ASTM E105-58(1996)
(Practice)Standard Practice for Probability Sampling Of Materials
Standard Practice for Probability Sampling Of Materials
SCOPE
1.1 This practice is primarily a statement of principles for the guidance of ASTM technical committees and others in the preparation of a sampling plan for a specific material.
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Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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An American National Standard
Designation: E 105 – 58 (Reapproved 1996)
Standard Practice for
Probability Sampling Of Materials
This standard is issued under the fixed designation E 105; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope intermediate step of an estimate, the decision process will
follow definite rules. In acceptance sampling, for example,
1.1 This practice is primarily a statement of principles for
these are often based on predetermined risks of taking the
the guidance of ASTM technical committees and others in the
undesired action when the true levels of the characteristic
preparation of a sampling plan for a specific material.
concerned have predetermined values; for example, acceptable
2. Terminology and rejectable quality levels may be specified.
4.2 The minimum requirements that must be met in order to
2.1 Definitions of Terms Specific to This Standard:
obtain the characteristics mentioned in 4.1 appear in Section 5,
2.1.1 probability sampling plans make use of the theory of
which also indicates the minimum requirements for the de-
probability to combine a suitable procedure for selecting
scription of a satisfactory sampling plan.
sample items with an appropriate procedure for summarizing
the test results so that inferences may be drawn and risks
5. Minimum Standards for a Probability Sampling Plan
calculated from the test results by the theory of probability. For
5.1 For a sampling plan to have the requirements mentioned
any given set of conditions there will usually be several
in Section 4 it is necessary:
possible plans, all valid, but differing in speed, simplicity, and
5.1.1 That every part of the pile, lot, or shipment have a
cost.
nonzero chance of selection,
3. Aim of Probability Sampling 5.1.2 That these probabilities of selection be known, at least
for the parts actually selected, and
3.1 The purpose of the sample may be to estimate properties
5.1.3 That, either in measurement or in computation, each
of a lot, pile, or shipment, such as the percentage of some
item be weighted in inverse proportion to its probability of
constituent,thefractionoftheitemsthatfailtomeetaspecified
selection. This latter criterion should not be departed from; for
requirement, the average weight or quality of an item, the total
example, equal weights should not be used when the probabili-
weight of the shipment, or the probable maximum or minimum
ties of selection are unequal, unless calculations show that
content of some chemical.
biases introduced thereby will not impair the usefulness of the
3.2 The purpose may be the rational disposition of the lot or
results.
shipment, without the intermediate step of the formation of an
5.2 To meet the requirements of 5.1.1 and 5.1.2, the
estimate.
sampling plan must describe the sampling units and how they
3.3 The purpose may be to provide aid toward rational
are to be selected. It must specify that the selection shall be
action concerning the production process that generated the lot,
objectively at random. To achieve random selection, use
pile, or shipment.
random sampling numbers, since mechanical randomizing
4. Characteristics of a Probability Sampling Plan
devices usually lead to biases and are not standard tools. The
requirements of 5.1.3 may be met, in nonobvious ways, by
4.1 A probability sampling plan will possess certain char-
various special methods of computation.
acteristics of importance, as follows:
5.3 In meeting the requirements of 5.1.3, carefully state the
4.1.1 It will possess an objective procedure for the selection
purposes served by sampling, lest a relatively unimportant aim
of the sample, with the use of random numbers.
overbalance a more important one. For example, estimates of
4.1.2 It will include a definite formula for the estimate, if
the over-all average quality of a stock of items may be less
there is to be an estimate; also for the standard error of any
important than the rational disposition of subgroups of the
estimate. If the sample is used for decision without the
stock of inferior quality. In this case the method of using
subsamples of equal size drawn from each subgroup is more
efficient, although at some expense to the efficiency of the
This practice is under the jurisdiction of ASTM Committee E-11 on Statistical
estimate of the over-all average quality. Similarly, in accep-
Methods and is the direct responsibility of Subcommittee E11.10 on Sampling.
tance inspection, samples of equal size drawn from lots that
Current edition approved Sept. 22, 1958. Published November 1968. Originally
published as E 105 – 54. Last previous edition E 105 – 56 T. vary widely in size serve primarily to provide consistent
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Please contact ASTM International (www.astm.org) for the latest information.
E 105 – 58 (1996)
judgment with respect to each lot, and secondarily to provide 6.1.2 The physical difficulties or the costs of drawing into
an estimate of the process average. Where the estimate of the the sample the specific ultimate sample units to be specified in
over-all average of a number of lots is the important objective,
the sampling plan.
samples proportional to the sizes of the subgroups will usually
6.2 There may be little information on the nature of the
yield an efficient estimate. For other possible criteria, sizes
distribution of the desired property in any given lot or in the
intermediate between equal and proportional sampling from
universe of such lots, or on the magnitude and stability of the
the subgroups will be appropriate.
components of variance involved. This circumstance is to be
5.4 It is not easy to describe in a few words the many sorts
expected if the manufacturing process has not had the benefit
of plans that will meet the requirements of 5.1.2. Nor is it easy
of statistical methods to eliminate assignable causes of vari-
to describe how these plans differ from those that do not satisfy
ability. It will then be difficult to specify in advance the exact
the requirement. Many standard techniques, such as pure
size of sample for a prescribed degree of precision.
random unstratified sampling, random stratified sampling, and
6.3 As experience is acquired, however, the sample can be
sampling with probabilities in proportion to size, will satisfy
increased or decreased to meet the requirements more exactly
the requirement; likewise every plan will do so where the
and more economically. In any case, a valid estimate can be
sample is made up of separate identifiable subsamples that
made of the precision provided by any probability sample that
were selected independently and by the use of random num-
was selected, based on an examination of the sample itself. In
bers.
this connection, random fluctuations that arise from the mea-
5.5 A probability sampling plan for any particular material
surement process must be considered and appropriate allow-
must be workable, and if several alternative plans are possible,
ance made, if necessary.
each of which will provide the desired level of precision, the
6.4 Because of the physical nature, condition, or location of
plan adopted should be the one that involves the lowest cost.
the material at the time of intended sampling, selection of the
5.6 Aprobability sampling plan must describe the sampling
units specified in a proposed sampling plan may not be
units and how they are to be selected (with or without
feasible, physically or economically. No matter how sound a
stratification, equal probabilities, etc.).The sampling plan must
given sampling plan is in a statistical sense, it is not suitable if
also describe:
the cost involved is prohibitive or if the work required is so
5.6.1 The formula for calculating an estimate (average
strenuous that it leads to short cuts or subterfuge by those
concentration, minimum concentration, range, total weight,
responsible for the sampling.
etc.),
5.6.2 A formula or procedure by which to calculate the
7. Planning for Sampling
standard error of any estimate from the results of the sample
itself, and
7.1 Different problems or difficulties are encountered with
5.6.3 Sources of possible bias in the sampling procedure or
various kinds of materials, and they require specific solutions
in the estimating formulas, together with data pertaining to the
for individual cases. Some general features of solutions to
possible magnitudes of the biases and their effects on the uses
common difficulties are as follows:
of the data.
7.1.1 Lackofspecificinformationonthepertinentstatistical
5.7 The development of a good sampling plan will usually
characteristics of the class of material to be sampled may
take place in steps, such as:
sometimes be overcome to a satisfactory degree, without
5.7.1 A statement of the problem for which an estimate is
excessive cost or delay, by investigation and utilization of
necessary,
existing, apparently unrelated data
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