起源故事 · 福特 Q1 与汽车业门槛
Origin Story · Ford Q1 and the Auto Industry Gate
1986 年,福特汽车启动 Q1 供应商评级,把 Cpk ≥ 1.33 写进了零部件验收门槛。从那一年起,Cpk 不再只是统计学家的玩具,
而是汽车业的通用语言 —— 它弥补了 Cp 的盲点:同一个 Cp=2.0,可以是中心精准的好过程,也可以是严重偏心的废品厂。
Cpk 用 min 这个数学小动作,把偏心的代价一刀显化出来。今天你在 IATF 16949 / PPAP 文件里看到的所有 Cpk 数字,源头都在福特这一笔。
In 1986 Ford launched its Q1 supplier program and wrote Cpk ≥ 1.33 into the part-acceptance gate. From that year on, Cpk stopped being a statistician's toy
and became the auto industry's common language — patching Cp's blind spot: the same Cp = 2.0 can be a precisely centered hero process or a badly offset scrap line.
With the small mathematical move of min, Cpk puts the cost of offset on the table in one shot. Every Cpk number you see in an IATF 16949 / PPAP file today traces back to that Ford signature.
1 三步看清 Cpk:钟形 → 双臂 → 取短 Three Looks at Cpk: Bell → Two Arms → Take the Shorter
中心居中centered2 Cp 与 Cpk 的差距:偏心代价体温计 Cp vs. Cpk: The Offset-Cost Thermometer
灰色是 Cp(潜力天花板),红色是 Cpk(今天实际能力)。差距大 → 调中心便宜;差距小但都低 → 必须降 σ。 Grey is Cp (your potential ceiling), red is Cpk (what you actually deliver). Big gap → recenter μ, it's cheap. Small gap but both low → you have to shrink σ.
3 现实里的 Cpk Cpk in the Real World
注塑壁厚:USL/LSL=2.05/1.95,μ=1.96,σ=0.015 → Cp≈1.11 但 Cpk≈0.22,偏心毁了一切。调模温把中心拉回 2.00 就能救活。
Injection-molded wall thickness: USL / LSL = 2.05 / 1.95 mm, μ = 1.96 mm, σ = 0.015 mm → Cp ≈ 1.11, but Cpk ≈ 0.22. Offset wrecks everything — bump mold temp to drag the center back to 2.00 and the process is rescued.
CNC 孔径:μ 正中规格,σ 小 → Cp=Cpk=1.67,关键件优秀级。这是 Cpk 该有的样子。
CNC bore diameter: μ dead center, tight σ → Cp = Cpk = 1.67, critical-part excellent. This is what Cpk looks like when everything's right.
包装净含量:只允许多不允许少,单边 LSL 规格,Cpk 退化为 (μ−LSL)/3σ。法规罚款就盯着这个数。
Package net weight: must be at least the labeled amount, never less — single-sided LSL, so Cpk collapses to (μ − LSL) / 3 σ. This is the number regulators fine you on.
烘焙温度:温控偏低 5°C,即使精度极高,Cpk 也低 —— 因为 Cpk 的短板是离最近规格的距离,精度救不了系统性偏移。
Baking temperature: oven running 5 °C cold — even razor-thin σ can't lift Cpk, because the short side is distance to the nearest spec, and precision doesn't undo a systematic offset.
一句话In One Line
Cp 给你"潜力天花板",Cpk 告诉你"今天实际过到什么程度"。Cp 1.67 + Cpk 0.5 =
设备很好但操作员把刀具装偏了。改进路线很清楚:先看 Cp/Cpk 差距大不大 —— 差距大 → 调 μ(SOP / 夹具 / 对刀,便宜);差距小但都低 → 投资降 σ(换设备 / 改材料,贵)。
Cpk 永远 ≤ Cp,相等的那一刻就是过程完美居中的瞬间。
Cp gives you the "potential ceiling"; Cpk tells you "what you actually delivered today". Cp 1.67 + Cpk 0.5 =
great machine, operator mounted the tool off-center. The roadmap is clean: check the gap — wide gap → adjust μ (SOP, fixturing, tool offset — cheap); narrow gap but both low → spend money on σ (new equipment, better material — expensive).
Cpk is always ≤ Cp; the moment they tie is the moment the process is perfectly centered.
常见误用Common Mistakes
Cpk 算成 |USL−LSL|/(6σ)。那是 Cp;Cpk 一定带 μ,必须分别算左右距再取 min。
Calculating Cpk as |USL − LSL| / (6 σ). That's Cp. Cpk must include μ — compute left and right distances separately, then take the min.
Cpk = (USL−μ)/3σ 单边公式照搬给双边规格。双边规格必须 min(左距,右距);单边规格才退化为单侧。
Using the single-sided formula (USL − μ) / 3 σ when the spec is two-sided. Two-sided specs need min(left, right). Only a truly single-sided spec collapses to the one-side form.
Cpk > 1 就 OK 交付。行业默认 1.33;关键件 1.67;安全 / 医疗 2.0。1.0 意味着规格刚好压在 ±3σ,PPM 约 2700,量产必出问题。
"Cpk > 1 — ship it." Industry baseline is 1.33; critical parts 1.67; safety / medical 2.0. Cpk = 1.0 means the spec sits exactly on ±3 σ — about 2 700 ppm — and volume production is guaranteed to bite.