August 22, 1966 M20-2

APPENDIX A

**GLOSSARY OF TERMS**

[Accuracy:]{.underline} Refers to the deviation of an estimate from the
true population (or proc­ess) value; not the same as precision.

[Adequate Sample:]{.underline} Pertains most commonly to the size of a
sample; a sample is adequate if its size is large enough to give the
degree of precision or reliability required in a given sample estimate.

[AQL\--\"acceptable quality]{.underline} level\": The fraction
defective, percent in error, or num­ber of errors per 100 items or
workunits that, for a given activity, work process or popu­lation, has
been administratively determined to be acceptable or tolerable.

[Assignable]{.underline} Cause: A source of variation in the output of a
process which is other than chance. The presence of such a nonchance
(nonrandom) factor usually is indicated when a sample plot on a control
chart falls outside the control limits\--i.e., outside the range within
which chance variations are expected to fall. Nonrandom sequences of
sample plots within the control limits may also -indicate that an
assignable cause is operating. It is presumed that assignable causes,
once their presence is indicated, can be located and, if desirable,
removed or their influence reduced. Examples of assignable causes of
varia­tion include a new worker, absence of a supervisor in a critical
area, a change in form, a change in instructions, etc.

[Attributes]{.underline}, Sampling for: Estimation of quality by noting
the presence or absence of some characteristic (attribute) in each of
the units in the sample under consideration, and counting how many units
do or do not possess it. An example is counting the number of units in a
sample that are \"in error\" or are \"not in error.\"

[Bias:]{.underline} Systematic error, leading to distortion in one
direction of a statistical result; distinct from random error, where
distortions in both directions may be largely self canceling.

[Binomial Distribution:]{.underline} The usual technical or mathematical
definition is beyond the scope or purpose of this manual. However, the
binomial distribution is of special importance in statistical quality
control because of its relation to problems involving fraction
defective, proportion or percent \"in error,\" etc. The probability of a
specified number of work units \"in error\" in any sample of a given
size can be determined by the binomial expansion if the true proportion
of workunits \"in error\" in the parent population is known. From this
it can be seen that the binomial distribution describes the sampling
distribution of a \"percent in error.\" This is why the formula for the
standard deviation of the binomial is used to establish three standard
deviation control limits for percent in error, although the normal
distribution approximation to the binomial is often the basis for
interpreting the sample results.

[Complement:]{.underline} As used herein, the difference between any
given fraction or propor­tion and unity; the value required to complete
the whole; if the proportion is expressed as a percentage, the
difference between that percentage and 100%. As examples, in each of the
following three pairs of values, 1/4 and 3/4, 0.85 and 0.15, 98% and 2%,
each value is the complement of the other.

[Confidence]{.underline} Interval: The interval between two values,
known as confidence limits, within which it may be asserted, with a
specified degree of confidence as to the correctness of the assertion,
that the true population value lies.

[Confidence]{.underline} Limits: The values which form the upper and
lower limits to the con­fidence interval.

[Constant-Cause System:]{.underline} Variations in the quality or other
characteristics of in­dividual units of output of a work process are the
result of the random-like variability of the many factors which in
combination constitute the process: Forms, materials, equip­ment, people,
methods and procedures, the working environment, etc. A work process may
be thought of as a complex set of causes or conditions which together
produce a given

**App. A-1**

M20-2 August 22, 1966

APPENDIX A

end result. If the set of causes and conditions remains essentially
unchanged, it is said to represent a constant-cause system. This
distribution or the variation pattern of a constant-cause system is
predictable or \"stable\" within specified mathematical limits. When a
work process exhibits the stability of a constant-cause system, it is
said to be in statistical control.

[Control]{.underline} Chart: A graphic device for detecting lack of
statistical control. Lack of statistical control in data from a process
indicates that observed variations in quality are greater than should
occur by chance. The criteria by which lack of control is detected
involve the position, order, trend, or grouping of successive plots of
sample results.

