FH07 · REFERENCE SHEET

MSA 测量系统分析公式总表 MSA Formula Sheet

把 GR&R 变异分解、%GRR、ndc、%Tolerance、偏倚、线性、稳定性与 Kappa 放在同一张速查表中。自上而下重要度递减：先背 T1，再熟练 T2，最后按需查 T3。 One working sheet for GR&R variance components, %GRR, ndc, percent tolerance, bias, linearity, stability, and Kappa. Importance drops as you move down: memorize T1, work fluently with T2, and pull T3 when the measurement study calls for it.

覆盖范围 Coverage
T1 → T3
核心 MSA 工具链 core MSA stack
T1

必背 · 先信得过尺子，再谈过程 Memorize · Trust the Measurement System Before the Process

4 张核心卡 4 core cards
T1-1

总变异分解 Total Variation Decomposition

F42 深潜 → F42 deep dive →
σ2total = σ2part + σ2gauge

读作：看到的总变异 = 零件真实差异 + 量具带来的差异。Read it as: Observed total variation equals real part-to-part variation plus variation added by the gauge.

  • σ2part 零件间真实变异 true part-to-part variation
  • σ2gauge 测量系统引入的变异 variation introduced by the measurement system
何时用： Use it when: 区分观测总变异中有多少来自零件，有多少来自量具。 You need to separate real part variation from variation added by the gauge.
⚠ ✗ 把标准差直接相加得到总变异 → ✓ 独立变异源先加方差 σ²，再开方回到 σ。 ✗ Add standard deviations to get total variation → ✓ Add independent variance components in σ², then take the square root if σ is needed.
T1-2

量具变异分解 Gauge Variation Decomposition

F42 深潜 → F42 deep dive →
σ2gauge = σ2repeatability(EV) + σ2reproducibility(AV)

读作：量具误差 = 同人同件重复不准，加换人不一致。Read it as: Gauge error equals repeatability error on the same part plus disagreement across appraisers.

  • EV 重复性：同一条件下设备的短期变异 repeatability: short-term equipment variation under the same conditions
  • AV 再现性：作业者之间的变异 reproducibility: variation across appraisers
何时用： Use it when: 判断 GR&R 问题主要来自设备重复性，还是作业者再现性。 You need to determine whether GR&R is driven by equipment repeatability or appraiser reproducibility.
⚠ ✗ 只报总 GR&R，不拆 EV 与 AV → ✓ 分量定位后再决定修量具、方法还是培训。 ✗ Report only total GR&R and hide EV versus AV → ✓ Use the components to target the gauge, method, or appraiser training.
T1-3

%GRR 判定 %GRR Acceptance

F42 深潜 → F42 deep dive →
%GRR = σgauge/σtotal × 100%
<10% acceptable  ·  10–30% marginal  ·  >30% unacceptable

读作：量具变异占总变异的百分比——尺子的噪声占比。Read it as: Gauge variation as a percentage of total variation—the share of noise coming from the ruler.

  • σgauge 测量系统标准差 measurement-system standard deviation
  • σtotal 观测总标准差 total observed standard deviation
何时用： Use it when: 按研究总变异评价量具占比：<10% 可接受，10–30% 边缘，>30% 不可接受。 You need gauge contribution relative to study variation: below 10% is acceptable, 10–30% is marginal, and above 30% is unacceptable.
⚠ ✗ 用范围过窄的零件做研究后据 %GRR 淘汰量具 → ✓ 让样本覆盖实际过程范围，并同时查看 %Tolerance。 ✗ Reject a gauge from %GRR after studying a narrow part range → ✓ Cover the operating range and review percent tolerance as well.
T1-4

ndc 可区分类别数 ndc Distinct Categories

F43 深潜 → F43 deep dive →
ndc = 1.41 × σpart/σgauge
floor(ndc),  ndc≥5

读作：这把尺子能把零件分出几个档——至少要 5 档。Read it as: How many distinct buckets this ruler can separate the parts into—at least five are required.

