起源故事 · 一把丈量过程的通用尺子 Origin Story · A Common Ruler for Any Process
二十世纪中后期,全球制造业被一个难题困扰:怎么用一个数字说清"这个过程到底行不行"?日本企业率先把过程波动与规格范围之比提炼成指数, 后来福特等美国巨头在供应商管理里大力推行,Cp 与 Cpk 由此成为采购、质量、工程之间的通用语言。 从此"你的 Cpk 多少"就像问"身高多少"一样直接 —— Cpk≥1.33 几乎成了进入大厂供应链的隐形门槛。 Through the mid-to-late 20th century, manufacturers everywhere wrestled with the same question: how do you summarize "is this process any good?" in a single number? Japanese plants were the first to distill the answer as a ratio of process spread to spec width; Ford and other US giants then pushed it hard through supplier management, and Cp and Cpk became the common language linking purchasing, quality, and engineering. "What's your Cpk?" is now as routine as asking someone's height — and Cpk ≥ 1.33 has become the unspoken threshold for getting into a tier-one supply chain.

1 钟形曲线钻规格门,挤出门外就是缺陷 The Bell Walks Through the Gate — Whatever Spills Out Is a Defect

调一调试试drag & explore

2 Cp 是潜力,Cpk 是实绩 —— 差距来自偏移 Cp Is Potential, Cpk Is Actual — the Gap Is the Off-Center Tax

居中时 Cp = Cpk,两条一样高;一偏移,Cpk 立刻掉下来。Cp − Cpk 的缺口,就是"没站正"交的学费。 When centered, Cp = Cpk — both bars match. Drift even slightly and Cpk falls first. The Cp − Cpk gap is the tuition you pay for not standing in the middle.

3 现实里的过程能力指数 Cp / Cpk in the Real World

供应商验收:客户常要求关键特性 Cpk≥1.33(甚至 1.67),作为批量供货的准入条件。 Supplier qualification: customers routinely demand Cpk ≥ 1.33 (sometimes 1.67) on critical characteristics before opening up volume.
过程改善目标:当前 Cpk 低,先看是偏移(调中心)还是波动大(降方差),对症下药。 Improvement targeting: when Cpk is low, first diagnose whether you are off-center (recenter) or simply too noisy (reduce variance) — treat the right disease.
关键尺寸控制:轴径、孔径等配合尺寸用 Cpk 量化,避免装配卡死或松旷。 Critical dimensions: shaft and bore diameters live or die by Cpk — too tight and parts seize, too loose and the fit rattles.
SPC 前置门槛:先确认过程稳定(受控),再算能力指数才有意义 —— 失控的过程算 Cpk 没意义。 SPC prerequisite: confirm the process is in statistical control first; capability indices are only meaningful on a stable process — running Cpk on an out-of-control process is statistical theater.
一句话In One Line
Cp = 规格宽 ÷ 6σ,衡量过程理论上能不能塞进规格 —— 是"潜力"。但它默认你站在正中央。 Cpk 把均值偏移罚进去:Cpk = min[(USL−μ), (μ−LSL)] ÷ 3σ,取离最近那道门的距离,是"实绩"。 Cp 永远 ≥ Cpk;只有完美居中时两者相等。 所以提升能力有两条路:把曲线变瘦(降 σ)或把它推回中心(调 μ)。 注意 Cp/Cpk 用的是"组内短期 σ",对应的长期版本 Pp/Ppk 用整体 σ,两者之差揭示过程的长期漂移。 Cp = spec width ÷ 6σ — whether the bell can theoretically fit inside the spec, the "potential". It quietly assumes you stand in the center. Cpk pays the off-center tax: Cpk = min[(USL − μ), (μ − LSL)] ÷ 3σ, scored by the distance to the nearest spec limit — the "actual". Cp is always ≥ Cpk; they meet only when the process is perfectly centered. So there are exactly two ways up: make the bell leaner (cut σ) or push it back to center (move μ). Note: Cp / Cpk use short-term within-subgroup σ; the long-term twins Pp / Ppk use overall σ, and the gap between them exposes long-term drift.
常见误用Common Mistakes
过程没受控就算 Cpk。先用控制图确认稳定,失控过程的能力指数没有预测意义。 Calculating Cpk on an unstable process. Use a control chart to confirm statistical control first — capability on an out-of-control process predicts nothing.
只报 Cp、不报 Cpk。Cp 高 Cpk 低 = 有潜力但没居中,必须两个一起看。 Reporting Cp alone. High Cp with low Cpk means "potential exists, centering doesn't" — always report both side by side.
数据非正态硬套公式。右偏数据先做 Box-Cox 变换或用非正态能力法(见第 49 页)。 Forcing the normal-based formula on skewed data. Transform first (Box-Cox) or use a non-normal capability method (see page 49).

过程能力指数