Nist Stat Handbook

NIST/SEMATECH e-Handbook of Statistical Methods (NIST HB 151)

Source: NIST/SEMATECH (US Government work, public domain) | Chapters: 8

When to use

Use this skill when you need applied frequentist statistics for engineering, metrology, or quality work, drawing from the NIST/SEMATECH e-Handbook of Statistical Methods (NIST HB 151). It is the right pack for exploratory data analysis and the four univariate assumptions (4-plot), measurement process characterization including bias/precision, calibration designs, gauge R&R, and ISO/GUM uncertainty budgets, production process characterization covering stability vs. capability, process modeling and regression (LS/WLS/NLS/LOESS), design of experiments (screening, fractional/factorial, response-surface, Taguchi), statistical process control (Shewhart/CUSUM/EWMA charts, capability indices, acceptance sampling), product/process comparisons (hypothesis tests and confidence intervals for one, two, or more groups, ANOVA, multiple comparisons), and reliability (lifetime and repair-rate models, accelerated testing, reliability growth).

Prerequisites: none, plain Markdown; no MCP server, API key, or licence tier needed at runtime.

How to Use This Skill

• Without arguments — load the Core Frameworks below: the EDA mindset, the characterization→modeling→improvement→control→comparison→reliability arc, and the routing rules for picking a method.
• With a statistical task — route to the right chapter and pattern. Examples: "is my data in control?" → ch01 (4-plot); "state the uncertainty of this result" → ch02 (GUM budget); "design an experiment to optimize yield" → ch05 (DOE); "which control chart for small drifts?" → ch06 (CUSUM/EWMA); "compare three machines" → ch07 (ANOVA + multiple comparisons); "fit a life distribution" → ch08 (Weibull).
• With a chapter — ch01 EDA · ch02 measurement/uncertainty · ch03 process characterization · ch04 regression · ch05 DOE · ch06 SPC · ch07 comparisons · ch08 reliability.

Supporting files: glossary.md, patterns.md, cheatsheet.md.

Prerequisites: none — plain Markdown; no MCP server, API key, or runtime licence needed.

What this Handbook is. A practitioner's reference for engineering statistics — measurement, process, and quality work — not a mathematical-statistics textbook. Its through-line is the engineering scientific method: characterize a process, model it, improve it by experiment, hold the gains with control charts, compare alternatives with the right test, and predict how long it will last. The signature attitude (from ch01) is look at the data before imposing a model.

Core Frameworks & Mental Models

The EDA stance — let the data reveal the model (ch01)

Classical analysis imposes a model (normality, linearity), then estimates and tests it. Exploratory Data Analysis (EDA) holds that decision back: plot the data first and let its structure surface. The unifying baseline is the univariate model Y = c + ε and its four assumptions — the data have (1) fixed location, (2) fixed scale, (3) randomness (no autocorrelation), and (4) a fixed distribution. The 4-Plot (run-sequence, lag, histogram, normal-probability) tests all four at a glance. Pass all four ⇒ the process is "in statistical control" and predictable. A failed panel is a diagnostic pointing at a physical cause. Residuals are the universal diagnostic: an adequate model leaves structureless residuals.

Characterizing a measurement process — goodness decomposed (ch02)

Treat measurements as the output of a process and ask how good they are. Goodness splits into bias (quantitative offset from the reference/true value), short-term variability / precision (level-1), long-term / day-to-day variability (level-2, often larger than precision for very precise instruments), and uncertainty. The engine is the check standard — a database of repeated measurements on a stable surrogate — monitored by an individuals Shewhart chart (and EWMA for small shifts). Calibration designs are redundant least-squares intercomparison schedules (anchored by a restraint = the known reference value) that assign values while cancelling constant left-right bias and linear drift. Gauge R&R nested designs separate repeatability, reproducibility, and stability. Uncertainty follows the ISO/GUM framework: every component a standard deviation, grouped by Type A (from statistical analysis) vs. Type B (other means), combined by root-sum-squares with sensitivity coefficients, expanded by a coverage factor U = k·u (k≈2 ⇒ ~95%), with Welch-Satterthwaite for unknown degrees of freedom.

Characterizing a production process — stability before capability (ch03)

Frame the process as a black box (inputs / controlled factors / uncontrolled noise / output), then expand drivers with a fishbone diagram. Distribution = location + spread + shape. Models span the Continuous Linear Model (CLM), ANOVA, and discrete (contingency/chi-square) forms. Two rules dominate: add variances, never standard deviations when combining error; and establish stability before claiming capability — Cp/Cpk on an out-of-control process are meaningless. Interpret graphically, then confirm numerically. The most expensive mistake is skimping on planning.

