DOE Dictionary
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# | A |
B | C |
D | E |
F | G |
H | I |
J | K | L
| M
N | O | P
| Q | R | S
| T | U
| V | W | X
| Y | Z
#:
| 2-level design - an experiment
where all factors are set at one of two levels, denoted
as low and high (-1, 1 or 1, 2) |
|
| 2-tailed test - also known as a
two-sided test; it is a hypothesis test with a two-sided
alternative hypothesis. That is, one could possibly
err on either side of the center. |
|
| 3-level design an experiment where
all factors are set at one of three levels, denoted
as low, medium, and high (-1, 0, 1, or 1, 2, 3) |
|
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A:
| alpha risk - the probability of
concluding the alternative hypothesis (H1)
when the null hypothesis (H0)
is true. |
|
| aliasing - when two factors or
interaction terms are set at identical levels throughout
the entire experiment (i.e., the two columns are 100%
correlated). |
|
| alternative hypothesis - the hypothesis
to be accepted if the null hypothesis is rejected. It
is denoted by H1. |
|
| analysis of variance (ANOVA) -
a procedure for partitioning the total variation. It
is often used to compare more than two population means. |
|
| assignable cause (of variation) -
significant, identifiable change in a response which
is caused by some specific variable from the cause and
effect diagram. |
|
| attributes data (quality) - data
coming basically from GO / NO-GO, pass/fail determinations
of whether units conform to standards. Also includes
noting presence or absence of a quality characteristic. |
|
| average (x)
(of a statistical sample) - also called the sample
mean, it is the arithmetic average value of all of the
samle calues. It is calculated by adding all of the
sample calues together and dividing by the number of
elements (n) in the sample. |
|
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B:
| balanced design - a 2-level experimental
design is balanced if each factor is run the same number
of times at the high and low levels. |
|
| bar chart - a graphical method
which depicts how data fall into different categories. |
|
| Β (Beta) risk - the probability
of concluding the null hypothesis (H0)
when the alternative (H1) is
true. |
|
| bias (in measurement) - systematic
error which leads to a difference between the average
result of a population of measurements and the true,
accepted value of the quantity being measured. |
|
| bias (in measurement) - systematic
error which leads to a difference between the average
result of a population of measurements and the true,
accepted value of the quantity being measured. |
|
| Box-Behnken design - systematic
error which leads to a difference between the average
result of a population of measurements and the true,
accepted value of the quantity being measured. |
|
| brainstorming - a group activity
which generates alist of possible factors and levels,
and the method by which the results may be evaluated. |
|
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C:
| calibration (of instrument) -
adjusting an instrument using a reference standard to
reduce the difference between the average reading of
the instument and the "true" value of the
standard being measured, i.e., to reduce measurement
bias. |
|
| capability (of process) - a measure
of quality for a process usually expressed as sigma
capability, Cpk, or defects per
million (dpm). It is obtained by comparing the actual
process with the specification limit(s). |
|
| causality - the assertion that
changes to an input factor will directly result in a
specified change in an output. |
|
| cause-and-effect diagram - a pictorial
diagram showing possible causes (process inputs) for
a given effect (process output). |
|
| center points - experimental runs
with all factor levels set halfway between the low and
high settings. |
|
| central composite design - a 3-level
design that starts with 2-level fractional factorial
and some center points. If needed, axial points can
be tested to complete quadratic terms. Used typically
for quantitative factors and designed to estimate all
linear effects plus desired quadratics and 2-way interactions. |
|
| central tendency - a measure of
the point about which a group of values is clustered;
some measures of central tendency are mean, mode, and
median. |
|
| characteristic - a process output
which can be measured and monitored for control and
capability. |
|
| chi-square distribution - the
distribution of chi-square statistics. |
|
| chi-square - the test statistic
used when testing the null hypothesis of independence
in a contingency table or when testing the null hypothesis
of a set of data following a prescribed distribution.
|
|
| classical methods - statistical
experimental design thoughts and processes orignally
developed by Fisher and other as early as the 1920's.
