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Section III: Measure Phase 20 questions

Measure carries 20 of the 100 scored questions on the 2022 CSSGB exam, tied with Define as the largest section. It answers two questions before any analysis: can we trust the data (measurement system analysis), and how is the process performing now (baseline and capability)? It also holds most of the exam’s basic probability and statistics.

Key topics

Topic	What to know
Process analysis and documentation	Process maps and flowcharts, written procedures and work instructions; using them to understand the current state.
Probability and statistics	Basic probability (independent and mutually exclusive events, addition and multiplication rules) and the central limit theorem.
Statistical distributions	Normal, binomial, Poisson, and the t, chi-square and F distributions: when each applies.
Collecting and summarizing data	Data types and measurement scales, sampling and data collection (check sheets, data collection plans), descriptive statistics, graphical methods (histogram, box plot, scatter diagram, normal probability plot).
Measurement system analysis	Repeatability, reproducibility, %GRR, number of distinct categories, bias, linearity, stability; attribute agreement analysis.
Process and performance capability	Specification vs. process limits, capability studies, Cp/Cpk and Pp/Ppk, short-term vs. long-term variation, sigma level.

Measurement system analysis

%GRR (of study variation or tolerance)	Usual interpretation (AIAG guideline)
< 10%	Acceptable
10–30%	May be acceptable depending on the application and cost
> 30%	Unacceptable; improve the measurement system

Repeatability (EV): variation when the same appraiser measures the same part repeatedly with the same gage.
Reproducibility (AV): variation between appraisers measuring the same parts with the same gage.
Variances add: σ²_GRR = σ²_{repeatability} + σ²_{reproducibility}.
Number of distinct categories (ndc) = 1.41 × (σ_parts / σ_GRR); 5 or more is recommended.

Capability indices

Cp  = (USL − LSL) / 6σ_within
Cpk = min[(USL − μ) / 3σ_within , (μ − LSL) / 3σ_within]
Pp, Ppk: same formulas with the overall (long-term) standard deviation

Example: USL = 60, LSL = 40, μ = 52.1, σ = 2.0
  Cp  = 20 / 12 = 1.67
  Cpk = min[7.9 / 6, 12.1 / 6] = min[1.32, 2.02] = 1.32

Cpk ≤ Cp always; they are equal only when the process is centered.
Cp = Cpk = 1.0 on a normal process puts about 0.27% outside the limits.
Cpk ≥ 1.33 is a common minimum; many customers require more for critical characteristics.
High Cp with low Cpk means the spread fits but the process is off-center: re-center first.
Capability indices are only meaningful for a stable (in-control) process.

Central limit theorem

Sample means are approximately normally distributed for a large enough sample, whatever the shape of the population, with standard error σ/√n. Example: σ = 2.0 and n = 16 gives a standard error of 2.0 / 4 = 0.5. This is why X̄ charts work well even for moderately non-normal data.

Common exam traps

Repeatability vs. reproducibility. Same person, same gage, repeated readings → repeatability. Different appraisers → reproducibility (often a training or method problem).
Ordinal is not interval. Ratings of 1–5 are ordered but not equally spaced; temperature in °C is interval (no true zero), weight is ratio.
Mutually exclusive ≠ independent. Mutually exclusive events cannot occur together, so (when each has nonzero probability) they are not independent.
Ppk vs. Cpk. Ppk uses overall variation and is usually lower than Cpk; a large gap suggests the process shifts over time.

Learn pages for this section

Data types & measurementScales, sampling Basic statisticsMean, s, normal MSA basicsGage R&R, bias Process capabilityCp, Cpk, DPMO Run chartsBaseline patterns

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Section names and question counts follow the 2022 CSSGB Body of Knowledge (110 questions, 100 scored). Topic summaries are our paraphrase; check the current BoK on asq.org for the official wording.

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