[Control Limits:]{.underline} Values on a control chart, above and below
the central horizontal line corresponding to the true average value of a
quantitative characteristic of a particular process under examination,
between which a stated proportion of the sample statistics obtained from
repeated sampling from that process should fall, The control limits
dis­cussed in this manual and shown in the table in appendix E, mark off
intervals of three standard deviations above and below the (presumed)
process average (underlying percent in error of the sampled population)
and, in accordance with the assumption of an approxi­mately normal
distribution of the sampling error, should therefore include about 99.7
percent of the sample statistics derived from a large number of
successive samples of the appropriate fixed size.

[Controlled]{.underline} Process: As used in SQC, a process for which
the control chart shows no sample plot or points outside the control
limits and no nonrandom variation within the limits.

[Cumulative Sample:]{.underline} A sample obtained by combining or
pooling two or more samples drawn independently from the same
population; where sampling is from the outflow of a continuing work
process, samples drawn at periodic intervals are often cumulated over
several periods of time; examples are the cumulation of samples taken
daily, weekly, monthly, or at other intervals of time; where the
conditions of a work process remain statistically stable, samples may be
cumulated indefinitely over time to provide larger samples and greater
estimating precision as needed.

[Error:]{.underline} (1) When applied to an individual work unit, an
error is any nonconformance of the work unit with specified
requirements; (2) as commonly used in statistics, \"error\" denotes the
difference between an observed value and its \"true\" value (see
\"sampling error \").

[Error, Range of:]{.underline} A range of values bracketed around a
sample statistic (determined by various multiples of the standard
deviation of the sampling distribution of the given statistic) within
which the true value may be supposed to lie with a certain probability;
also used to indicate the range bracketed around a population value
within which a specified proportion of all sample statistics should
fall.

[Errors Per 100 Work Units:]{.underline} The number of errors contained
in any given number of

work units reviewed, divided by the total number of work units reviewed,
and multiplied by 100. In equation form:

> [Errors per 100 work units]{.underline} = (Number of [errors) X
> 100]{.underline}
>
> Number of work units reviewed

For the purpose of applying control limits for percentages to the number
of errors per 100 work units, the number of errors may be treated as a
percentage.

[Error]{.underline} Rate: The underlying \"rate\" at which errors
normally occur in a process (an error being defined as any
nonconformance to some specified requirement); an error rate is usually
expressed in terms of either (1) the proportion or percentage of units
in error, where a \"unit in error\" is construed to mean a unit
containing or associated with one or more errors, or (2) the number of
errors per 100 units, where every individual error contributes to the
total count, even though it be one of several involving the same unit.
The ratio of the number of errors per 100 units may in most cases be
treated, for control-chart purposes, as though it were a percentage in
error.

App. A-2

August 22, 1966 M20-2

APPENDIX A

[Estimate:]{.underline} As used herein, refers to a value derived from a
random sample which is us d to -estimate\" the true population value.

Fraction Defective: The fraction which expresses the ratio of the number
of work units in error (i.e., that are defective) in a lot or in a
sample to the total -number of work units in the lot or sample.

Frequency: The number of occurrences of a given event, attribute, or
quality charac­teristic, the number of units of a population or of a
sample falling into a specified class.

[Frequency]{.underline} Distribution: The way in which the frequencies
of the members (units) of a population or a sample are distributed
according to the values of some characteristic that is being studied,

[Independence:]{.underline} The usual technical or mathematical
definition is beyond the scope or purpose of this manual; as used
herein, independence refers to a condition under which the drawing or
selection of any population unit into a given sample is not influenced
or controlled by any other drawing or selection (except as any such
selection limits the popu­lation units available for succeeding draws).

[independent]{.underline} Samples: Successive samples are said to be
independent if the selection of sample units in any sample is
independent of the selection of units in any other sample.

Infinite Population: A population which is indefinitely large; a
population which can­not be exhausted through repeated sampling. The
value of work units which could be pro­duced by a work process operating
indefinitely under essentially constant conditions is regarded as an
infinite population, and the total number of work units actually
produced is regarded as a \"sample\" from this infinite population.