Uses ANOVA as the primary analysis tool, along with
orthogonal designs such as fractional factorials, latin
squares, Plackett-Burman, Box-Behnken, central composite,
and D-optimal. |
|
| coefficient of variation - the
ratio of the standard deviation to the mean. It is a
standardized method of looking at variation. |
|
| coefficient of determination (r-squared)
- the square of the sample correlation coefficient;
it represents that strength of a model.(1 - r-squared)
x 100% is the percentage of noise in the data not accounted
for by the model. |
|
| common causes of variation - those
sources of variability in a process which are truly
random, i.e., inherent in the process itself. |
|
| confidence interval - range within
which a parameter of a population (e.g., mean, standard
deviation, etc.) may be expected to fall, on the basis
of measurement, with some specified confidence level
or confidence coefficient. |
|
| confidence limits - the upper
and lower boundaries of a confidence interval. |
|
| control (of process) - a process
is said to be in a state of statistical control is the
process exhibits only random variations (as opposed
to systematic variations and / or variations with known
sources). When monitoring control with control charts,
a state of control is exhibited when all points remain
between set control limits without any abrnomal (non-random)
patterns. |
|
| control chart - the basic tool
of statistical process control. It consists of a run
chart, together with statistically determined upper
and lower control limits and a centerline. |
|
| correlation coefficient (R) -
a measure of the linear relationship between two random
variables. Not as useful as r-squared, the coefficient
of determination. |
|
| controllable factors - factors
the experimenter has control of during all phases, i.e.,
experimental, production, and operational phases. |
|
| Cp - during
process capability studies, Cp
is a capability index which shows the process capability
potential but does not consider how centered the process
is. Cp may range in value from 0 to infinity, with a
large value indicating greater potential capability.
A value of 1.33 or greater is usually desired. |
|
| Cpk - during
proces capability studies, Cpk
is an index used to compare the natural toleranceof
a process with teh specification limits.Cpk
has a value equal to Cp if the
proces is centered on the nominal; if Cpk
is negative, the process mean is outside the specification
lmits; if Cpk is between 0 and
1 then the natural tolerances of the process fall outside
the spec limits. If Cpk is larger
than 1, the natural tolerances fall completely within
the spec limits. A value of 1.33 or greater is usually
desired. |
|
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D:
| D-optimal design - an experimental
design in which the minimum number of runs is based
on degrees of freedom needed to analyze the desired
effects. Not necesarily orthogonal or balanced, it does
minimize the correlation (confounding) between factors. |
|
| defect - departure of a quality
characteristic from its acceptable level or state, i.e.,
the measured value of the characteristic is outside
of specification. Also referred to as non-conformance
to requirements. |
|
| defective unit - a sample (part)
which contains one or more defects, making the sample
unacceptable for its intended, normal usage. |
|
| defining relationship - a statement
of one or more factor word equalities used to determine
the aliasing structure in a fractional factorial design.
|
|
| defining words - factor word equalities
in building a defining relationship. |
|
| degrees of freedom - a parameter
in the t, F, and x-squared distributions. It is a measure
of the amount of independent information available for
estimating the population variance, a-squared. It is
the number of independent observations minus the number
of parameters estimated. |
|
| design array - (also referred
to as design matrix) - an array representing the experimental
settings. Usually contains values ranging from -1 to
+1, but could be wider is using a CCD. The rows represent
the runs and the columns represent the factors. |
|
| deviation - the difference between
an observed value and the mean or average of all observed
values. |
|
| discrete random variable - a variable
that is based on count data (number of defects, number
of births, number of deaths, etc.). It supposedly has
a countable number of possible outcomes. |
|
| dispersion (of a statistical sample)
- the tendency of the values of the elements in a sample
to differ from each other. Dispersion is commonly expressed
in terms of the range of the sample (difference between
the lowest and highest values) or by the standard deviation. |
|
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E:
| estimation - an approach to making
inference about population parameters. This includes
both point estimates and interval estimates (confidence
intervals). |
|
| experimental design - purposeful
changes to the inputs (factors) to a process (or activity)
in order to observe corresponding changes in the outputs
(responses). A means of extracting knowledge from a
process (or activity). |
|
| exponential distribution - a probability
distribution mathematically described by an exponential
function. Used to describe the probability that a product
survives a length of time t in service, under the assumpution
that the probability of a product failing in any small
time interval is independent of time. |
|
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F:
| F table - provides a means for
determining the significance of a factor to a specified
level of confidence by comparing calculated F ratios
to those from the F distribution (see Appexndix F).
