Measurement System Analysis (MSA / Gage R&R)
Assess your measurement system with the three standard MSA procedures: Type 1 as a Cg/Cgk study on a reference standard, Type 2 as a Gage R&R with appraiser influence and Type 3 as an automated study without an appraiser. Paste measurement series straight from Excel, enter the tolerance and get the capability indices with a traffic-light rating – switchable between the AIAG, VDA 5 and ISO 22514-7 evaluation worlds, live with every input.
MSA calculator (measurement system analysis)
A calibrated standard is measured repeatedly many times. Rated are the repeatability (Cg), the systematic deviation (bias, contained in Cgk) and the resolution (%RE). Use: release a new gauge, caliper or sensor. Capable from Cg ≥ 1.33 and Cgk ≥ 1.33 at %RE ≤ 5 %.
AIAG rates the observed variation directly. The headline metric for Gage R&R is %GRR relative to the total variation (study variation) together with ndc. Limits: %GRR ≤ 10 % capable, ≤ 30 % conditional, ndc ≥ 5.
Model: average-range method (ARM) with K constants per AIAG. Type 1 follows the Cg/Cgk convention (Bosch booklet 10 / VDA 5), with L switchable between ±3s and ±2s. All verdicts are relative to the entered tolerance; without a tolerance the tolerance-based metrics are omitted. The ANOVA method and the full VDA 5 / ISO 22514-7 uncertainty budget (Q_MS/Q_MP) are reserved for the full version. A sizing and rating tool, not a substitute for a normative capability proof per IATF 16949 / PPAP.
Results
Calculating …
Formulas and fundamentals
Type 1 (gauge capability) evaluates repeated measurements of a calibrated standard against a share of the tolerance. From the mean x̄g and the sample standard deviation sg (with n−1) of the n repeated measurements follow the pure-scatter capability index Cg = (p·T)/(L·sg) and the index reduced by the magnitude of the systematic deviation Cgk = ((p/2)·T − |bias|)/((L/2)·sg) with bias = x̄g − x_m. The tolerance share p is typically 0.20, the reference convention L selects between ±3s (L = 6, DE/Bosch/VDA default, 99.73 %) and ±2s (L = 4). In addition %RE = RE/T·100 checks the resolution (requirement ≤ 5 %) and a two-sided t-test with t = |bias|/(sg/√n) and n−1 degrees of freedom decides whether the systematic deviation is significant.
Type 2 (Gage R&R with appraiser) splits the total variation by the average-range method into repeatability and reproducibility. From the mean range R̄ follows the equipment variation EV = R̄·K1, from the range of appraiser means X_DIFF the reproducibility AV = √((X_DIFF·K2)² − EV²/(n·r)), together the measurement-system variation GRR = √(EV² + AV²). The part variation PV = Rp·K3 follows from the range of part means Rp, the total variation is TV = √(GRR² + PV²). The K factors are reciprocals of the constants d2 and d2* and depend on the number of measurements r, appraisers k and parts n. In Type 3 the appraiser term drops out, so AV = 0 and GRR = EV.
The rating uses the ratio of measurement variation to total variation or to the tolerance. %GRR (study variation) = 100·GRR/TV relates to the total variation, %GRR (tolerance) = 100·(6·GRR)/T to the tolerance, %Contribution = 100·GRR²/TV² works with variance shares and sums with the other sources to 100 %. The resolution ndc = trunc(1.41·PV/GRR) gives the number of distinct categories (truncated, not rounded). A measurement system is capable at %GRR ≤ 10 %, conditionally capable up to 30 %, above that not capable; additionally ndc ≥ 5 is required.
Worked example
Type 1: A caliper measures a standard x_m = 10.000 mm 50 times, tolerance T = 0.20 mm, resolution RE = 0.001 mm, L = 6, p = 0.20. From x̄g = 10.004 mm and sg = 0.004 mm follow bias = 0.004 mm, Cg = (0.2·0.20)/(6·0.004) = 1.67 and Cgk = (0.1·0.20 − 0.004)/(3·0.004) = 1.33. The resolution is sufficient at %RE = 0.5 %; the bias t-value 7.07 exceeds the critical value 2.01, so the deviation is significant and should be corrected.
Type 2: The canonical AIAG example with 10 parts, 3 appraisers and 3 measurements gives R̄ = 0.342, X_DIFF = 0.445 and Rp = 3.511. This yields EV = 0.202, AV = 0.230, GRR = 0.306, PV = 1.105 and TV = 1.146, hence %GRR (study var) = 26.7 % and ndc = 5. The measurement system is conditionally capable – the reproducibility between appraisers at %AV = 20 % is the dominant share.
Type 3: The same parts without appraiser influence (AV = 0) give GRR = EV = 0.202 and TV = 1.123, hence %GRR = 18.0 % and ndc = 7. The automated system distinguishes the parts much better because the dominant appraiser share is gone – a typical result for optical or fully automatic measuring cells.
Frequently asked questions
When do I use Type 1, 2 or 3?
Type 1 (Cg/Cgk) releases a new gauge: many repeated measurements of a calibrated standard, rating scatter, systematic deviation and resolution. Type 2 (Gage R&R) secures a manual measuring station operated by several appraisers – the operator is a separate source of variation. Type 3 is for measurements without a human operator (optical inspection, camera, laser, automatic cell); the appraiser term drops out while the real repeatability including handling is captured.
What do Cg and Cgk mean?
Cg rates only the gauge repeatability against an assigned share of the tolerance (typically 20 %). Cgk additionally subtracts the magnitude of the systematic deviation (bias) and is therefore always less than or equal to Cg. The gauge is capable from Cg ≥ 1.33 and Cgk ≥ 1.33. A large bias pushes Cgk below Cg – a correction or re-adjustment of the gauge then helps.
How do %GRR (study var), %tolerance and %contribution differ?
%GRR (study var) relates the measurement variation to the observed total variation TV and is the classic AIAG headline metric. %Tolerance (P/T) relates the same measurement variation to the tolerance and is decisive under VDA 5 and ISO 22514-7. %Contribution works with variances (squares) and sums over all sources to 100 %. These are three different numbers – the calculator reports all three separately so nothing gets mixed up.
What does the ndc value tell me?
ndc (number of distinct categories) is the number of classes the measurement system can reliably distinguish within the part variation: ndc = trunc(1.41·PV/GRR). From ndc ≥ 5 the resolving power is considered sufficient. A low ndc means the measurement variation is too large relative to the part variation to tell parts apart reliably. The value is truncated, not rounded.
How do AIAG, VDA 5 and ISO 22514-7 differ?
AIAG rates the observed variation directly (Cg/Cgk, %GRR against the total variation, ndc). VDA 5 and the equivalent ISO 22514-7 instead rate the measurement uncertainty against the tolerance and separate measurement system (Q_MS, laboratory conditions) from measurement process (Q_MP, real conditions). In Types 1 to 3 the calculator shows the tolerance-based metric as the headline under the VDA/ISO view; the full Q_MS/Q_MP uncertainty budget is reserved for the full version.
How do I enter the measurements?
Fastest by copy-paste from Excel: copy the selected cells and paste them into the input field. Columns are separated by tabs, rows by line breaks; both decimal comma and decimal point are accepted. For Type 1 a single list of values is enough. For Type 2 each row is a part with columns ordered by appraiser and measurement; for Type 3 each row is a part with its repeated measurements. The sample-data button loads a matching data set to try out.
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