起源故事 · Motorola 与 Mikel Harry Origin Story · Motorola and Mikel Harry
1980 年代,Motorola 的 Mikel Harry 翻看多年生产数据,发现工厂的过程均值会"偷漂"—— 刀具磨损、班次更替、季节变化、原料批次,长期里均值会在 ±1.5σ 内随机游走。 所以"短期 6σ → 3.4ppm"这个口号,其实是 (6 − 1.5) = 4.5σ 单边 = 3.4ppm。 这个 1.5σ 不是数学定理,是 Motorola 的工程经验值——后来成了 Six Sigma 全球流派最大的"潜规则"。 In the 1980s, Motorola's Mikel Harry pored over years of production data and noticed that factory process means "silently drift" — tool wear, shift changes, seasonal swings, and raw-material batches send the long-run mean on a random walk within roughly ±1.5 σ. So the slogan "short-term 6 σ → 3.4 ppm" is really (6 − 1.5) = 4.5 σ one-tail = 3.4 ppm. That 1.5 σ is not a theorem; it is Motorola's engineering rule of thumb — and it became the biggest unspoken convention in every Six Sigma school worldwide.

1 短期视角 vs 长期视角:同一过程,两种 ppm Short-term vs Long-term Lens: One Process, Two ppm Numbers

长期尾部更胖long-term tail fatter

蓝色 = 短期理论钟形(μ 居中)。红色 = 长期实际钟形(μ 向右漂了 shift)。USL 右侧的阴影面积就是超规率 —— 红色阴影明显比蓝色大,这就是 1.5σ shift 让 ppm 暴涨的原因。 Blue = the short-term theoretical bell with μ centered. Red = the long-term actual bell after μ drifts to the right by shift. The shaded area beyond USL is the defect rate — the red area is clearly much larger than the blue. That's why the 1.5 σ shift blows ppm up.

2 动画:均值在 ±shift 之间随机游走 Animation: μ Random-Walks Between ±shift

累积超规 0Cumulative defects 0

点"让均值来回漂",看钟形以 ~0.5Hz 在 [μ − shift, μ + shift] 之间游走。右侧累积超规计数实时跑——你会发现长期视角下,即使你"瞬时看一眼"过程很稳,客户感受到的不良率却高得多。 Click "Animate the drifting mean" and watch the bell oscillate at ~0.5 Hz between μ − shift and μ + shift. The live defect counter on the right keeps tallying — you'll find that even when an instantaneous snapshot looks rock-steady, the long-term defect rate the customer feels is much higher.

3 1.5σ shift 在现实里 The 1.5 σ Shift in Practice

Six Sigma 经典口号:"6σ = 3.4ppm"就是这么算的 —— 短期 6σ 扣 1.5 = 长期 4.5σ 单边 ≈ 3.4ppm。 The Six Sigma slogan: "6 σ = 3.4 ppm" comes from exactly this — short-term 6 σ minus 1.5 = long-term 4.5 σ one-tail ≈ 3.4 ppm.
学术派反对:认为 1.5 太武断,应该实测漂移量而不是假设。Pp/Ppk 直接用长期数据更诚实。 The academic camp pushes back: 1.5 is too arbitrary — drift should be measured, not assumed. Pp / Ppk, which use long-term data directly, are more honest.
半导体行业:不用 1.5 shift,直接拿长期数据算 Zbench。工艺漂移很小,Motorola 的经验值不适用。 Semiconductor industry: skips the 1.5 shift and computes Zbench directly from long-term data. Process drift is tiny in a fab, so Motorola's rule of thumb doesn't fit.
Minitab 默认:Capability Sixpack 默认开启 1.5 shift,但可以在选项里关掉。报告时务必注明哪种模式。 Minitab default: Capability Sixpack turns the 1.5 shift on by default, but you can disable it in the options. Always state which mode the report used.
一句话In One Line
1.5σ 是 Motorola 留下的工程经验,不是物理常数。它把"短期理论"和"长期客户感受"折中—— 短期 σ 容易测(几小时内的 R̄/d2),长期 σ 才是客户真正承受的(几周/几月的所有数据)。 它们的差距,Motorola 取 1.5。学术派反对,实务派接受。真要严谨,就直接用 Pp/Ppk——它们自带长期视角,不需要这个"折扣假设"。 The 1.5 σ is Motorola's engineering rule of thumb, not a physical constant. It splits the difference between the short-term theoretical view and what the customer feels in the long run — short-term σ is easy to measure (R̄ / d₂ over a few hours), but long-term σ is what the customer actually lives with (weeks or months of pooled data). Motorola pegs that gap at 1.5. Academics object, practitioners accept. If you want true rigor, skip the assumption and use Pp / Ppk — they carry the long-term view by construction and need no "discount".
常见误用Common Mistakes
把 1.5σ 当数学定理。它是 1980 年代 Motorola 经验值,行业各家差异很大;有研究测出 0.5–2.0 都有。 Treating the 1.5 σ as a mathematical theorem. It's a 1980s Motorola rule of thumb; industries vary widely — measured shifts range from 0.5 to 2.0 in published studies.
报告 Cp=2.0 不说有没有 1.5 调整。必须注明 short-term(σ_within) 还是 long-term(σ_overall),否则 ppm 差 10×。 Reporting Cp = 2.0 without saying whether the 1.5 adjustment is applied. Always label whether the figure is short-term (σ_within) or long-term (σ_overall) — otherwise the implied ppm can be off by 10×.
服务业也套 1.5。1.5 来自半导体/汽车制造的均值漂移特性;服务流程的漂移特征完全不同,直接实测。 Applying the 1.5 shift to service processes. The 1.5 comes from semiconductor and automotive mean-drift behavior; service-process drift looks nothing like that — measure it directly.

1.5σ shift