[Interval Estimate:]{.underline} An estimate of population value given
in the form of a specified interval or range of values, with a lower and
upper limit, within which the population value is asserted to lie. Where
sampling is the basis for the estimate, the specification of the
interval is ordinarily accompanied by a statement of the degree of
confidence\--usually in a probabilistic sense\--that can be placed in
the correctness of the assertion. An interval estimate is thus
distinguished from a point estimate, where a single value is taken as
the estimate of the population value.

[Judgment Sample:]{.underline} A sample in which the sample units are
selected by some measure of human judgment rather than by a selection
procedure based on assigned probabilities.

[Lot:]{.underline} A group, aggregate, collection or batch of similar
objects or things; in quality

control a lot is usually considered to be a homogeneous group of parts,
products or units

produced under essentially the same conditions, with a common origin or
source; an ex-

ample is the output during an interval of time of one machine, one crew,
or one work process. Units from different and nonhomogeneous sources
ordinarily should not be mixed into one lot.

Mean: The sum of the observed values in a population or in a sample
divided by the total number of such values in the population or sample.

[Moving]{.underline} [Average (or]{.underline} Total): See moving
sample.

Moving [Sample:]{.underline} As used herein, a series of cumulative
samples where each is ob­tained by combining smaller samples drawn during
successive subperiods of time from the outflow of a continuing work
process, and where the total cumulated samples cover a series of time
periods of fixed length but continually changing limits; for example, a
\"12-month moving sample\" is a series of cumulated samples, changing
with each suc­cessive month, where each sample is the aggregate total of
the individual \"monthly\" samples for the most recent 12 months (the
current month plus the I I months preceding); where the component or
subperiod samples are of equal size, sample error percentages or other
sample statistics may simply be [averaged]{.underline} to obtain the
same result otherwise obtained through cumulating the samples
themselves.

App. A-3

M20-2 August 22, 1966

APPENDIX A

[Nonsampling Error:]{.underline} The error or deviation from the true
population value in sample estimates which cannot be attributed to
chance sampling variations. Examples are errors resulting from
imperfections in the selection of sample units, bias in the estimating
pro­cedure used, and mistakes in arithmetical calculations.

[Normal Distribution:]{.underline} The usual technical or mathematical
definition is beyond the scope or purpose of this manual. For purposes
of quality control and sampling as dis­cussed herein, the normal
distribution is important mainly because of its use in describing and
measuring sampling error. The normal distribution presents a
symmetrical, bell shaped curve which describes the sampling distribution
of many common sample statistics. While the sampling distributions of
proportions and \"percents in error,\" as used in quality control, are
more correctly described by the binomial distribution, they are often
closely approximated by the normal distribution, and it is common
practice to use the normal dis­tribution for this purpose. The normal
distribution provides the theoretical basis for the determination of
confidence limits and quality control limits, for the specification of
par­ticular levels or degrees of confidence involved in making sample
estimates and in evaluat­ing sampling error, and for the interpretation
of control chart evidence. For example, control limits on quality
control charts are commonly set at three standard deviations above and
below the process average because in a normal distribution, which is
regarded as describing the distribution of observations obtained from
samples randomly drawn from a process which is in statistical control,
99.73 percent of all observations should fall in this range; it is
therefore deemed reasonable to conclude that an observation falling
outside this range is evidence that certain nonrandom forces or
\"assignable causes\" are influenc­ing the process.

[Observation:]{.underline} A statistical measurement; the value or the
characteristic associated with any individual unit drawn from a
population of data; also, the value of a given statistic, such as a
mean, ratio or percentage, derived from any sample of two or more units
drawn from the same population.

[Parameter:]{.underline} A value, property, or characteristic of a
population, as distinguished from a sample. Examples are a mean,
proportion or percentage, total, range, standard deviation, etc.

[Percentage]{.underline} A proportion multiplied by 100 (see
proportion\"); a specific amount found by taking a certain percent
(rate) of a base; for example, the percentage obtained by taking 25% of
80 (the base) is 20.

