Home / Lean Six Sigma / Measurement system analysis (MSA)
Find out whether inspectors repeat their own decisions, agree with each other and match the standard in visual or go/no-go inspection. Use it before trusting a human inspection (PPAP, customer complaint, new inspector): you need each appraiser's answers per sample and, if known, the correct answer; you get percent agreement with its uncertainty range, kappa (agreement net of chance) and what to fix first.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
Key: # inspected = samples rated; # matched = samples where all answers agreed; Percent = matched ÷ inspected; CI = range where the true percentage should lie. Kappa: 1 = perfect, above 0.75 = good, 0 = same as guessing; P(vs > 0) below 0.05 means agreement better than chance. # OK / NOK = parts wrongly classified in one direction (see column order); Mixed = the appraiser changed answer between trials.
% of samples where each appraiser repeated their own answer, with the CI.
How to read: horizontal axis = each appraiser; point = % of samples where they repeated the same answer; vertical bar = confidence interval. Higher is more consistent. A point below 90% or a long bar needs attention.
% of samples where all of the appraiser's answers matched the standard, with the CI.
How to read: each point is the appraiser's hit rate against the correct answer; the bar is the uncertainty. Ideally all are close to 100%. An appraiser well below the others needs their criterion recalibrated.
Fleiss' kappa within the appraiser and against the standard, with the 0.75 and 0.90 references.
How to read: bars = kappa of each appraiser (one color for “Within”, with themself; another for “vs standard”, see the legend). Dashed lines: 0.75 (minimum acceptable) and 0.90 (very good). A bar below 0.75 is a warning; below 0.40 agreement is poor.
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It is the "gage R&R" of visual or go/no-go inspection: several inspectors rate the same samples more than once, blind, and the study shows whether each repeats their own answer (within appraiser), whether they agree with each other (between appraisers) and whether they get the right answer (vs standard). It is required by the MSA manual and PPAP for characteristics inspected by attributes.
Per the MSA manual: about 50 samples, with clearly good, clearly bad and borderline parts; 3 appraisers who inspect day to day; 2 or 3 trials in random order, without the appraiser knowing which part they see. An expert or a measurement sets the standard for each sample. Paste one line per rating: sample; appraiser; response; standard.
A sample counts as matched only if all answers agree, so the percentage drops quickly with more trials and appraisers. The exact confidence interval shows the uncertainty: in the default example (30 samples) the CI is about 30 points wide; with 50 samples it narrows.
Kappa removes the agreement that would happen by chance: 1 is perfect and 0 is the same as guessing. The MSA manual sees kappa above 0.75 as good and prefers above 0.90; below 0.40 agreement is poor. Fleiss' kappa works for any number of ratings; Cohen's compares exactly two.
When responses are ordered, like a 1 to 5 scale or minor/moderate/severe. Kappa treats every miss the same; Kendall's coefficient of concordance (W) and correlation with the standard (τ) give credit to close answers. Choose "Ordinal" and use numbers as responses to guarantee the order.
For two-class responses, the table splits consistent errors (the appraiser always gave the wrong answer) by direction, for example accepting a bad part or rejecting a good one, from mixed ones (changed answer between trials). Accepting a bad part is the costliest error for the customer; rejecting a good one costs rework. Mixed errors point to borderline parts or a vague criterion.
If an appraiser is inconsistent with themself, improve conditions (light, time, position) and build a limit-sample catalogue. If they are consistent but wrong against the standard, recalibrate their criterion. If the team disagrees, align the acceptance standard with everyone together. Repeat the study afterwards; where possible, replace visual inspection with a go/no-go gauge or a measurement.
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