起源故事 · 福特 Q1/QS-9000 把数字翻成行话
Origin Story · Ford Q1 / QS-9000 Turned Numbers Into Industry Slang
1980 年代,福特 Q1 计划和后来的 QS-9000 把 Cpk 1.33 定为关键件门槛、Cpk 1.67 为安全件门槛,
行业很快约定了一张"Cpk → ppm"速查表。这张表是质量经理和管理层沟通的通用语言——
Cpk 1.0 听起来不错,翻成 2700 ppm 立刻明白为什么客户不收。算法很简单:
双侧居中时 ppm = 2 × (1 − Φ(3 × Cpk)) × 1e6。一个数字,把"过程窄到什么程度"翻译成"每百万件出几个废品",
再乘以单价、保修成本、品牌损失,就是能写进财务模型的钱。
In the 1980s, Ford's Q1 supplier program — followed by QS-9000 — locked Cpk 1.33 as the threshold for critical features and Cpk 1.67 for safety features.
The industry quickly memorized a "Cpk → ppm" lookup that became the shared language between quality engineers and management.
Cpk 1.0 sounds fine — until it translates into 2700 ppm and you see why the customer refuses the lot. The math is simple:
for a centered, two-sided spec, ppm = 2 × (1 − Φ(3 × Cpk)) × 1e6. One number converts "how lean is the process"
into "how many rejects per million", and once you multiply by unit price, warranty cost and brand damage,
you get a figure that belongs in the finance model.
1 Cpk → ppm 对数悬崖 Cpk → ppm: The Log-Scale Cliff
2 行业速查表 · 双面打印贴墙上 Industry Lookup · Print It and Pin It to the Wall
| Cpk | 双侧 ppmtwo-sided ppm | 良率 %yield % | Sigma Level | 行业类比industry analogue |
|---|
3 这些 ppm 在哪里出现 Where These ppm Numbers Show Up
汽车安全气囊点火器:要求 Cpk ≥ 1.67,即 0.57 ppm。千万件出货 5.7 次失误,这就是"安全件"标准。
Airbag igniter: spec is Cpk ≥ 1.67, i.e. 0.57 ppm. About 5.7 misfires per 10 million units — that's the "safety feature" bar.
普通螺栓:Cpk 1.33 就 OK(63 ppm)。乘以单价 0.05 元,每百万件赔 3 元,可接受。
Generic bolts: Cpk 1.33 is fine (63 ppm). At $0.01 a piece, you eat $0.63 of scrap per million — acceptable.
半导体光刻:Cpk 2.0+(0.002 ppm)。一片晶圆 200 美元,缺陷一次损失 5 万,必须六西格玛。
Semiconductor lithography: Cpk 2.0+ (0.002 ppm). A wafer is $200 and one defect cascades into $50k of lost dies — Six Sigma is mandatory.
服务业:Cpk 0.67 还能活——餐厅平均 ~67000 ppm 抱怨率,行业接受。说明 ppm 标准强烈行业相关。
Service industry: Cpk 0.67 still runs a business — restaurants average ~67,000 ppm complaint rate, and the industry tolerates it. Acceptable ppm is deeply industry-specific.
一句话In One Line
Cpk 表是"质量语言换钱语言"的字典。
客户经理看 Cpk 1.33 没感觉,看到 63 ppm 立刻能算赔偿;管理层看 Cpk 1.67 → 2.0 觉得"只多一点",
看到 ppm 从 0.57 → 0.002 才知道差了 285 倍。
速查表的存在,就是为了让数字直观——但记住:这张表的所有数字都假设过程居中(Cp = Cpk)。
一旦 μ 偏离 M(上一页的居中度 k > 0),实际 ppm 要按 Z_USL 和 Z_LSL 分别算,这张表只给你一个最优情况的下限。
This table is the dictionary that translates quality talk into money talk.
A buyer feels nothing at Cpk 1.33, but 63 ppm tells them what warranty reserve to book. Execs see Cpk 1.67 → 2.0
and think "just a nudge" — until ppm drops from 0.57 → 0.002, a 285× gap.
The lookup exists to make numbers feel real — but remember: every entry here assumes a centered process (Cp = Cpk).
Once μ drifts off the midpoint (k > 0, see the previous page), real ppm must be computed from Z_USL and Z_LSL separately,
and this table only gives you the best-case floor.
常见误用Common Mistakes
Cpk 表偏心也直接套。这张表假设居中(Cp = Cpk)。偏心时(k > 0)必须分别算 Z_USL = (USL−μ)/σ 与 Z_LSL = (μ−LSL)/σ,各侧 ppm 单独求,再相加。
Applying this table to an off-center process. The lookup assumes Cp = Cpk. When k > 0, compute Z_USL = (USL − μ)/σ and Z_LSL = (μ − LSL)/σ separately, find the ppm of each tail, then sum them.
到 Cpk 1.33 就够了,所有行业都行。行业基准不同:汽车关键件 1.67,医药 2.0,航空安全件 2.0+。1.33 是历史 QS-9000 的最低线,不是天花板。
Believing Cpk 1.33 is universally good enough. Benchmarks differ: 1.67 for automotive critical features, 2.0 for pharma, 2.0+ for aerospace safety items. 1.33 is the historical QS-9000 floor, not a ceiling.
把 ppm 直接换算成销售损失。ppm 只是起点。还要乘以产品单价、保修成本、召回连带损失、品牌折损——一颗气囊点火器 ppm 0.57 看着小,出一次事赔上千万。
Converting ppm straight into lost revenue. ppm is only the starting point. Multiply by unit price, warranty cost, recall exposure and brand damage — an airbag igniter at 0.57 ppm looks tiny, but a single field event can cost tens of millions.