Glossary

Frequency table of two categorical characteristics — the basis for mosaic plot, heatmap and the chi-square test.

Measure of the heaviness of the tails of a distribution relative to the normal.

Nominal, ordinal, interval or ratio — decides which statistics, charts and tests are admissible at all.

The distribution of one characteristic alone (marginal) versus its distribution within a category of the other (conditional).

Sum of all values divided by their count — the most common measure of central tendency.

Middle value of a sorted dataset — the 50 % value.

Difference between the largest and smallest value — the simplest measure of dispersion.

Measure of the asymmetry of a distribution about its mean.

Square root of the variance — measure of dispersion in the original units of the data.

Mean squared deviation of values from the mean — a measure of dispersion in a dataset.

Ratio of specification width to short-term variation — ignores the location of the mean.

Extends Cp by the location — assesses the actual short-term capability accounting for off-centring.

Long-term counterpart to Cp — uses total sample variation instead of within-subgroup variation.

Long-term counterpart to Cpk — uses overall variation and accounts for mean location.

Compares a process's natural variation to its specification limits — condensed into indices such as Cp, Cpk, Pp, Ppk.

Process capability metric — the standard normal Z value of the total fraction outside the specification limits (Z.bench).

Tolerance limits set by the customer or designer — the reference base of any process capability measure.

The interesting counter-assumption to the null hypothesis — e.g. "the means differ".

Omnibus test for means across three or more groups — F statistic from between-group vs. within-group variance.

Tests categorical frequencies against an expectation — for independence, goodness of fit, or a required variance.

Effect size for the association of two categorical characteristics — between 0 (independent) and 1 (perfect).

Magnitude of an effect independent of sample size — complements the p-value, which only shows significance.

Statistical decision procedure — checks whether an observed deviation is a real effect or chance.

Test of the assumption that data come from a normal distribution — a precondition of many parametric procedures.

The "nothing is going on" assumption that a hypothesis test tries to refute — e.g. "the means are equal".

Probability of seeing data at least as extreme as observed, if the null hypothesis were true. Small = data hard to explain under H₀; not the probability that H₀ is true.

Probability of detecting an effect that really exists — usual target 0.80 or 0.90.

Pre-set risk threshold for wrongly rejecting H₀ — usually α = 0.05.

Family of tests for means under normality assumption — using the t-distribution as reference.

A quantity computed from the data (e.g. t, z, F, χ²) from which the p-value of the test is derived.

Rejecting H₀ when it is actually true — a "false alarm".

Failing to reject H₀ when it is actually false — a real effect is missed.

Test of equal variances across several groups — precondition of the t-test and ANOVA.

Umbrella concept of trueness and precision — how close a measurement gets to the true value overall.

Difference between the mean of repeated measurements and the known reference value.

MSA Type 1 metric for repeatability — compares measurement spread with a defined fraction of the tolerance.

MSA Type 1 metric combining repeatability and bias in a single figure.

Kappa statistic for exactly two raters on nominal or binary characteristics.

Without a reference, the majority vote of the appraisers is used as the reference per part; ties leave the part ambiguous.

SDT decision threshold of a binary appraiser — reveals whether they lean towards "OK" or "NOK", independent of their discriminability.

SDT discriminability of a binary appraiser — how well they distinguish OK from NOK, independent of their decision threshold.

Linear regression of the metric over time, followed by a two-sided t-test on the slope β₁ — detects a creeping trend in a stability study.

Fraction of an appraiser's ratings that agree with the reference — the central AIAG metric in attribute MSA.

Fraction of truly good parts that an appraiser wrongly rates as NOK — in binary attribute MSA.

Kappa statistic for more than two raters on nominal or binary characteristics — overall agreement.

Study that decomposes measurement variation into repeatability (EV), reproducibility (AV), and part variation (PV).

Statistical measure of agreement between raters, corrected for chance agreement.

Change of bias across the measurement range — does the system read equally true at every reference point?

The dispersion attributable to a measurement result — assessed as a share of the tolerance (Q_MS).

Fraction of truly bad parts that an appraiser wrongly rates as OK — in binary attribute MSA.

Resolution metric from Gage R&R: how many levels the system can tell apart within the part range?

Variation between the parts themselves — should dominate the measurement-system variation in Gage R&R.

Closeness of measurements to each other — small spread, regardless of position relative to the reference value.

Calibrated part with a known, traceable value — prerequisite for bias assessment in MSA Type 1.

Precision under the tightest conditions: same operator, same instrument, same part, short time.

Precision under changed conditions — different operators, instruments, or laboratories on the same part.

Psychophysics framework that separately estimates a binary judge's discriminability (d′) and decision threshold (c).

Checks whether a measurement system stays constant over weeks or months — a reference part measured repeatedly on a control chart, complemented by a drift test.

Closeness of the expected measurement value to the reference value — absence of systematic bias.

Kappa statistic for ordinal scales — weighs near misclassifications more mildly than distant ones.

Confidence interval for a proportion with better coverage than the Wald interval, especially for small n and proportions near 0 or 1.