If the F ratio is greater than the table value, there
is a significant effect. |
|
| factor - an input to a process
which can be manipulated during experimentation. |
|
| failure rate - the average number
of failures per unit time. Used for assessing reliability
of a product in service. |
|
| fault tree analysis (FTA) - a
technique for evaulating the possible causes which might
lead to the failure of a product. For each possible
failure, the possible causes of the failure are determined;
then the situation leading to those causes are determined;
and so forth, until all paths leading to possible failures
have been traced. The result is a flow cart for the
failure process. Plans to deal with each path can then
be made. |
|
| feedback - using the results of
a process to contol it. The feedback principle as wide
application. An example would be using control charts
to keep production personnel informed o the results
of a process. This allows them to make the suitable
adjustments tot he process.Some form of feedback on
the results of a process is essential in order to keep
the process under control. |
|
| fishbone diagram - see cause-and-effect
diagram. |
|
| flow chart or diagram (for programs,
decision making, process development) - a pictorial
representation of a process indicating the main steps,
branches, and eventual outcomes of the process. |
|
| foldover design - a way to obtain
a resolution four (RIV) design
based on two designs of RIII.
Used when the confirmation runs from a resolution III
design differ substantially from their prediction and
the experimenter desires to de - alias the 2 - way interactions
from the main effects. |
|
| fractional factorials - instead
of using a full factorial, a subset or fraction of it
can be used if the experimenter can assume some interactions
will not occur. |
|
| freehand regression line - the
best-fit line drawn by "eyeballing." |
|
| full factorial - all possible
combinations of the factors and levels. Given k factors,
all with two levels, there will be 2k
runs. If the factors have three levels, the 3k
runs would be needed. |
|
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G:
| Gaussian distribution - the engineering
name for the normal distribution. |
|
| gradient - the slope at a point
on a surface. |
|
| grand average - overall average
of data. |
|
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H:
| histogram - a bar chart that depicts
the frequencies of numerical or measurement data. |
|
| hypothesis test - a procedure whereby
one of two mutually exclusive and exhaustive statements
about a population parameter is concluded. Infrmation
from a sample is used to infer something abuot a population
from which the sample was drawn. |
|
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I:
| inner array - a Taguchi term used
in parameter design to identify the combinations of
controllable factors to be studied in a designed experiment.
Also called a "design array" or "design
matrix." |
|
| interaction - 2 factors (input
variables) are said to interact if one factor's effect
on the response is dependent upon the level of the other
factor. |
|
| Ishikawa diagram - see cause-and-effect
diagram. |
|
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J:
| just-in-time (KIT) manufacturing -
a strategy that coordinates scheduling, inventory,
and production to move away from the batch mode of production
in order to improve the quality and reduce inventories. |
|
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L:
| latin squares - provides a means
for determining the significance of a factor to a specified
level of confidence by comparing calculated F ratios
to those from the F distribution (see Appexndix F).