Modeling a process — function plus error (ch04)

The general statistical model is y = f(x; β) + ε: a deterministic function of the factors plus random error. Four method families build it — linear least squares, nonlinear least squares, weighted least squares (WLS) for non-constant variance, and LOESS for local, assumption-light smoothing. A model is used to estimate, predict, calibrate, and optimize. Six standard assumptions (random errors, mean zero, constant variance, known distribution, independence, correct functional form) are checked through residual analysis — the same look-at-the-residuals discipline as EDA.

Improving by experiment — sequential DOE (ch05)

Design of Experiments varies factors together to estimate effects efficiently; its four objective classes are comparative, screening, response-surface, and regression. The strategy is a staircase, not one big experiment: screen many factors cheaply with fractional factorial / Plackett-Burman designs, test curvature with center points, foldover to de-alias, then spend three-level response-surface runs (CCD, Box-Behnken) near the optimum. Resolution (III/IV/V) is the confounding dial; the defining relation and generators set the aliasing. One-factor-at-a-time is a trap — it misses interactions. Taguchi robust design (parameter design via inner/outer arrays, then tolerance design) minimizes sensitivity to noise. Always randomize; finish with confirmation runs.

Holding the gains — statistical process control (ch06)

SPC/SQC uses control charts to separate common-cause from special-cause variation. Phase I builds and validates limits from history; Phase II monitors new data. Chart families: Shewhart (X-bar & R/s, individuals) for large shifts; CUSUM (V-mask) and EWMA (memory depth λ) for small sustained drifts; attributes charts for counts; Hotelling's T² for correlated multivariate data. Control limits ≠ specification limits (voice of the process vs. voice of the customer). Compare charts by Average Run Length (ARL): sensitivity is bought with false alarms (WECO rules). Decide the response in advance with an OCAP. Acceptance sampling (OC curve, AQL/LTPD, producer's/ consumer's risk, AOQ/AOQL) governs lot accept/reject decisions.

Comparing alternatives — the right test (ch07)

Route by how many processes: one (t/z, chi-square, exact-binomial/Wilson), two (two-sample/paired t, F-test, two-proportion z / Fisher exact), or three-plus (ANOVA then a multiple-comparison procedure — Tukey, Scheffé, Bonferroni, Tukey-Kramer, Marascuilo; Kruskal-Wallis if non-normal). The spine is test ⇔ interval duality: reject exactly when the hypothesized value falls outside the matching confidence interval. ANOVA analyzes variances to draw conclusions about means; fixed vs. random effects changes the inferential target. Use exact methods for small samples, approximations (with their validity gates) for large; "failure to reject" is not proof of equality.

Predicting how long it lasts — reliability (ch08)

Reliability is quality over time — R(t) = probability of surviving past t. The first fork is non-repairable vs. repairable. Non-repairable units get a lifetime distribution (Weibull, lognormal, exponential, gamma, extreme value, Birnbaum-Saunders), reasoned about via the hazard rate h(t) (a speedometer) and the bathtub curve; data are censored (Type I by time, Type II by count) and information scales with the number of failures. Repairable systems get a repair-rate model (HPP; NHPP Power Law / Duane-AMSAA for reliability growth under TAAF) reasoned about via N(t), M(t), m(t) — they have no single failure rate. System reliability is built bottom-up from series/parallel/k-of-n/standby blocks (series = product of part reliabilities). Accelerated testing needs a justified acceleration model (Arrhenius, Eyring, Coffin-Manson) that rescales time.

