起源故事 · QS-9000 引入"客户视角"
Origin Story · QS-9000 Brings in the "Customer's View"
1989 年，福特、克莱斯勒、通用汽车联手发布 QS-9000 供应商质量体系，第一次把 Pp/Ppk 写进强制条款。
他们发现：用 R̄/d2 算的 σ_within 总是偏小，供应商拿着 Cpk=1.5 的报告交货，客户端却屡屡发生超规。
差别在于 "组间漂移" —— 换班、换料、换温度时整个分布慢慢平移，组内瞬时 σ 看不出来。
于是引入 σ_overall：把所有数据点合并，用 √[Σ(xᵢ−x̄̄)²/(N−1)] 直接算，同时吸收 σ_within 与 σ_between。
这就是今天 AIAG SPC 手册第 1 章里"短期 vs 长期能力"的源头。
In 1989 Ford, Chrysler, and General Motors jointly released the QS-9000 supplier quality system —
the first standard to write Pp/Ppk into the mandatory clauses.
They had noticed that σ_within from R̄/d2 was systematically too small: suppliers were shipping with Cpk = 1.5 reports while the customer kept seeing out-of-spec parts.
The missing piece was "between-subgroup drift" — every shift change, raw-material lot, or temperature swing nudged the whole distribution sideways,
which the within-subgroup σ simply could not see.
So they introduced σ_overall: pool every raw data point and compute √[Σ(xᵢ − x̄̄)² / (N − 1)] directly, capturing both σ_within and σ_between in one shot.
That's the origin of the "short-term vs long-term capability" split in chapter 1 of today's AIAG SPC manual.
1 组间漂移如何"膨胀" σ_overall How Between-subgroup Drift "Inflates" σ_overall
σ_overall ≈ σ_within2 方差相加，标准差走斜边 Variances Add — Standard Deviation Travels Along the Hypotenuse
σ_within² + σ_between² = σ_overall²，正好是直角三角形勾股定理。 两条直角边是独立的方差分量，斜边就是合并后的总标准差 —— 这就是"平方加和再开方"的几何意义。 σ_within² + σ_between² = σ_overall² — literally the Pythagorean theorem in a right triangle. The two legs are independent variance components; the hypotenuse is the pooled total standard deviation. That's the geometric meaning of "square, add, take the root."
3 现实里的 σ_overall σ_overall in the Real World
试生产 30 件：σ_within=0.5，σ_overall=0.55 → 比值 1.1，过程很稳，PPAP 通过有把握。
30-piece pilot run: σ_within = 0.5, σ_overall = 0.55 → ratio 1.1. Process is rock-steady, PPAP approval looks safe.
量产 1 个月：σ_within=0.5，σ_overall=1.2 → 比值 2.4，组间漂移严重，去查换班/换料/温控。
One month into production: σ_within = 0.5, σ_overall = 1.2 → ratio 2.4. Heavy between-subgroup drift — go investigate shift changes, lot changes, and temperature control.
Minitab Capability：默认同时输出 Within 与 Overall 两组指标，差距大就该警觉。
Minitab Capability: outputs Within and Overall metrics side by side by default — a wide gap is a red flag.
AIAG SPC 手册：第 1 章定义 short-term capability(Cp/Cpk) vs long-term performance(Pp/Ppk)，分母就是这两个 σ。
AIAG SPC Manual: chapter 1 defines short-term capability (Cp/Cpk) vs long-term performance (Pp/Ppk), with these two σ values as the respective denominators.
一句话In One Line
σ_within 是"现在这一秒的瞬时波动"，σ_overall 是"一年下来的长期波动"。
两者比值 = 过程稳定性的体温计：
比值 ≈ 1 → 过程很稳，组间没漂；比值 > 1.5 → 有显著漂移，必须用 SPC 控制图把异常因揪出来。
Cp/Cpk 用 σ_within，Pp/Ppk 用 σ_overall —— 同一份数据算出两套指标，差距越大，客户感受越糟。
σ_within is "the jitter happening right this second"; σ_overall is "the spread you'd see across a whole year."
The ratio between them is your stability thermometer:
ratio ≈ 1 → process is steady, no between-subgroup drift; ratio > 1.5 → meaningful drift, time to pull out the SPC control chart and chase the special causes.
Cp/Cpk uses σ_within, Pp/Ppk uses σ_overall — one dataset, two scorecards. The wider the gap, the worse the customer's actual experience.
常见误用Common Mistakes
把每个子组的 σ 直接算平均当 σ_overall。必须把所有原始点合并再算 √[Σ(xᵢ−x̄̄)²/(N−1)]，否则会丢掉组间漂移信息。
Averaging each subgroup's σ and calling that σ_overall. You must pool every raw point and compute √[Σ(xᵢ − x̄̄)² / (N − 1)] — averaging σ's throws away the between-subgroup drift signal.
σ_overall = σ_within + σ_between（直接相加）。必须平方相加再开方（正交分解）：σ_overall = √(σ_within² + σ_between²)。
σ_overall = σ_within + σ_between (simple addition). Square, add, then take the root (orthogonal decomposition): σ_overall = √(σ_within² + σ_between²).
30 个点就报 σ_overall。至少 100+ 数据，跨多班次/多天/多批次，才能真正捕捉到长期漂移。
Reporting σ_overall from only 30 data points. You need 100+ points spanning multiple shifts, days, and lots to actually capture long-term drift.