MSA 测量系统分析

两个概念

• 分辨力（Discrimination / Resolution）：量具能检出的最小变化量，通常就是最小读数（如 0.01 mm）。
• 数据分级数 NDC：NDC = 1.41 × PV / GRR，表示测量系统能把过程变差有效分成多少个可区分的类别。

判定

本模块的两种用法

1. 读取 GR&R 结果（默认）：选择「GR&R 交叉型」或「GR&R 嵌套型」作为数据来源，程序直接取 PV 与 GRR 计算 NDC，并把该研究的原始数据画成直方图检查取值台阶数。
2. 独立分辨力检查：手动输入量具分辨率与变差跨度（公差或 6σ），程序做 10:1 规则检查并给出建议分辨率。

分辨力不足对结论的影响

提高 NDC 的两条路

• 降低量具变差 GR&R：改进重复性与再现性（见 GR&R 章节）。
• 扩大取样范围：使零件覆盖真实过程变差以提高 PV（此项最常被忽略）。
• 若两项措施均已实施而 NDC 仍 < 5，表明量具分辨率本身不足，需更换量具。

Two concepts

• Discrimination (resolution): the smallest change the gage can detect, usually the smallest increment (e.g. 0.01 mm).
• Number of distinct categories (NDC): NDC = 1.41 × PV / GRR, the number of distinguishable categories the system can resolve within the process variation.

Acceptance

Two ways to use this study

1. From a GR&R result (default): choose the crossed or nested GR&R as the source; the program takes PV and GRR, computes NDC and plots the raw readings to check how many distinct steps the data actually contain.
2. Standalone resolution check: enter the gage resolution and the variation span (tolerance or 6σ) and the program applies the 10:1 rule and recommends a resolution.

Why insufficient NDC is misleading

Two ways to raise NDC

• Reduce gage variation GRR: improve repeatability and reproducibility (see the GR&R sections).
• Widen the sampling range so that parts span the true process variation and PV increases; this is the option most often overlooked.
• If NDC remains below 5 after both measures, the gage resolution itself is inadequate and the gage should be changed.

稳定性是什么

稳定性描述测量系统随时间保持统计受控的能力，即同一零件在不同时间的测量结果是否一致。漂移、磨损、老化与温漂均会破坏稳定性。

标准做法

1. 选 1 个零件或标准件（建议有已知参考值，可同时进行偏倚检验）。
2. 按固定时间间隔（每班、每天、每周……）抽取子组，n ≥ 20 组（AIAG 第4版原文：g ≥ 20 个子组，示例为 20 组 × 5 次 = 100 个读数；20 个子组是 AIAG 规定的最低要求，实务中常取更多）。
3. 每组测 m = 3~5 次（本程序默认 20 组 × 5 次）。
4. 程序绘制 Xbar-R 控制图，并做漂移回归与偏倚 t 检验。

控制限

A₂、D₃、D₄ 按子组大小 m 取自标准 SPC 常数表（m = 2~10）。

判异规则（程序内置）

第一原则——先看极差图：极差图代表重复性；若极差图失控，均值图的控制限本身即不可靠，此时均值图的任何信号都不得采信。

• 点超出控制限（3σ）；
• 连续 9 点位于中心线同侧（阶跃偏移；本程序采用 Nelson 判异规则，若组织采用更严的西方电气规则——连续 8 点同侧——或 7 点判据，请在图上人工复核）；
• 连续 6 点持续上升或下降（渐变趋势）；
• 时间回归斜率 t 检验显著（漂移）；
• 填写参考值时，偏倚 t 检验显著。

图形判读

• ① 均值图：核查是否出界，有无连续同侧（阶跃）、连续升降（渐变）或周期性（温湿度、换班）。
• ② 极差图：核查重复性是否随时间恶化（极差变宽表示量具劣化）。
• ③ 趋势图：拟合直线的斜率为漂移速率；斜率显著表明量具正在缓慢变化，可据此缩短校准周期或进行定期修正。

判定与改进

无任何判异信号时判定为 稳定（受控）；任一信号出现即判定为 不稳定，应查明特殊原因（校准记录、维修、换人、环境变化、标准件损坏），消除后重新收集数据复评。若存在显著漂移，宜按漂移速率设定校准周期。

What stability is

Stability describes whether the system remains in statistical control over time: the same part should give the same result when measured today and several months later. Drift, wear, ageing and thermal effects all degrade stability.

Standard procedure

1. Pick one part or master (preferably with a known reference so a bias test runs alongside).
2. At fixed intervals (per shift, daily, weekly...) collect n ≥ 20 subgroups (AIAG 4th ed.: g ≥ 20 subgroups; its example is 20 × 5 = 100 readings — 20 subgroups is the AIAG minimum, more are common in practice).
3. Measure m = 3-5 times per subgroup (the default here is 20 × 5).
4. The program draws Xbar-R charts and runs the drift regression and bias t-test.