If the F ratio is greater than the table value, there
is a significant effect. |
|
| LCL (lower control limit) - for
control charts: the limit above which the process subgroup
statistics (X, R, etc.) must remain when the process
is in control. Typically 3 standard deviations below
the center line. |
|
| least squares - a method of curve-fitting
that defines the "best" fit as the one that
minimizes the sum of the squared deviations of the data
points from the fitted curve.. |
|
| level - a setting or testing value
of a factor. |
|
| level of significance - a measure
of the outcome of a hypothesis test. It is the P-value
or probability of making a Type 1 error. |
|
| linear graph - a tool used bu
Taguchi to identify sets of interacting columns in orthogonal
arrays. |
|
| loss function - a technique for
quantifying loss due to product deviations from target
values. |
|
| lower confidence limit - the smaller
of the two numbers that form a confidence interval. |
|
| LSL (lower specification limit) -
the lowest value of a product dimension or measurement
which is acceptable. |
|
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M:
| main effect - the influence a single
factor has on the response when it is changed from one
level to another. Often used to represent the "linear
effect" associated with a factor. |
|
| mean square error - a weighted
average of the variances for each run. |
|
| mean - the average of a set of
values. We usually use x
or y to denote a sample
mean, whereby we use the Greek letter μ to denote
a population (or true) mean. |
|
| measure of central tendency -
numerical measures that depict the center of a data
set. The most commonly used measures are the mean and
the median. |
|
| modeling designs - designed experiments
used to build a linear and / or non-linear relationship
of the output(s) with a reasonable number (<
5) of inputs. |
|
| MTBF (mean time between failures) -
mean time between successive failures of a repairable
product. This is a measure of product reliability. |
|
| multicollinearity - the existence
of strong correlations between input factors or independent
variables. High levels of multicollinearity will prevent
terms from being evaluated independently. |
|
| multiple regression - a model
where several independent variables are used to predict
on dependent variable. |
|
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N:
| natural tolerances (of a process) -
3 standard deviations on either side of the center
point (mean value). In a normally distributed process,
the natural tolerances encompass 99.73 % of all measurements. |
|
| noise - unexplained variability
in the response. Typically due to variables which are
not controlled. |
|
| nominal - the desired mean value
for a particular product dimension; the target value. |
|
| nonconforming unit - a sample
(part) which ahs one or more nonconformities, making
the sample unacceptable for its intended use. |
|
| normal distribution - the distribution
characterized by the smooth, bell-shaped curve. |
|
| null hypothesis (H0)
- the conclusion that typically includes equality,
i.e., H0: μ1
= μ2 or H0:
σ1 = σ2. |
|
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O:
| one-at-a-time approach - a popular
but inefficient way to conduct a designed experiment. |
|
| outer array - a Taguchi term used
in parameter design to identify the combinations of
noise factors to be studied in arobust designed experiment. |
|
| out of control (of a process) -
a process is said to be aout of control if it exhibits
variations larger than its control limits, or shows
a systematic pattern of variation. |
|
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P:
| P (2 tail) - the probability that
a term does not belong in a regression model. Typically,
Rules of Thumb will state that P(2 tail) <
.1 indicate the term should be place |
|
| P-value - the probability of making
a Type 1 error. This value comes from the data itself.
It also provides the exact level of significance of
a hypothesis test. |
|
| Pareto chart - a bar chart for
attribute (or categorical) data that is presented in
descending order or frequency. |
|
| percent defective - for acceptance
sampling; the percentage of units in a lot which are
defective, i.e., of unacceptable quality. |
|
| population - a set or collection
of objects or individuals. It can also be the corresponding
set of values which measure a certain characteristic
of a set of objects or individuals. |
|
| predicted value of y - a value
of the response (dependent) variable y that is computed
from the predication equation for some particular value
of the input (independent) variable x. It is lableled
ŷ and is computed from ŷ = b0
+ b1 x. |
|
| primary reference standard (for measurements)
- a standard maintained by the National Institute
of Standards and Technology (NIST) for a particular
measuring unit. The primary reference standard duplicates
as nearly as possible the internation stndard and is
used to calibrate other (transfer) standards, which
in turn are used to calibrate measuring instruments
for industrial use. |
|
| probability - a measure of the
likelihood of a given event occuring. It is a measure
that take on value between 0 and 1 inclusive, with 1
being the certain event and 0 meaning that there is
relatively no chance at all of the event occurring.
How probabilities are assigned is another matter. The
relative frequency approach to assigning probabilities
is one of the most common. |
|
| process capability - comparing
actual process performance with process specification
limits. There are various measures of process capability,
such as Cpk, σ-level, and
dpm (defects ber million). |
|
| process control - a process is
said to be in control or it is a stable predictable
process if all special causes of variation have been
removed. Only common causes or natural variation remains
in the process. |
|
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N:
| quality assurance - the function
of assuring that a product or service will satisfy given
needs. The function includes necessary verification,
audits, and evaluations of quality factors affectingthe
intended usage and customer satisfaction. This function
is normally the responsibility of one or more upper
management individuals overseeingthe quality assurance
program. |
|
| quality characteristic - a particular
aspect of a product which relates to its ability to
perform its intended function. |
|
| quality function - the function
of maintaining product quality levels; i.e., the execution
of quality control. |
|
| quality specifications - particular
specifications of the limits within which each quality
characteristic of a product is to be maintained in order
to meet the minimum functional requirements of the customer.
