故事 · 把尺子翻译成"看得见几档"
Origin Story · Turning the Gauge Into "How Many Categories Can You See"
%GRR 是个比例,工程师看了知道好坏,却不容易想象它意味着什么。于是 AIAG 又给出一个更"画面感"的指标 —— ndc(number of distinct categories):
把整个过程的散布,按测量系统能分辨的最小台阶切成格子,能切出几格,就是 ndc。
它的公式 ndc = 1.41 × (σ过程 / σGRR) 几乎就是信噪比 —— 过程信号是测量噪声的几倍,再乘上 √2 的几何修正。
如果 ndc = 1,整段过程在尺子眼里只是"一坨",连"高 / 低"都分不出;ndc = 2 只够分"两堆";只有 ndc ≥ 5,你才能看出趋势、设控制限、追改进。
这就是为什么它和 %GRR 总是成对出现:同一个测量系统的两种说法。
%Study Variance is a ratio — engineers can tell good from bad, but it is hard to picture what the number actually means. So AIAG gave us a more visual companion: the Number of Distinct Categories (NDC).
Take the full spread of the process and chop it into bins, each one width of the smallest step the measurement system can resolve — how many bins fit is your NDC.
The formula NDC = 1.41 × (σpart / σGRR) is essentially a signal-to-noise ratio: how many times bigger is the process signal than the measurement noise, multiplied by the √2 geometric correction.
NDC = 1 means the entire process looks like a single blob to the gauge — you cannot even split "high" from "low". NDC = 2 only gives you two heaps. Only when NDC ≥ 5 can you see trends, set control limits, and track real improvement.
That is why NDC and %Study Variance always travel together — they are two ways of telling the same measurement-system story.
1 把过程范围切成格子:能分几档? Slice the Process Range Into Bins — How Many Categories Do You Get?
ndc 0蓝色横条是过程的真实范围,每个格子宽 = 测量系统能分辨的最小台阶。格子越多(ndc 越大),尺子越能看清细节;ndc < 5 时格子太粗,整段被涂红 —— 这种尺子做不了过程控制。 The blue bar is the true process range; each cell is one resolution step of the measurement system. More cells (larger NDC) means the ruler sees finer detail. When NDC < 5 the cells are too coarse and the whole bar turns red — that gauge cannot drive process control.
2 信噪比越高,能分的档次越多 Higher Signal-to-Noise, More Categories Resolved
横轴是信噪比 σ过程/σGRR,纵轴是 ndc(=1.41×比值)。绿区 ndc≥5合格、红区 ndc<5不合格。当前位置的小球随你拖滑块移动 —— 越往右上,尺子越精细。 The x-axis is the SNR σpart/σGRR, the y-axis is NDC (= 1.41 × ratio). Green zone NDC ≥ 5 passes, red zone NDC < 5 fails. The dot tracks your slider live — the further up and to the right it sits, the finer the gauge.
3 现实里的 ndc NDC in the Real World
ndc ≥ 5:AIAG 标准。低于 5 说明测量分辨力不足,控制图上的点动了你也判不准。
NDC ≥ 5: the AIAG threshold. Anything below means resolution is too weak — even when points move on the control chart you cannot judge whether the shift is real.
与 %GRR 互通:ndc 小 ⟺ %GRR 大,二者描述同一件事;报告里通常一起给。
Locked to %Study Variance: small NDC ⟺ large %GRR — they describe the same reality, and any MSA report should report both together.
测量分辨力:仪表读数刻度(分辨力)太粗也会拖低 ndc,不止是抖动问题。
Display resolution counts too: a coarse instrument scale (limited discrimination) pulls NDC down even if repeatability looks fine — it isn't only about jitter.
过程控制前提:ndc 不够,SPC 与过程能力分析的结论都站不住脚,得先修尺子。
Prerequisite for process control: with NDC too low, neither SPC nor capability analysis is defensible — repair the gauge before drawing any process conclusion.
一句话In One Line
ndc 把抽象的测量误差翻译成一句大白话:我这把尺子,在整个过程范围里能分出几格。
它的核心是信噪比 —— 过程的真实散布(信号)是测量误差(噪声)的几倍。倍数越高,能切的格子越细,趋势越看得清。
系数 1.41(√2)来自把"零件分布"和"测量分布"的几何关系折算成可分辨档数。
它和 %GRR 是同一现实的两种语言:%GRR 说"误差占多少比例",ndc 说"还剩多少分辨力"。
记住一句话:ndc < 5 的尺子,连过程是好是坏都分不清,谈何改进。
NDC turns abstract measurement error into one plain sentence: how many bins can my ruler split the process into.
At its core sits the signal-to-noise ratio — how many times bigger the true part spread (signal) is than the measurement error (noise). The larger that ratio, the finer the bins, the clearer the trend.
The constant 1.41 (√2) falls out of converting the geometric relationship between part distribution and measurement distribution into a count of distinguishable categories.
NDC and %Study Variance are two languages for one truth: %GRR reports "what fraction is error", NDC reports "how much resolution is left".
Remember the rule: a ruler with NDC < 5 cannot even tell whether the process is good or bad — improvement is out of the question.
常见误用Common Mistakes
ndc 用四舍五入。ndc 必须向下取整(truncate),4.9 也只能算 4 档,不能凑成 5。
Rounding NDC to the nearest integer. NDC must be truncated (floored) — 4.9 is four categories, never five. No rounding up to slip past the gate.
只看 %GRR 忽略 ndc。当过程变异本身很小时,%GRR 可能合格但 ndc 仍不足,两个都要看。
Watching %GRR and ignoring NDC. When part-to-part variation is small to begin with, %GRR can look fine while NDC still fails — always report both.
把 ndc 当过程能力。ndc 只评测量系统的分辨力,跟产品是否满足规格(Cpk)是两回事。
Mistaking NDC for process capability. NDC scores only the gauge's resolution; whether the product meets its specification (Cpk) is a completely separate question.