Control limits

A2, D3 and D4 are the standard SPC constants for subgroup size m (m = 2-10).

Out-of-control rules applied

First principle — read the R chart first: it represents repeatability; if the R chart is out of control the Xbar limits are themselves unreliable and no signal on the Xbar chart may be relied upon.

• Point beyond the control limits (3 sigma);
• 9 points in a row on one side of the centre line (step shift; this program applies the Nelson rules — if your organisation uses the stricter Western Electric rule of 8 in a row, or 7, verify those cases by eye);
• 6 points in a row steadily increasing or decreasing (trend);
• Time-regression slope significant (drift);
• With a reference entered, bias t-test significant.

Reading the charts

• 1. Xbar chart: out-of-control points, runs on one side (step change), runs up or down (gradual change), cycles (temperature, humidity, shift).
• 2. R chart: whether repeatability degrades over time (a widening R indicates gage deterioration).
• 3. Trend chart: the fitted line gives the drift rate. A significant slope indicates slow change; use it to shorten the calibration interval or schedule periodic correction.

Verdict and improvement

No signal: stable (in control). Any signal: unstable; identify the special cause (calibration record, repair, operator change, environment, damaged master), eliminate it and re-collect the data. Where drift is significant, set the calibration interval from the drift rate.

偏倚是什么

偏倚 = 观测平均值 − 真值（参考值）。它描述测量系统的准确度。偏倚可能来自量具零点错误、测头磨损、标准件误差、测量力、温度、照明视差等。

标准做法（独立样本法）

1. 取 1 个零件或标准件。
2. 用更高等级的量具/计量室测其参考值 X_ref。
3. 由一名操作者，用正常方式，重复测量 n ≥ 10 次（AIAG 偏倚研究对 1 个零件重复测量次数，通常取10或15）。
4. 程序计算偏倚、标准误、t 值与置信区间。

计算

判定

• 0 落在置信区间内（|t| ≤ 临界值）：不能拒绝“偏倚 = 0”的原假设，判定为偏倚不显著、可接受（注意：不显著不等于偏倚确实为 0，只表示没有足够证据证明存在显著偏倚）。
• 0 不在区间内：偏倚显著，不可接受，应校准、修正或维修后重新评价。
• %Bias 是辅助指标，实务上常以 ≤ 10% 为参考（AIAG 未给硬性阈值）。

图形判读

• ① 单值图：点应在均值线两侧随机波动，不应有趋势或周期；存在趋势表明温漂或磨损，此时偏倚并非常数，应先进行稳定性研究。
• ② 偏倚置信区间：区间跨过 0 线表示不显著；完全位于 0 线一侧表示显著。
• ③ 直方图：应近似对称且为单峰；明显双峰提示装夹或读数方式不一致。（直方图是 AIAG 偏倚分析「控制图法」规定的图形步骤之一：子组容量 m ≥ 2 时相对参考值绘制，用于识别特殊原因与异常。）

常见误区

• 仅测量 3～5 次即下结论：样本量过小，置信区间过宽，既无法判定显著，也无法判定不显著。
• 参考值本身不准确：参考值应由更高等级、可溯源的标准或计量室确定，其不确定度应显著小于被测测量系统自身的重复性（计量领域常按不确定度比 TUR ≥ 4:1～10:1 选取，属计量惯例，并非 AIAG MSA 的规定）。
• 误认为偏倚合格即全部合格：偏倚仅评价单个测量点；整个量程应由线性研究评价。

What bias is

Bias = observed average − true value (reference). It describes the accuracy of the system. Sources include a wrong zero point, probe wear, master error, measuring force, temperature and parallax.

Standard procedure (independent sample method)

1. Take one part or master.
2. Determine its reference value Xref with a higher-order gage or metrology lab.
3. Have one operator measure it n ≥ 10 times in the normal manner (the AIAG bias study repeats one part; its example uses 15 readings — the default here is 15).
4. The program computes bias, standard error, the t value and the confidence interval.

Calculation

Acceptance

• 0 inside the CI (|t| ≤ critical): the null hypothesis "bias = 0" cannot be rejected, so the bias is judged not significant and acceptable (not significant does not prove the bias is exactly zero — only that there is insufficient evidence of a significant bias).
• 0 outside the CI: the bias is significant and not acceptable; recalibrate, apply a correction or repair, then re-evaluate.
• %Bias is an auxiliary metric; ≤ 10% is a common practical reference (AIAG gives no hard threshold).