In fractional designs, effects are no longer estimated separately but as sums — e.g. main effect A + interaction BC.

3-level response-surface design without corner points — for processes where extreme combinations of all factors simultaneously are not permitted.

Extra runs at the middle of the design region — for curvature test and pure-error estimation of the standard deviation.

Response-surface design of corner points, star points and centre points — standard for optimisation with curvature.

Algorithmically generated design that maximises the determinant of the information matrix ${\mathbf{X}}^{\top }\mathbf{X}$ — for situations no standard design fits.

Modern screening design with 3 levels that additionally resolves curvature and isolated two-factor interactions.

Design with replicates per point — jointly models mean AND dispersion as functions of the factors.

Systematic experiment planning so that a minimum number of runs yields maximum insight into factors, main effects, and interactions.

Small-scale DoE on the running process — cautious, repeated factor variation for continuous improvement.

An input deliberately varied in a designed experiment — e.g. temperature, pressure, material type.

A deliberately chosen fraction of the full factorial — fewer runs, at the cost of effect aliasing governed by design resolution.

Every combination of all levels of all factors is run — maximum separability, but effort grows exponentially.

Two factors do not act independently — the effect of A depends on the level of B.

Concrete value a factor is set to in the experiment — standard: 2 levels (−1 / +1) for screening, 3+ for optimisation.

The average influence of a single factor on the response, averaged over all other factor levels.

Design for recipes whose components sum to 100 % — proportions cannot vary independently.

Highly efficient screening design for many factors in multiples of 4 runs — only main effects identifiable.

Random run order — prevents time-related drift from being confounded with factor effects.

A truly independent repeat of a run — foundation for estimating pure error.

Classifies fractional designs (III / IV / V) by which effect orders are aliased with which.

The output measured in the experiment — e.g. yield, strength, cycle time. What is to be optimised or understood.

Family of DoE methods that models the response as a smooth function of the factors — typically with a quadratic model.

A DoE plan aimed at filtering the truly effective factors out of many candidates — not at optimising.

Robustness-oriented experimental design using orthogonal arrays and the signal-to-noise ratio as response.

Additive decomposition of total variance into the contributions of individual sources — estimated via the ANOVA/EMS method or REML.

Three 1σ-wide bands between the centre line and the control limits — the basis of Nelson rules 5–8.

Attribute control chart for defect counts per unit — Poisson-distributed.

Reference level of a control chart — mean of observations or subgroup means.

Natural, unavoidable variation of a process arising from many small influences — inherent to the system, not attributable to any single source.

Time-series chart of a process metric with statistical limits — separates common from special causes.

Action limits on a control chart, usually at ±3σ from the centre line — NOT the same as specification limits.

Cumulative-sum control chart — accumulates deviations from the target and alarms when a threshold $h$ is crossed.

Time-weighted control chart — each point is an exponentially weighted average; sensitive to small persistent shifts.

Control chart for individual values (n = 1) — uses the moving range of consecutive values as σ estimator.

Pattern rules for detecting special causes on control charts — 8 rules that go beyond the plain ±3σ test.

Attribute control chart for the fraction of defective units per sample — binomial-distributed.

Time-series chart with median line and runs tests — the pre-analysis for a control chart, without any spread assumption.

A systematic influence beyond the process's normal common-cause variation — the trigger of a rule violation on a control chart.

Small group of observations collected under conditions as similar as possible — the base unit of X̄-R and X̄-S charts.

Classical control chart for continuous measurements in subgroups — X̄ tracks location, R tracks spread.

R² variant that penalises extra predictors — rises only when a new X truly contributes.

Measure of the linear relation between two variables — value between −1 (perfectly opposed) and +1 (perfectly aligned).

Family of regression models for non-normal responses (binary, counts, proportions) — link function plus exponential-family distribution.

The dispersion of the residuals is not constant — it varies with the X value or fitted value (funnel shape in the residual plot).

Standard regression for continuous, normally distributed Y — model $Y={\beta }_0+\sum {\beta }_j{X}_j+\epsilon$, estimated by least squares.

GLM for binary responses (0/1, pass/fail) — models the probability $P(Y=1|X)$ via the logit link.

Two or more predictors are strongly correlated — the regression can no longer cleanly separate their individual contributions.

GLM for count data with overdispersion — like Poisson but with an extra dispersion parameter $\theta$.

Standard effect measure of logistic regression — factor by which the odds $p/(1-p)$ change per unit of X.

In Poisson models: observed variance exceeds the mean — the Poisson assumption is violated.

The model fits noise in the training data — R² looks great, new data disappoints.

GLM for count data (0, 1, 2, …) — models the expected value via log link, assuming variance ≈ mean.

Substitute measures for R² in GLM — quantify improvement of the model over the null model.

Share of Y variation the regression model explains — 0 = nothing, 1 = perfect.

Effect measure of Poisson and negative binomial regression — factor by which the expected count changes per unit of X.

Describes the relation between a response Y and one or several predictors X as a mathematical model — not just "do they move together" but a predictive equation.

