起源故事 · 摩托罗拉的"百万分之几"
Origin Story · Motorola's "Parts Per Million"
1980 年代,摩托罗拉的工程师 Bill Smith 发现:对很多产品,根本量不出连续的尺寸,只能数"有几台坏的"。
为了让全公司用同一把尺子比较千差万别的流程,他们把不良率统一放大成每百万次机会里的缺陷数(DPMO),
再换算成 sigma 水平 —— 于是"六个西格玛"成了全公司的语言。它的潜台词是:连续也好、计数也好,最终都翻译成同一个分数,可以排队、可以对标。
In the 1980s, Motorola engineer Bill Smith noticed that for many products there is simply no continuous dimension to measure — all you can do is count how many came out bad.
To compare wildly different processes on a single ruler, the company normalised the defect rate into defects per million opportunities (DPMO),
then translated that into a sigma level — and just like that, "Six Sigma" became the lingua franca of the entire company. The hidden message: continuous data or counted data, in the end they all translate into the same score, which means they can be ranked and benchmarked side by side.
1 把一整批货摊开,数红点 Lay the whole batch out and count the red dots
计数型attribute data2 同一把尺:PPM 翻译成 Sigma One Ruler: Translating PPM into Sigma
这条标尺把"百万分之几缺陷"和"几个 σ"一一对应。3.4 PPM = 6σ(含 1.5σ 偏移),66807 PPM ≈ 3σ。差距是指数级的 —— 多一个 σ,缺陷少一个数量级。 This scale maps "defects per million" to "sigma" one-to-one. 3.4 PPM = 6σ (with the 1.5σ shift baked in); 66 807 PPM ≈ 3σ. The gap is exponential — every extra sigma drops the defect rate by an order of magnitude.
3 现实里的离散能力 Discrete Capability in the Real World
漏检与错装:装配线上"装对了没有、漏了没有"是典型计数型,用 DPMO 衡量装配能力。
Missed inspections & mis-assemblies: on the line, "right or wrong, present or missing" is textbook attribute data — DPMO is how you score assembly capability.
订单准确率:电商发错货、发漏货按"单"计数,每百万单的差错数直接对标 sigma。
Order accuracy: an e-commerce wrong-ship or short-ship is counted per order; errors per million orders map straight onto a sigma level.
一次合格率 FPY:一次做对的比例,是离散能力最常用的口径,串起来就是滚动产出率。
First Pass Yield (FPY): the share built right the first time — the most common discrete-capability metric, and stringing FPYs together gives you Rolled Throughput Yield.
服务差错率:呼叫中心答错、医院开错药,每百万次服务的差错数同样可以 sigma 化。
Service error rate: a wrong answer at a call centre or a wrong medication in a hospital — errors per million transactions can be sigma-scored the same way.
一句话
In One Line
Cpk 需要尺寸和分布,计数型数据两样都没有,于是换路:数缺陷 → 算比率 → 放大成 PPM → 翻译成 sigma。
sigma 水平的妙处在于它是通用货币 —— 把焊接、发货、问诊这些八竿子打不着的流程放到同一根标尺上排队。
但记住那个约定俗成的 1.5σ 偏移:业界统一把长期漂移加进去,于是短期算出来的 Z 再 +1.5,才得到大家挂在嘴边的"6σ = 3.4 PPM"。
Cpk wants dimensions and distributions. Attribute data has neither, so we switch lanes: count defects → compute the ratio → scale to PPM → translate to sigma.
The power of the sigma level is that it acts as a common currency — putting welding, shipping and clinical diagnosis on the same ruler so utterly unrelated processes can be ranked side by side.
And don't forget the conventional 1.5σ long-term shift: the industry adds it to absorb drift, so you take the short-term Z, add 1.5, and arrive at the famous "6σ = 3.4 PPM" everyone quotes.
常见误用
Common Mistakes
对计数型数据硬套 Cpk。没有连续尺寸就别算 Cpk,用 PPM/DPMO 与 sigma 水平。
Forcing Cpk onto attribute data. With no continuous dimension, drop Cpk entirely — use PPM/DPMO and the binomial Cpk-equivalent sigma level instead.
混淆"缺陷"和"缺陷品"。一件可有多个缺陷:DPMO 数缺陷,PPM 通常数不良品,别张冠李戴。
Confusing "defects" with "defective units". A single unit can carry several defects: DPMO counts defects, PPM usually counts defective units — don't mix them up.
只用几十件就报 sigma。罕见缺陷需要大样本,几十件算出的 PPM 抖动巨大、不可信。
Reporting a sigma level off a few dozen units. Rare defects need large samples; PPM computed from a few dozen units is hopelessly noisy and not trustworthy.