[Percent in Error:]{.underline} The number of work units containing one
or more errors divided by the total number of work units reviewed,
expressed as a percentage. In equation form:

Percent in error = [(Number of]{.underline} work units in error) X 100

Number of work units reviewed

[Population:]{.underline} The totality or aggregate of all items,
objects, cases, individuals, work units, or other units or measures in
which there is interest; may be finite or infinite; same as
\"universe.\"

[Precision:]{.underline} Refers to the standard deviation of a sample
estimate; the smaller the standard deviation, the greater the precision.
The ranges between the upper and lower three standard deviation control
limits for specified percentages in the table shown in appendix E of
this manual are indicators of precision. In general, the precision of an
estimate varies inversely with the square root of the number of
observations upon which it is based.

[Probability:]{.underline} Commonly used in the sense of relative
frequency of occurrence; the probability of an event is said to be the
relative frequency of occurrence of the event in an indefinitely large
number or series of observations; refers to the likelihood of
occurrence.

[Probability Sampling:]{.underline} Any method of selection of a sample
which is based on the theory of probability; probability sampling
requires that at any stage in the operation of selection, the
probability of any unit or set of units being selected must be known.
Prob­ability sampling is the only general method of sampling known which
makes it possible to obtain a mathematical measure of the precision of
the sample estimate.

App. A-4

August 22, 1966 M20-2

APPENDIX A

[Process:]{.underline} Any set of conditions or causes which in
combination and working together produce a given result; a \" work
process\" may be considered as the combination of par­ticular workers,
skills, techniques, procedures, materials, machines, equipment, etc.,
which working together result in the production of certain identifiable
services or end products.

[Process Average:]{.underline} The underlying \"true\" average of the
conceptually infinite popula­tion of completed end products or work units
that in theory might be generated by a given work process when operating
under a stable system of chance causes; in practice it usually
represents the average of a long series of independent samples drawn
from a process presumably operating within a state of statistical
control.

[Process Average Percent in Error:]{.underline} The underlying \"true\"
percentage of units in error in the total output of a work process; the
probability that a unit selected at random from a process which is
statistically under control is in error (see \"Process Average \").

[Proportion:]{.underline} The ratio of the number of units possessing a
certain attribute, as for example, a particular quality characteristic,
in a population or in a sample, to the total number of units in the
population or sample.

[Quality Control:]{.underline} A method of controlling the quality of
the output of a process by detecting the presence of and eliminating
systematic variations in quality (\"assignable causes\"), or reducing
them to an acceptable level, leaving the remaining variation to chance.
A process in which variation is due almost entirely to chance causes is
said to be \"in statistical control.\" The expression \"quality
control\" is also used in the broad sense of the control of quality by
any method whatever.

[Random:]{.underline} By chance (see \"random sampling\").

[Random Numbers:]{.underline} Sets or tables of numbers, generated by a
randomizing process, used for the drawing of random samples (see app.
C).

[Random]{.underline} Sampling: The process of selecting a sample from a
population so that every unit in the population has an equal and
independent chance of being included in the sample.

[Random Start:]{.underline} In selecting a systematic random sample at
intervals of some speci­fied number of units in an ordered population, it
is often desirable to select the first unit at random from the first
such number of units in the population. Such selection is then said to
have given the sample a \"random start-\"

[Range:]{.underline} The largest Minus the smallest of a set of values.

[Reliability:]{.underline} Synonymous with precision; refers to the
uniformity of sample results when obtained from repeated samples of the
same size and type from the same population; as used in this manual, it
is not to be confused with other uses of the term, as for example, in
the concept of product reliability\" as discussed in current literature
in engineering and quality control.

[Risk:]{.underline} As used herein, refers to the degree of risk
associated with given degrees of confidence, in the sense that if, for
example, a statement is made \"with 95 percent con­fidence\" that the
true population parameter lies within a specified interval, there is a
\"5 percent risk\" that the parameter actually lies outside that
interval.

[Runs:]{.underline} A series of successive sample plots on a control
chart which taken as a sequence exhibit such relationship, in a
probability sense, as to indicate that nonrandom factors have influenced
the process.

SQC: Statistical quality control.