Chapter Index

Topic Index

• 4-Plot / four univariate assumptions → ch01, cheatsheet
• Acceleration models (Arrhenius/Eyring/Coffin-Manson) → ch08
• Acceptance sampling / OC curve / AQL / LTPD → ch06, cheatsheet
• ANOVA (one-way / two-way / fixed-random effects) → ch07, ch03, ch05
• Average Run Length (ARL) → ch06
• Bathtub curve / hazard rate → ch08
• Bias / accuracy (measurement) → ch02
• Black-box & fishbone (cause-and-effect) diagram → ch03
• Calibration designs / restraint / drift & left-right bias → ch02
• Capability (Cp, Cpk) / stability vs. capability → ch06, ch03, cheatsheet
• Censoring (Type I / Type II) → ch08
• Check standard → ch02, patterns
• Confidence intervals / test–interval duality → ch07, cheatsheet
• Confounding / aliasing / resolution (III/IV/V) → ch05
• Control charts (Shewhart / CUSUM / EWMA / attributes / T²) → ch06, cheatsheet
• Design of Experiments (DOE) / objective classes → ch05, patterns
• EDA (exploratory data analysis) philosophy → ch01
• Error propagation / add variances / sensitivity coefficients → ch02, ch03, patterns
• Factorial & fractional factorial / Plackett-Burman → ch05
• Foldover / center points → ch05
• Gauge R&R (repeatability / reproducibility / stability) → ch02
• Goodness-of-fit (Anderson-Darling, K-S, chi-square, Shapiro-Wilk) → ch07, ch08
• Hotelling's T² (multivariate SPC) → ch06
• Hypothesis tests by group count (1/2/3+) → ch07, cheatsheet
• ISO/GUM uncertainty / Type A & Type B / expanded uncertainty → ch02, patterns, cheatsheet
• Lifetime distributions (Weibull / lognormal / exponential / gamma) → ch08, glossary
• LOESS / local regression → ch04
• Multiple-comparison procedures (Tukey / Scheffé / Bonferroni) → ch07
• Out-of-Control Action Plan (OCAP) → ch06
• Phase I vs. Phase II (SPC) → ch06
• Process model y = f(x;β)+ε / regression (LS/WLS/NLS) → ch04
• Randomized block / completely randomized designs → ch05
• Reliability R(t) / non-repairable vs. repairable → ch08, patterns
• Reliability growth / Duane / AMSAA / TAAF → ch08
• Residual analysis → ch04, ch01
• Response surface (CCD / Box-Behnken / RSM) → ch05
• Run-sequence / lag / histogram / normal-probability plots → ch01
• Sampling / stratification / sample size → ch03
• Sequential experimentation strategy → ch05, patterns
• Series / parallel / k-of-n / standby system models → ch08
• Statistical Process Control (SPC / SQC) → ch06
• Taguchi / parameter & tolerance design → ch05
• Three-level standard-deviation model (Level 1/2/3) → ch02
• Uncertainty budgets / Welch-Satterthwaite → ch02, cheatsheet
• WECO rules / control vs. specification limits → ch06

Supporting Files

• glossary.md — key statistical, metrology, DOE, SPC, and reliability terms, alphabetical, with chapter references
• patterns.md — ten reusable techniques (4-plot gate, black-box framing, GUM uncertainty budget, stability-before-capability, chart selection, sequential DOE, comparison-test routing, reliability fork, check-standard control) with When/How/Trade-offs
• cheatsheet.md — chapter map, the four assumptions, comparison-test selector, control-chart selector, DOE & reliability decision tables, uncertainty-in-one-screen, and tells & smells

Scope & Limits

Covers: applied (frequentist) statistics for engineering, metrology, and quality across the eight Handbook chapters — exploratory data analysis; measurement-process characterization and ISO/GUM uncertainty; production-process characterization; process modeling and regression; design of experiments; statistical process control and acceptance sampling; hypothesis testing, confidence intervals, ANOVA and multiple comparisons; and product reliability (lifetime models, accelerated testing, reliability growth, basic Bayesian reliability).

Does not cover / thin on: the original web Handbook is an HTML/web-native reference of many short interlinked pages with extensive per-distribution formula galleries, worked case studies, datasets, plot/figure images, and Dataplot/R code blocks — this pack synthesizes the concepts and method-selection logic in original words and deliberately does not reproduce those galleries, case studies, datasets, images, or code (they are described, not copied — a quality and licence-safety choice). It is also thin on: modern machine learning / statistical learning; Bayesian methods beyond conjugate reliability priors; time-series analysis and forecasting; Bayesian/optimal experimental design; survey/causal-inference methodology; and software-specific how-tos. For SE-process context see sebok, dau-se-guidebook, nasa-npr-7123; this pack is the quantitative-methods companion to those.

Source version: NIST/SEMATECH e-Handbook of Statistical Methods, NIST Handbook 151 (2012 edition, last updated October 2022). Public domain — a work of the U.S. Government (17 U.S.C. 105); free to reproduce, transform, and redistribute, including commercially. SEMATECH co-developed the content; attribution to NIST/SEMATECH is a courtesy, not an obligation, and neither endorses this pack.