|
|
| quality control - the process of
maintaining an acceptable level of product quality. |
|
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R:
| random sample - a sample selected
from a population in such a way taht every element of
the population has an equally likely chance of being
selected. |
|
| random - varying with no discernable
pattern. |
|
| range - a measure of the variability
in a data set. It is a value, namely the difference
between the largest and smallest values in a data set. |
|
| regression analysis - a statistical
technique for determining the mathematical relation
between a measured quanitity and the variables it depends
on. |
|
| regression line - the line that
is fit to a st of data points by using the method of
least squares. |
|
| reliability - the probability
that a product will function properly for some specified
period of time; under specified conditions. |
|
| repeatability (of a measurement) -
the extent to which repeated measurements of a partcular
object with a particular instrument produce the same
value. |
|
| reproducibility - the variation
between individual people taking the same measurement
and using the same gaging. |
|
| residual - the difference between
an observed value and a predicted value: residual =
y - ŷ. |
|
| resolution (of a measuring instrument)
- the smallest unit of measure which an instrument
is capable of indicating. |
|
| Rule of Thumb (ROT) - a simplified,
practical procedure that can be used in place of a formal
statistical test that will produce approximately the
same result. |
|
| run chart - a basic graphical
toolthat charts a process over time, recording either
individual readings or averages over time. . |
|
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S:
| sample size - the number of elements,
or units, in a sample. |
|
| sample - a set of values or items
selected from some population. |
|
| sampling variation - the variation
of a sample's properties from the properties of the
population from which it was drawn. |
|
| sampling - the process of selecting
a sample of a population and determining the properties
of the sample. The sample is chosen in such a way that
its properties are representative of the population.
|
|
| sampling variation - the variation
of a sample's proerties from the properties of the population
from which it was drawn. |
|
| sampling - the process of selecting
a sample of a population and determining the properties
of the sample. The sample is chosen in such a way that
its properties are representative of the population. |
|
| scatterplot - a 2-dimensional
plot for displaying bivariate data. |
|
| screening designs - designed experiments
used to identify the "vital few" factors from
a large number of factors (> 6) to be tested. |
|
| short-run SPC - a set of techniques
used for SPC in low-volume, short duration manufacturing
or service. |
|
| sigma limits - for histograms;
lines marked on the histogram showing the points n standard
deviations above and below the mean. |
|
| sigma (σ) - the standard
deviation of a statistical population. |
|
| Sigma capability - a commonly
used measure of process capability that represents the
number of standard deviations between the center of
a process and the closest specification limit. |
|
| signal-to-noise (s/n) - a comparison
of the influence of controllable factors (signals) to
the influence of noise factors. The higher the s/n value,
the better. |
|
| significance level - see level
of significance. |
|
| simple linear regression - a model
where one independent variable is used to predict one
dependent variable. |
|
| simulation (modeling) - using
a mathematical model of a system or process to predict
the performanceof the real system. The model consists
of a set of equations or logic rules which operate on
numerical values representing the operating parameters
of the system. The result of the equation is a prediction
of the system's output. |
|
| skewed distribution - a distribution
that (graphically) has a onger tail on the right than
it does on the left (or vice versa), i.e, it is not
symmetric about its center point. Numerically, a distribution
is skewed if the mean and the median are not the same.
|
|
| slope - the term b in the prediction
equation ŷ = b0 + b1
x. |
|
| special causes of variation -
those nonrandom causes of variation that can be detected
by the use of control charts and good process documentation. |
|
| specification (spec) limits -
the bounds of acceptable values for a given product
or process. They should be customer driven. |
|
| SSE - sum of squares due to error,
or some of squared residuals. |
|
| SST - total sum of squares, or
the sum of squared deviations of the observed values
from the mean. |
|
| stability (of a process) - a process
is said to be stable is it shows no recognizable pattern
of change. |
|
| standard (measurement) - a reference
item providing a known value of a quantity to be measured.
