Patrick F. Dunn, Measurement, Data Analysis, and Sensor Fundamentals for Engineering and Science, 2nd Edition

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466 Measurement and Data Analysis for Engineering and Science

Nth-order replication level level at which more than one random error

beyond that in the ﬁrst-order replication level is considered

null method use of a Wheatstone bridge to determine an unknown resis-

tance by having two of its other four resistances ﬁxed and varying the

fourth until the bridge is balanced

null set set of all occurrences in which a desired event is not the outcome

numerical equation equation containing only the measures of physical

quantities

octave frequency ratio of 2:1

odd function function symmetric about the origin

order degree in a continuum of size or quantity

orthogonal property of two functions whose inner product is equal to zero

over an interval

outcome result of a test

over-damped having a damping ratio greater than unity

overall uncertainty measure of the uncertainty in a variable; the product

of the coverage factor and the combined standard uncertainty

parameter variable or function of variables that is ﬁxed during an experi-

ment

passive requiring an external power supply to produce a voltage or current

pedagogical class of experiment designed to teach the novice or to demon-

strate something that is already known

periodic repeating itself in time

permutations number of ways that a set can be arranged respective of its

members’ order

phase lag lag of an output signal with respect to an input signal

Poisson distribution a continuous distribution describing rarely occurring

events

pooled formed into one set from a set of replicated experiments each involv-

ing multiple measurements

population collection of all possible values of a random variable

potential diﬀerence diﬀerence between two electric potentials

Glossary 467

power spectrum plot of a signal’s power versus frequency

precision variation of a variable’s values obtained by repeated measurements

precision error see random error

precision interval interval characterized by the product of a coverage factor

and a random uncertainty

probability number of speciﬁc occurrences over the total number of occur-

rences

probability density function (pdf ) function when integrated yields the

probability

probability distribution function (PDF) integral of the probability den-

sity function; also known as the cumulative probability distribution func-

tion

ramp method method to perform electronically analog-to-digital conversion

by increasing a voltage and comparing it to the analog input signal’s

voltage

random having no particular order

random error error related to the scatter in the data obtained under ﬁxed

conditions; also known as the precision error

random uncertainty estimate of the random error

random variable variable whose value has no deterministic relation to any

of its other values

range lower to upper limits of an instrument or test

reactance inﬂuence of a coil of wire upon an alternating current passing

through it that impedes the current

readability closeness with which the scale of the instrument is read

reduced-chi square variable χ

variable normalized by the number of de-

grees of freedom

regression analysis process identifying the regression coeﬃcients in the

method of least squares

regression coeﬃcients coeﬃcients found in the method of least squares

relative accuracy accuracy divided by the true value

relative systematic uncertainty ratio of the reliability of the systematic

uncertainty to the systematic uncertainty

468 Measurement and Data Analysis for Engineering and Science

reliability estimate of the accuracy of a systematic uncertainty

repeatability ability to achieve the same value upon repeated measurement

repetition repeated measurements made during the same test under the

same operating conditions

replacement return of members to their set after selection, thereby allowing

for their re-occurrence

replicates experiments identical to the original

replication duplication of an experiment under similar operating conditions

resistance deﬁned by Ohm’s law as the ratio of voltage to current

resolution smallest physically indicated division that an instrument displays

or is marked

result variable that is a function of one or more measurands

ringing frequency frequency at which a second-order system rings or con-

tinually oscillates

rise time time required for a ﬁrst-order system to respond to 90 % of a step

change

root mean square (rms) positive square root of the mean of the squares

round oﬀ truncate a number to its desired length

sample subset of the population

sample mean mean of a sample

sample variance variance of a sample

sample-to-sample measurand values are recorded for multiple samples

scattergram discrete representation of an analog signal

scientiﬁc method method of investigation involving observation and theory

to test scientiﬁc hypotheses

second central moment the variance

sensor device that senses a physical stimulus and converts it into an impulse

sequential systematically increased

set group of all occurrences in which a desired event is the outcome

settling time time beyond which a second-order system’s response remains

within ±10 % of its steady-state value

Glossary 469

signal measurement system’s representation of the temporal variation of a

measurand

signal conditioning preparing the signal in its ﬁnal form to be processed

optimally and then recorded

signal processing operating on a signal to obtain desired results

signal sample period time period used to determine the statistical proper-

ties of a signal

signiﬁcant ﬁgures number of digits required to express a result