Reading the charts

• 1. Run chart: points should scatter randomly about the mean with no trend or cycle. A trend indicates thermal drift or wear; bias is then not a constant and a stability study should precede the bias study.
• 2. Bias confidence interval: if the interval crosses 0 the bias is not significant; if it lies entirely on one side it is significant.
• 3. Histogram: should be approximately symmetric and unimodal; a clear double peak suggests inconsistent fixturing or reading. (The histogram is one of the graphical steps prescribed by the AIAG bias analysis "control chart method": with subgroup size m ≥ 2 it is drawn against the reference value to detect special causes.)

Common mistakes

• Concluding from 3-5 repeats: with n this small the confidence interval is so wide that no conclusion can be drawn.
• An inaccurate reference: the reference must come from a higher-order, traceable standard or metrology lab, with an uncertainty clearly smaller than the repeatability of the system under study (metrology practice often uses a test uncertainty ratio of 4:1 to 10:1 — a metrological convention, not an AIAG MSA requirement).
• Assuming that an acceptable bias implies an acceptable system: bias evaluates a single point; the whole range is covered by linearity.

线性是什么

线性描述偏倚在整个工作量程上的变化。理想情况下，量具在各测量点的偏倚都应接近 0；若偏倚随尺寸增大而系统性增大或减小，则为线性不良。

标准做法

1. 选 g ≥ 5 个零件，其参考值均匀覆盖量具的工作量程（不应集中于中间）。
2. 用更高等级量具确定每个零件的参考值 X_ref,i。
3. 由一名操作者对每个零件随机顺序重复测量 m ≥ 10 次。
4. 程序计算各点偏倚，做最小二乘回归并给出置信带。

计算

判定

• 主判据：若“偏倚 = 0”的水平线整个落在回归线的置信带内，则线性可接受；否则不可接受。（置信带 = 回归线的 95% 置信区间，即拟合值 ± t·s·√(1/g + (xᵢ−x̄)²/Sxx)，不是回归线本身。）
• 量化参考：%Linearity < 5% 为优；5%～10% 为边缘；> 10% 为不良。
• 各点偏倚 t 检验显著的测量点，需要优先处理。

图形判读

• ① 偏倚 vs 参考值：点应贴近 0 线，拟合线应平缓；置信带应包含 0 线。
• ② 各水平偏倚柱：核查偏倚随量程的走向。递增或递减表明存在斜率；U 形或倒 U 形通常表示非线性（线性模型可能不适用，应查看残差）。
• ③ 残差图：残差应随机散布于 0 线两侧；若呈现明显弯曲（如先正、后负、再正），表明存在非线性项，仅做单点线性修正不足。

改进

• 整机多点校准（而非仅校准单点）；
• 建立线性修正曲线 / 查找表，由量具或软件自动补偿；
• 更换磨损测头、导轨、传感器；
• 控制温度（热膨胀是线性误差的常见来源）；
• 缩小实际使用量程，只在该区间内保证精度。

What linearity is

Linearity describes how bias changes across the operating range. Ideally the bias is close to zero at every point; if it increases or decreases systematically with size, linearity is inadequate.

Standard procedure

1. Select g ≥ 5 parts whose reference values evenly span the operating range (do not cluster them in the middle).
2. Determine each reference value Xref,i with a higher-order gage.
3. Have one operator measure each part m ≥ 10 times in random order (the AIAG linearity example is 5 parts × 12 readings; the default here is 12).
4. The program computes the bias at each level, fits OLS regression and draws the confidence band.

Calculation

Acceptance

• Main criterion: if the "bias = 0" line lies entirely within the confidence band, linearity is acceptable; otherwise not. (The confidence band is the 95% confidence interval of the regression line, i.e. fitted value ± t·s·√(1/g + (xᵢ−x̄)²/Sxx) — not the regression line itself.)
• Quantitative reference: %Linearity < 5% good; 5%-10% marginal; > 10% poor.
• Any level whose bias t-test is significant needs attention first.

Reading the charts

• 1. Bias vs reference: points should lie close to the 0 line and the fitted line should be flat; the band should contain the 0 line.
• 2. Bias by level: examine the pattern; a rising or falling trend indicates a slope, and a U or inverted-U shape usually indicates non-linearity (check the residuals).
• 3. Residuals: should scatter randomly about 0. A clear curve (positive, negative, positive) indicates a non-linear term; a single linear correction is then insufficient.

Improvement

• Multi-point calibration of the whole gage instead of a single point;
• Build a correction curve or lookup table applied automatically;
• Replace worn probes, guides or sensors;
• Control temperature; thermal expansion is a common source of linearity error;
• Narrow the range actually used and guarantee accuracy only within it.

什么时候用

当每个零件均可由每位操作者重复测量时，采用交叉型设计。这是使用最广泛的 GR&R 方案，也是客户审核中最常被要求的项目。

标准做法

指标含义与公式

判定

六合一图逐图详解