  • 1.41 把零件变异与量具变异之比换算为可区分类别数 factor converting the part-to-gauge variation ratio into distinct categories
  • floor 结果向下取整，≥5 才合格 round down; at least 5 categories are required
何时用： Use it when: 判断量具能把实际零件差异分成多少个可靠类别。 You need to know how many reliably distinct part categories the measurement system can resolve.
⚠ ✗ 把 4.9 四舍五入成 5 并判合格 → ✓ ndc 必须向下取整，4.9 只能记为 4。 ✗ Round 4.9 up to 5 and pass the system → ✓ ndc is floored, so 4.9 reports as 4.
T2

常用 · 公差占比、计算方法与准确度 Working Set · Tolerance Share, Estimation Methods, and Accuracy

4 张常用卡 4 working cards
T2-5

%Tolerance Percent Tolerance

F42 深潜 → F42 deep dive →
%Tol = 6σgauge / (USL − LSL) × 100%
  • 6σgauge 量具的 6σ 研究宽度 six-sigma study width of the gauge
  • USL − LSL 规格公差宽度 specification tolerance width
何时用： Use it when: 评价量具消耗了多少公差，而不是相对于过程变异评价。 You need gauge spread relative to tolerance rather than relative to process variation.
T2-6

均值极差法 EV／AV Average-and-Range EV/AV

F42 深潜 → F42 deep dive →
EV = R̄ × K1
AV = √[(x̄diff × K2)2 − EV2/(n·r)]
(x̄diff × K2)2换人差异的平方Squared difference between appraisers EV2/(n·r)扣掉里面混着的重复性份额Subtract the repeatability share mixed into it
  • n / r 零件数／重复数 number of parts and number of replicates
  • K1, K2 由研究设计规模决定的常数；根号内为负取 0 constants from the study design; set a negative radicand to 0
何时用： Use it when: 用传统均值极差法快速估计设备变异 EV 与作业者变异 AV。 You need the traditional average-and-range estimates of equipment variation and appraiser variation.
T2-7

ANOVA 法 vs 极差法 ANOVA vs Average-and-Range

F42 深潜 → F42 deep dive → F18 深潜 → F18 deep dive →
ANOVA → part + appraiser + part×appraiser + repeatability
average-range → no separate part×appraiser term
  • part×appraiser 作业者×零件交互；ANOVA 法能分离，极差法不能 part-by-appraiser interaction, separated by ANOVA but not by the range method
  • AIAG 推荐 ANOVA 法 recommends the ANOVA method
何时用： Use it when: 需要分离作业者×零件交互并获得更完整的 GR&R 变异分量。 You need the part-by-appraiser interaction separated and a fuller GR&R variance decomposition.
T2-8

偏倚 Bias Bias

F16 深潜 → F16 deep dive →
bias = x̄ − reference
t = bias/(s/√n)
  • reference 可追溯的基准值 traceable reference value
  • t 检验偏倚是否显著非 0 的统计量 test statistic for whether bias differs materially from 0
何时用： Use it when: 检查量具平均读数相对已知基准是否存在系统偏移。 You need to test whether the gauge reads systematically high or low against a known reference.
T3

进阶 · 量程、时间与属性一致性 Advanced · Range, Time, and Attribute Agreement

3 张进阶卡 3 advanced cards
T3-9

线性 Linearity Linearity

F22 深潜 → F22 deep dive →
bias = a + b×reference
  • b 偏倚随基准值变化的斜率 slope of bias against the reference value
  • b ≠ 0 斜率显著非 0，表示线性不合格 a significant nonzero slope indicates failed linearity
何时用： Use it when: 用多个水平的基准件检查量具偏倚是否随量程改变。 You need to know whether gauge bias changes across the measurement range.
T3-10

稳定性 Stability Stability

F31 深潜 → F31 deep dive → F33 深潜 → F33 deep dive →
same reference over time → X̄-R / I-MR → drift signal
  • X̄-R 每个时间点有重复测量时监控 monitoring when replicated readings are available at each time point
  • I-MR 每个时间点只有单次测量时监控 monitoring when only one reading is available at each time point
何时用： Use it when: 对同一标准件做长期测量，并用控制图识别量具漂移。 You need long-term readings of one reference standard monitored for gauge drift.
T3-11

属性一致性 Kappa Attribute Agreement Kappa

F44 深潜 → F44 deep dive →
κ = (po − pe)/(1 − pe)
κ≥0.75 good  ·  κ<0.40 poor
  • po 观察到的一致率 observed agreement
  • pe 随机机会下的期望一致率 agreement expected by chance
何时用： Use it when: 评价属性判定超出随机机会的一致性；κ≥0.75 好，κ<0.40 差。 You need chance-corrected agreement for attribute decisions; κ≥0.75 is good and κ<0.40 is poor.
相关教学页 Related teaching pages
57 · 量具 GR&R 57 · Gauge R&R 58 · Kappa 属性 MSA 58 · Kappa attribute MSA
其他公式总表 Other formula sheets
FH01 流程能力 FH01 Capability FH02 假设检验 FH02 Hypothesis Testing FH03 方差分析 FH03 ANOVA FH04 回归 FH04 Regression FH05 DOE FH06 SPC FH07 MSA

MSA 测量系统分析公式总表