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Statistical Uncertainty Analysis for Engineering Measurements

30 Chapters
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01
Measurement uncertainty in engineering
error vs. uncertainty, true value, measurand, and the role of statistics in experimental practice.
Measurementuncertainty
02
Probability foundations for measurement
random variables, probability density functions, cumulative distribution functions, and expectation for sensor data.
Probabilityfoundations
03
Descriptive statistics of repeated measurements
sample mean, variance, standard deviation, median, range, and robust summaries for noisy engineering data.
Descriptivestatistics
04
Common probability distributions in metrology
normal, uniform, triangular, Student's t, and their use in modeling measurement errors.
probabilitydistributions
05
Propagation of uncertainty
first-order Taylor series method, sensitivity coefficients, and application to multi-input measurement models.
Propagationuncertainty
06
Type A evaluation of standard uncertainty
statistical analysis of repeated observations, standard error of the mean, and degrees of freedom.
evaluationstandard
07
Type B evaluation of standard uncertainty
manufacturer specifications, calibration certificates, resolution, and assumed distributions.
evaluationstandard
08
Combined standard uncertainty
law of propagation, correlation handling, and covariance terms in engineering measurement models.
Combinedstandard
09
Expanded uncertainty and coverage factors
confidence intervals, Student's t coverage factor, and reporting uncertainty at a stated level of confidence.
Expandeduncertainty
10
Outlier detection and treatment in measurement data
Grubbs' test, Dixon's Q test, and engineering judgment for rejecting suspect observations.
detectiontreatment
11
Calibration and uncertainty
least-squares linear calibration, residuals, calibration standard uncertainty, and propagation to measured values.
Calibrationuncertainty
12
Uncertainty budgets
constructing a budget table, identifying sources, quantifying contributions, and documenting an uncertainty analysis.
Uncertaintyconstructing
13
Monte Carlo simulation for uncertainty propagation
sampling input distributions, nonlinear measurement models, and output distribution estimation.
simulationuncertainty
14
Sensitivity analysis and dominant uncertainty contributors
ranking sources, reducing uncertainty, and design of experiments for measurement improvement.
Sensitivityanalysis
15
Uncertainty in dimensional metrology
length, angle, form, and surface texture measurements with micrometers, calipers, and CMMs.
Uncertaintydimensional
16
Uncertainty in temperature measurement
thermocouples, RTDs, thermistors, reference junctions, and calibration uncertainty effects.
Uncertaintytemperature
17
Uncertainty in pressure and flow measurement
transducers, manometers, orifice plates, and flow meter calibration uncertainty.
Uncertaintypressure
18
Uncertainty in electrical measurements
digital multimeters, voltage references, current shunts, and traceability to electrical standards.
Uncertaintyelectrical
19
Uncertainty in force, torque, and mass measurement
load cells, torque transducers, balances, and deadweight calibration.
Uncertaintymeasurement
20
Uncertainty in dynamic measurements
sampling rate, aliasing, filtering, FFT, and time-domain vs. frequency-domain uncertainty.
Uncertaintymeasurements
21
Regression and response surface uncertainty
model form error, parameter confidence intervals, and prediction intervals in engineering models.
Regressionresponse
22
Interlaboratory comparisons and proficiency testing
reproducibility, repeatability, z-scores, and En values for measurement quality.
Interlaboratorycomparisons
23
Traceability and the measurement chain
SI units, national standards, calibration hierarchy, and uncertainty accumulation along the chain.
Traceabilitymeasurement
24
Case study
uncertainty analysis of a strain gauge bridge measurement including excitation, gauge factor, and amplifier effects.
uncertaintyanalysis
25
Case study
uncertainty analysis of a thermal conductivity experiment using steady-state heat flow and temperature sensors.
uncertaintyanalysis
26
Case study
uncertainty analysis of a vibration measurement on a rotating machine using accelerometers and signal conditioning.
uncertaintyanalysis
27
Software tools for uncertainty analysis
spreadsheet methods, GUM-compliant calculators, Monte Carlo packages, and Python/R workflows.
Softwareuncertainty
28
Reporting and documenting uncertainty
GUM framework, NIST guidelines, uncertainty statements, and compliance with ISO/IEC 17025.
Reportingdocumenting
29
Validation and verification of uncertainty analyses
internal checks, comparison with reference values, and peer review of measurement models.
Validationverification
30
Capstone project
end-to-end uncertainty analysis for a selected engineering measurement system, from model definition to final report.
Capstoneend-to-end