ashfordeOU Measurement Systems Analysis (manufacturing-quality/as9100/measurement-systems-analysis)
Use when the task is judging whether an aerospace measurement system is adequate for its measurement task: operator-part trial data feeds the range-based Gage R and R study, the percent GRR scores the system against the acceptance bands, and the number of distinct categories scores its resolving power.
Domain quick reference
- Gage R and R splits measurement error into repeatability (equipment variation EV, the spread of repeated readings by one appraiser on one part) and reproducibility (appraiser variation AV, the spread of appraiser averages on the same parts).
- Range method: for each appraiser-part cell the range of the trials is R, the average of all cell ranges is rbar, and EV = K1 * rbar with K1 = 4.56 for 2 trials and 3.05 for 3 trials.
- AV = sqrt((K2 * xdiff)^2 - EV^2 / (trials * parts)) with xdiff the spread of the appraiser averages and K2 = 3.65 for 2 appraisers, 2.70 for 3; a negative radicand clamps AV to zero, meaning the appraisers agree within equipment variation.
- GRR = sqrt(EV^2 + AV^2), part variation PV = K3 * Rp with Rp the spread of the part averages, total variation TV = sqrt(GRR^2 + PV^2).
- Percent GRR = 100 * GRR / TV. Acceptance criteria: under 10 percent the measurement system is acceptable, 10 to 30 percent is conditional (acceptable only for specific applications), over 30 percent is unacceptable and the gage must be improved or replaced.
- Number of distinct categories ndc = floor(1.41 * PV / GRR); the common guidance is five or more categories for an adequate system.
- Variable gage studies use continuous readings; attribute gage studies use go/no-go or classification results and need agreement and Kappa analysis, not the range method.
- Calibration vs MSA: calibration verifies the instrument against a standard with traceability (see calibration-control); MSA quantifies how much of the observed variation comes from the measurement system itself.
- AS9100 frames monitoring and measuring resources as controlled and fit for purpose (paraphrase of clause 7.1.5 practice); the Gage R and R study is the common aerospace evidence that a gage is fit for its measurement task, summarized here without clause text.
Workflow
- Collect the operator-part measurement table: every appraiser measures every part with the same number of trials (2 or 3), the range method standard.
- Build the measurements dict: appraiser name to a list of parts, each part a list of trial readings, with identical part and trial counts across appraisers.
- Run the study with study_summary(measurements) to get EV, AV, GRR, PV, TV, the percentage contributions, and the ndc.
- Read the percent GRR verdict from the summary, or score a percent directly with acceptance_verdict(grr_pct).
- Judge resolving power with number_distinct_categories(pv, grr); five or more categories is the common adequacy threshold.
- Validate inputs first: fewer than two appraisers, fewer than two parts, trial counts outside 2-3, inconsistent table dimensions, or negative readings raise ValueError.
Pitfalls
- Routing control chart questions here: X-bar and R chart limits, process capability Cp/Cpk, and Western Electric rules belong to statistical-process-control; a gage study measures the measurement system, not the production process.
- Routing instrument calibration questions here: TAR, calibration due dates, out-of-tolerance recall, and traceability belong to calibration-control; MSA is about measurement system variation, not instrument calibration state.
- Routing root cause questions here: 8D, five whys, and corrective action plans belong to corrective-action; a high percent GRR explains why a process looks out of control but is not itself a root cause analysis.
- Treating an attribute gage study like a variable one: go/no-go results need agreement and Kappa analysis, not the range method.
- Reading the percent GRR bands off the wrong edge: under 10 is acceptable, exactly 10 to 30 is conditional, over 30 is unacceptable; 30.1 is not conditional.
- Reporting AV as zero without the clamp note: the range method clamps a negative radicand to zero, which means the appraisers agree within equipment variation, not that appraiser bias is absent.
- Dividing by zero total variation: a study where every reading is identical has no variation to decompose; the summary reports zero percent GRR and an acceptable verdict.
- Taking ndc at face value when GRR is zero: with no measurement error the ratio is undefined and the summary returns None.
- Confusing calibration with MSA: a calibrated instrument can still have poor repeatability or reproducibility; calibration is a precondition, not a substitute, for a gage study.
Behavior contract (gate 3)
The Gage R and R logic is exercised by the gate 3 contract test: scripts/test_measurement_systems_analysis.py against scripts/measurement_systems_analysis_logic.py (stdlib unittest, offline). Run: python3 scripts/test_measurement_systems_analysis.py
Compliance
- Standards referenced, not reproduced: AS9100 clause 7.1.5 frames monitoring and measuring resources; the range-method constants and the acceptance bands are common MSA methodology, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.