knowledge at minimum cost. The range of
observations can be made: (2) an observed value or test
variation of the factors for any one EVOP experiment is usually quite
result obtained from an object or quantity of material.
small in order to avoid making out of tolerance products, which may
DISCUSSION—The second usage in the definition is generally limited
require considerable replication, in order to be able to clearly detect the
to generic descriptions such as in the definition of “population.” Terms
effect of small changes. E 1325
such as “observation,” “measurement,” “test result,” “unit,” “value” or
factorial experiment (general), n—in general, an experiment “yield” are more common in specific applications. A set as used here
may be one or more variables.
in which all possible treatments formed from two or more
factors, each being studied at two or more levels (versions)
level (of a factor), n—a given value, a specification of
are examined so that interactions (differential effects) as well
procedure or a specific setting of a factor.
as main effects can be estimated. E 1325
n
NOTE 17—88Version” is a general term applied both to quantitative and
2 factorial experiment, n—a factorial experiment in which n
qualitative factors. The more restrictive term 88level” is frequently used to
factors are studied, each of them in two levels (versions).
express more precisely the quantitative characteristic. For example, two
E 1325
versions of a catalyst may be presence and absence. Four levels of a heat
fractional factorial design, n—a factorial experiment in
treatment may be 100°C, 120°C, 140°C, and 160°C. E 1325
which only an adequately c
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