Difference between observed and predicted Y — what the model does not explain.

1–10 scale rating how reliably the failure is detected before the customer — a high value is bad.

The possible way a function deviates from its intended behaviour — core object of every FMEA row.

Systematic method to identify and prioritise potential failures in products or processes — before they occur.

1–10 scale rating how often the cause occurs — one factor of the RPN.

Product of S × O × D in the FMEA — a rough prioritisation, not an absolute risk measure.

1–10 scale rating the severity of the failure effect at the customer — one factor of the RPN.

Iterative why-questioning to trace the cause chain — ask "why?" at least five times until the true root cause is reached.

Justifies in money why the project is worth the time invested — and who confirms the benefit.

Rates which process inputs act most strongly on the customer-relevant outputs — the pre-selection of the critical X.

Measurable quality characteristics derived from the Voice of Customer — with target, limits and priority.

Five-phase framework of Six Sigma improvement: Define — Measure — Analyze — Improve — Control.

Represents a sequence as a chain of activities and decisions — the base form of all process displays.

Defines measurably what the project is to achieve — with baseline, target and deadline.

Visual cause collection with main branches (typically 6M) — bundles all possible influences on a problem for the Analyze phase.

Classifies requirements from the VoC→CTQ tree by how their fulfillment or absence affects customer satisfaction.

Asks each requirement twice — functional and dysfunctional; only both answers yield the category.

Total time from trigger to completion — and how much of it is actual processing.

Documented findings from a project — with cause and a concrete recommendation, not just an observation.

Lean process mapping for office and service processes — roles across steps, with times per step.

Any activity that consumes resources without creating customer value — classically in eight types.

80/20 rule — few causes produce most of the effect. The Pareto chart visualises this with sorted bars and a cumulative curve.

States in facts what happens, where, when and how often — no cause, no blame, no solution.

Detailed depiction of the actual process flow — foundation for the Measure and Analyze phases of DMAIC.

One-page contract between project team and sponsor — defines problem, goal, scope, team and schedule in the Define phase of DMAIC.

Delimits what belongs to the project and what does not — the defence line against scope creep.

Assigns four kinds of responsibility to each task — Responsible, Accountable, Consulted, Informed.

Looks for the cause behind the symptom — the point at which a measure removes the problem for good.

Compact process overview: Suppliers — Inputs — Process — Outputs — Customers. Standard Define-phase tool in DMAIC.

Data- and method-driven improvement philosophy — target: process capability at 6σ level (≈ 3.4 defects per million opportunities).

Who can influence the project or is affected by it — mapped by power, interest and attitude.

Spreads process steps across one lane per role — makes responsibilities and handovers visible.

Separates steps the customer pays for from those they would not pay for — the base question of every Lean analysis.

Translates customer statements in four stages into measurable requirements: statement, need, driver, CTx.

Systematic collection of customer statements and needs — the basis of every CTQ derivation.

Compares a measure across categorical levels — length encodes the value and is what the eye reads most accurately.

Five-number summary as a box with whiskers — the most compact way to compare several groups.

Line of constant response in a contour plot — its spacing shows how strongly a factor acts.

Colour-coded matrix over two categorical axes — makes hotspots in a cross tabulation visible at a glance.

Binned frequency display of a metric characteristic — shows location, spread and shape of the distribution.

Area-true display of a contingency table — column width shows the marginal, segment height the conditional distribution.

Graphical breakdown of a measurement's spread by up to four categorical factors — shows where the variation sits before a designed experiment is planned.

Shows how a whole splits across a few categories — the right choice only for very few sectors.

Warps the axis so a fitting distribution appears as a straight line — deviations become curvature.

Plots two metric characteristics against each other — the base form of every association analysis.

Altshuller's catalogue of abstract solution strategies — from 'segmentation' to 'parameter change', numbered 1–40.

Altshuller's solution catalogue for su-field analysis, in five classes — from model building to measurement and simplification.

39×39 lookup table: improving versus worsening parameter — the cell names the proven inventive principles.

Ratio of useful functions to cost and harmful effects — the directional measure of every TRIZ development.

The useful function is delivered with no system, no cost and no side effect — the target image set before any solution search.

Six canonical fields of action: Mechanical, Acoustic, Thermal, Chemical, Electrical, Magnetic.

One and the same parameter must take two opposite values at once — 'X should be A AND not-A'.

Inventory of all present substances, fields, spaces, times, information and functions — before any new component.

Four ways to resolve a physical contradiction: separation in time, space, condition or system level.

Models every interaction as a triangle of tool (S1), object (S2) and field (F), including the quality of the effect.

The level above and below the system under study — source of free resources and starting point for system jumps.

3×3 grid of time (past/present/future) and hierarchy (sub-/system/supersystem) that breaks tunnel vision.

One parameter improves only at the expense of another — the standard case for the contradiction matrix.

Recurring lines of development from patent analysis — the next stage is a testable innovation hypothesis.

Systematic innovation methodology distilled from patent analysis — resolves contradictions with proven patterns instead of trade-offs.