Standards may be primary - i.e., the standard essentially
defines the unit of measure - or secondary (transfer)
standards, which have been compared to the primary standard
(directly or by way of an intermediate transfer standard).
Standards are used to calibrate instruments which are
then employed to make routine instruments. |
|
| standard deviation - one of the
most common measures of variability in a data set or
in a population. |
|
| standardized normal distribution -
a normal distribution or random variable having a mean
and standard deviation of 0 and 1, respectively. It
is denoted by the symbol Z and is also called the Z
distribution. |
|
| stationary point - the corrolary
ina single variable calculus would be a critical point.
A stationary point is a point where the gradient is
zero, i.e, no slope at the point. |
|
| statistic - a value calculated
froma random sample which is used to estimate a population
parameter. |
|
| statistical inference - the process
of drawing concusions abouta population on the basis
of statistics. |
|
| statistical quality control (SQC) -
the application of statistical methods for measuring
and improving the quality of processes. SPC is one method
included in SQC. |
|
| statistical control (of a process) -
a process is said to be in a state of statistical
control when it exhibits only random variation and is
otherwise stable and predictable. |
|
| statistical process control - the
use of basic graphical and statistical methods for analyzing
and controlling the variation of a process, and thus
continuously improving the process. |
|
| statistics - numerical measures
obtained from a sample (as opposed to parameters, which
are numerical measures of a population). |
|
| system design - the selection of
materials, parts, products, factors, equipment, and
process parameters. |
|
| systematic variation (of a process)
- variation which exhibit a predictable pattern.
The pattern may be cyclic (i.e., a recurring pattern)
or may progress linearly (i.e. a trend). |
|
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T:
| t-distribution - a symmetric, bell-shaped
distribution that resembles the standardized normal
(or Z) distribution, but it typically has more area
in its tails than does the Z distribution. That is,
it has greater variability than the Z distribution. |
|
| t-test - a hypothesis test of population
means when small samples are involved. |
|
| Taguchi methods - experimental
design thoughts and processes as developed by Taguchi.
Based on philosophy of the loss function, he uses signal-to-noise
ratios as the primary analysis tool. Orthogonal design
matrices are tabled and originate from fractional factorials,
Plackett-Burman, and latin square designs. |
|
| test statistic - a single value
which combines the evidence obtained from sample data.
The P-value in a hypothesis test is directly related
to this value. |
|
| tolerance design - the specification
of appropriate tolerances, product parameters, and process
factors. |
|
| total quality management (TQM) -
a management philosophy of integrated control, including
engineering, purchasing, financial administration, marketing
and manufacturing, to ensure customer satisfaction and
economical cost of quality. |
|
| trend - a gradual, systematic change
with time or some other variable. |
|
| Tukey test - a statistical test
to measure the difference between several mean values
and tell the user which ones are statistically different
from the rest. |
|
| Type II error - concluding H0
and H1 is really true. |
|
| Type I error - concluding H1
(or rejecting H0) when H- is
really true. |
|
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U:
| UCL (upper control limit) - for
control charts: the upper limit below which a process
statistic (X, R, etc.)
must remain to be in control. Typically this value is
3 standard deviations above the center line. |
|
| uncontrollable factors - factors
that are difficult, undesirable, or impossible to change.
Also called "noise factors." The uncontrollable
factors included in a design matrix must be controllable
in the experimental phase. |
|
| uniform distribution - a distribution
in which all outcomes are equally likely. |
|
| USL (upper specification limit) -
the highest value of a product dimension or measurement
which is acceptable. |
|
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V:
| variability - the property of
exhibiting variation, i.e., changes or differences,
in key measurements of a process. |
|
| variables data - concerning the
values of a variable, or measurement data, as opposed
to attribute data. A dimensional value can be recorded
and is only limited in value by the resolution of the
measurement system. |
|
| variables - quantities which are
subject to change or variability. |
|
| variance - a measure of variability
in a data set or population. It is the square of the
standard deviation. |
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X:
| x and
R charts - for variables data; control charts for
thea verage and range of subgroups of data. |
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Y:
| y-intercept - the term b0
in the prediction equation ŷ = b0
+ b1 x. |
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Z:
| z-value - a standardized value
formed by subtracting the mean and then dividing this
difference by the standard deviation. |
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