simple RC ﬁlter ﬁlter comprised of a resistor and a capacitor

skewness third central moment normalized by the cube of the standard de-

viation

source groups groups that help to categorize sources of error, which are

typically grouped as calibration, data acquisition, and data reduction

standard known value usually used as a basis of calibration

standard deviation square root of the variance, which characterizes the

width of the probability distribution

standard deviation of the means (SDOM) standard deviation of the

mean values obtained from groups of repeated measurements

standard error of the ﬁt error characterizing the diﬀerences between data

and its curve ﬁt

standardized normal variate nondimensional variable indicating the num-

ber of standard deviations that a variable deviates from its mean value

static steady in time

static calibration calibration performed when the system is static

static sensitivity slope of a static calibration curve at a particular input

value

stationary each of a signal’s ensemble-averaged statistical properties are

time invariant

statistics branch of applied mathematics concerned with the collection and

interpretation of quantitative data and the use of probability theory to

estimate population parameters

steady-state response the periodic part of a second-order system’s re-

sponse

470 Measurement and Data Analysis for Engineering and Science

strongly stationary having all ensemble moments invariant with respect to

the record’s time

successive approximation method method to perform analog-to-digital

conversions electronically by subtracting the analog input signal from

a digital-to-analog converter’s output signal

supplementary nondimensional units that do not represent a fundamental

dimension

system of units system in which physical quantities can be expressed and

related to one another through physical laws

systematic error error related to the diﬀerence between a measured and

true value; sometimes called the bias error

systematic uncertainty estimate of the systematic error

third central moment see skewness

time history record plot of a signal’s amplitude versus time for a given

period of time

time lag delay in time between a signal’s input and output through a device

timewise experiment in which measurand values are recorded sequentially

in time

transducer device that changes an impulse into a desired quantity

transient response part of a second-order system’s response that decays in

time

transient solutions homogeneous solutions to a diﬀerential equation that

decay to zero in time

true mean value mean value of the population

true value error-free value of a variable

true variance variance of the population

uncertainty estimate of error in a variable

under-damped having a damping ratio less than unity

union set of all members of two sets that are in only one, only in the other,

or in both

unit precisely speciﬁed quantity in terms of which the magnitudes of other

quantities of the same kind can be stated

Glossary 471

unit equation equation in which only units are used or deﬁned

validational experiment conducted to validate a speciﬁc hypothesis

variables physical quantities involved in the process that can undergo change

and thereby aﬀect the process

variance statistical measure of the spread of values with respect to their

mean

variational experiment quantifying the mathematical relationships between

experimental variables

waveform actual shape of a signal

weakly stationary having the ensemble mean and autocorrelation invariant

with respect to the record’s time

Weibull distribution continuous distribution describing the time to failure

of a physical system

Wheatstone bridge electrical circuit consisting of four resistors in a speciﬁc

conﬁguration and a voltage source

windowing mathematical method that reduces the magnitude of a signal’s

record at its beginning and end

zeroth central moment integral of the probability density function; equals

unity if the probability density function is normalized correctly

zeroth-order replication level level at which only measurement system er-

rors are present

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Symbols

Chapter 2:

AC alternating current

C capacitance

DC direct current

E electric ﬁeld

T h

Th´evenin open-circuit voltage

electric force

I current

L inductance

P electric power

q charge

R resistance

reference temperature

Z impedance

capacitive reactance

inductive reactance

T h

Th´evenin circuit impedance

∆Φ potential diﬀerence

ρ electric resistivity

resistivity at reference temperature T

Φ electric potential

473

474 Measurement and Data Analysis for Engineering and Science

Chapter 3:

C capacitance

input signal

output signal

cutoﬀ frequency

G gain

L inductance

R resistance

resistance at reference temperature

T temperature

reference temperature

α, β, γ coeﬃcients of thermal expansion

∆t time lag

 relative permittivity



permittivity of free space

η material constant

ν Poisson’s ratio

ρ resistivity

φ phase lag

Chapter 4:

A relative accuracy

speciﬁc heat at constant volume

E total energy

F (t) input forcing function

h convective heat transfer coeﬃcient

I current

K static sensitivity

Symbols 475

k spring constant

n order

M magnitude ratio

q charge

Q rate of heat transfer

R resistance

homogeneous solution

particular solution

β lag time

δ fractional dynamic error

 absolute error

τ time constant

φ phase shift

ringing frequency

Chapter 5:

union

intersection

| subject to the condition

combinations of n objects taken m at a time

E[ ] or h i expected value

frequency density

∗

normalized frequency density

Ku kurtosis

permutations of n objects taken m at a time

p(x) probability density function

P (x) probability distribution function