起源故事 · 田口玄一与损失函数
Origin Story · Taguchi and the Loss Function
1970 年代,日本的 田口玄一(Genichi Taguchi)反对西方"规格内 = 零损失"的二值观。
他在丰田和电装的工厂里发现:产品越靠近目标 T,装配越顺、寿命越长、客户越满意;
只要偏离 T,损失就开始累积,即使还在 USL/LSL 之间。他用一个简单的二次函数 L(x) = k(x−T)²把这件事写出来 ——
这个观念后来直接催生了 Cpm 公式,把"对靶"加进了过程能力的语言。
In the 1970s, Genichi Taguchi rejected the Western binary view of "in-spec = zero loss".
Walking the floors at Toyota and Denso, he saw it plainly: the closer a part lands to target T, the smoother it mates, the longer it lasts, the happier the customer.
Drift off T and loss starts piling up — even while you're still between USL and LSL. He wrote it as a single quadratic, L(x) = k(x − T)² —
and that one line is what produced the Cpm formula, putting "hit the target" into the language of process capability.
1 μ 是当下,T 是该去的地方 μ Is Where You Are; T Is Where You Should Be
对靶2 田口损失函数 L(x) = k(x − T)² Taguchi Loss Function L(x) = k(x − T)²
3 现实里的 μ vs T μ vs T in the Real World
电池出厂 SOC:T = 50%,μ = 48% 略偏低,运输安全,但客户首充体验差一点。
Battery ship-out SOC: T = 50%, μ = 48% — slightly low. Safer in transit, but the customer's first charge feels just a bit off.
注塑件壁厚:T = 2.00mm,μ = 2.05mm 偏厚,规格内但每件多吃 2.5% 材料。
Injection-molded wall: T = 2.00 mm, μ = 2.05 mm — slightly thick. In-spec, but every part burns 2.5% extra resin.
食品咸度:T = 1.2%,μ = 1.5%,还在规格内但客户开始抱怨"今天有点咸"。
Food saltiness: T = 1.2%, μ = 1.5% — still in-spec, yet customers start saying "tastes a touch salty today".
交易延迟:T = 200ms,μ = 180ms,"过好"也可能浪费资源或暴露不一致,不是越快越好。
Trade latency: T = 200 ms, μ = 180 ms. "Too good" can waste resources or expose inconsistencies downstream — faster isn't always better.
一句话In One Line
μ 是当下,T 是该去的地方。
Cp 公式分子分母都不出现 T —— 它根本不认识目标;
Cpk 用 min(USL−μ, μ−LSL) 部分认识(μ 越偏向某一侧,Cpk 越低);
Cpm 把 (μ−T)² 直接塞进分母 —— 完全认识。
报告里只看合格率会丢掉这个故事;μ 和 T 的差,就是调机的方向。
μ is where you are now; T is where you should be going.
Cp has no T in its numerator or denominator — it doesn't know the target exists.
Cpk uses min(USL − μ, μ − LSL), so it knows T partially (drift toward one limit and Cpk drops).
Cpm jams (μ − T)² right into the denominator — it knows T fully.
Read only the pass rate and you lose this story; the gap between μ and T is the direction you turn the dial.
常见误用Common Mistakes
认为 μ 落在规格内 = 零损失。田口告诉你偏离 T 就有损失,二次曲线无情累积,规格内只是不退货而已。
Believing that μ inside spec means zero loss. Taguchi: drift off T and loss accrues on a quadratic curve — in-spec just means the part won't be returned.
默认 μ 应该 = M(规格几何中心)。客户目标 T 可能偏向规格一侧(如电池 SOC 偏低更安全),M ≠ T 时要按 T 调机。
Assuming μ should equal M (the geometric midpoint). Target T may lean to one side (battery SOC kept low for safety, for instance). When M ≠ T, tune toward T, not M.
报告只给"合格率"不给 μ−T 偏离。μ 和 T 的差是改进调机的方向,合格率藏不住的系统性偏移必须显式报。
Reporting only pass rate, hiding the μ − T offset. μ − T is the direction for the next tuning move; a systematic offset that pass rate can't see must be reported explicitly.