[Sample:]{.underline} Part of a population; a limited or finite number
of units selected from a population, usually by a prescribed procedure,
with the object of estimating certain para­meters (mean, total,
proportion, etc.) of the parent population, or of testing the validity
of certain assumptions or hypotheses with respect to particular
properties of the population.

App. A-5

M20-2 August 22, 1966

APPENDIX A

[Samp]{.underline}le Size. The number of units in the sample.

[Sample Statistic]{.underline}. Synonymous with \"statistic.\"

[Sample]{.underline} Unit: Any one of the units included in a given
sample.

[Sampling]{.underline} Distribution: The distribution of a (sample)
statistic, such as a sample mean or a sample proportion or percentage,
that would be formed by obtaining such statis­tics from all possible
samples of a given fixed size selected by some specified sampling
procedure; a population of all possible sample values of the statistic
under consideration.

[Sampling]{.underline} Error: That part of the difference between a
population value and an esti­mate of such value, obtained from a random
sample, which is due solely to the fact that only a sample of values is
observed; to be distinguished from errors due to biased or imper­fect
sample selection, and from errors of observation, recording,
calculation, etc.

[Sampling Unit:]{.underline} One of the units into which a population is
divided for the purpose of sampling; it may be an individual member or
element of the population, or a group or cluster of elements; the units
may differ at different stages in a sampling procedure.

[Significant:]{.underline} A difference is statistically significant if
it actually exists in the popula­tion. A difference observed in a sample
is judged not statistically significant if it could easily have occurred
purely as a result of random sampling variations.

[Simple Random Sample:]{.underline} A probability sample selected in
such a way that each unit of the population has an equal and independent
chance of being included in the sample; for samples of any given size,
all possible combinations of units that could form samples of that size
must have the same probability of selection.

[Standard]{.underline} Deviation: The most widely used measure of the
dispersion (scatter or variability) of a frequency distribution; the
positive square root of the mean of the squares of the deviations of all
values in a frequency distribution from their arithmetic mean. The
standard deviation of the sampling distribution of any given statistic
is also known as the standard error\" of that statistic.

[Standard]{.underline} Error: The standard deviation of the sampling
distribution of a given statistic; the term \"standard deviation\" is
often used in place of \"standard error,\" as when \"standard deviation
of a percentage\" is used in place of \"standard error of a per­centage\"
to indicate the precision of a particular sample estimate.

[Statistic:]{.underline} A value computed from a sample, such as a mean,
proportion, percentage, total, range, standard deviation, etc.

[Statistical Quality]{.underline} Control:. A technique for detecting,
by statistical means, the presence of systematic or nonrandom variations
in quality in the output of a process, thus making possible their
elimination or reduction to an acceptable level, leaving the remaining
variation to chance causes. A process operating under a stable system of
chance causes is said to be statistically under control.

[Systematic Random Sample]{.underline}. A sample obtained by selecting
from a file, list or ADP tape, individual units at equally spaced
intervals (as every 10th, 140th, 850th, etc., unit, as required to
obtain a total sample of a given size), with the starting point within
the first such interval being determined by random selection.

[Time-Stratified Sample:]{.underline} A term applied herein to the total
sample obtained by cu­mulating smaller independent random samples drawn
at periodic intervals over time from the outflow of a continuing work
process; an example is a \"monthly\" sample cumulated from a succession
of small samples drawn daily throughout the month; if there are present
in an operation or process sources of variation (in quality or other
characteristics) related to changes in time, a sample designed to
reflect the results of these influences (i.e., a sample appropriately
stratified by time) should in general provide greater precision in

App. A-6

August 22, 1966 M20-2

APPENDIX A

sample estimation than a sample not so designed; if there is no relation
between time and the variation of a characteristic, a time- stratified
random sample will provide about the same precision as a simple random
sample.

[Unit:]{.underline} One of the individual members or components of a
population or of a sample.

[Universe:]{.underline} Synonymous with \"population.\"

[Value:]{.underline} The magnitude or numerical measure of a
characteristic (whether a quality characteristic or otherwise) of either
an individual unit, or of a population or sample; an observation.

App. A -7