故事 · 摩托罗拉车间里偷偷溜走的均值
Origin Story · The Mean That Quietly Drifted at Motorola
1980 年代,摩托罗拉的工程师统计了大量过程后发现一个反复出现的规律:一台机器今天早上校准得完美居中,
可一个班次跑下来,刀具会磨损、车间温度会升高、换上的原料批次会有细微差别 —— 均值便悄悄地、缓慢地漂走。
短期看着稳如泰山的过程,长期统计下来,均值的游走幅度经验上约为 ±1.5σ。
客户买到的是长期产出,不是你校准那一刻的短期表现。为了让能力指标说真话,摩托罗拉约定:把短期 σ 水平减去 1.5 再查表。
于是理论 6σ 过程,长期按 4.5σ 计 —— 恰好 3.4 DPMO。这个数字从此成了六西格玛的图腾,也成了它最受争议的地方。
In the 1980s Motorola's engineers studied thousands of processes and kept seeing the same pattern: a machine could be perfectly centered at the start of a shift,
but by the end the cutter had worn, the room had warmed, and the new lot of raw material was a hair different — and the mean had quietly, slowly drifted.
A process that looked rock-steady short-term, when tallied over the long run, wandered by roughly ±1.5σ.
Customers experience the long-term output, not your calibration-moment short-term peak. To make capability metrics tell the truth, Motorola agreed to subtract 1.5 from short-term σ before quoting defects.
A theoretical 6σ process, judged long-term at 4.5σ, lands on 3.4 DPMO. That number became Six Sigma's totem — and its most-debated convention.
1 居中的蓝峰 vs 漂移后的橙峰 Centered Blue Peak vs. Shifted Orange Peak
σ 6.02 短期 vs 长期:同一个 σ 水平,两条命运 Short-term vs. Long-term: Same σ Level, Two Fates
纵轴对数刻度。蓝线是短期(居中)DPMO,6σ 处低到十亿分之二;橙线是长期(漂移 1.5σ)DPMO,6σ 处停在 3.4。两条线整整差了约 1.5σ 的水平身位 —— 这就是「以短期命名、按长期计费」。 Log scale on Y. The blue line is short-term (centered) DPMO — at 6σ it sinks to two parts per billion. The orange line is long-term (1.5σ shift) DPMO — at 6σ it sits at 3.4. The two lines are offset by roughly 1.5σ horizontally — "named in short-term sigma, billed in long-term sigma".
3 现实里的 1.5σ 漂移 The 1.5σ Shift in the Real World
长期漂移的真凶:刀具磨损、模具老化、温湿度变化、批次差异、换班操作差异 —— 都让均值在长期里慢慢游走。
What actually causes drift: tool wear, mold aging, temperature and humidity swings, lot-to-lot variation, shift-to-shift operator differences — they all nudge the mean over time.
3.4 DPMO 的真身:它是「长期 4.5σ」的尾部面积,不是「零缺陷」,也不是十亿分之二的理论值。
What 3.4 DPMO really is: the tail area of a long-term 4.5σ — not "zero defects", and not the two-in-a-billion theoretical value.
短期 vs 长期:报告能力时必须注明用的是短期(居中)还是长期(含漂移),两者相差约 1.5σ 量级。
Short-term vs. long-term: when reporting capability, always state whether the figure is short-term (centered) or long-term (with shift). The two differ by roughly 1.5σ.
过程稳定性:真实漂移因过程而异,1.5 只是保守通约。要靠控制图(下一章 SPC)实测,而非盲目硬套。
Process stability: real drift varies by process — 1.5 is a conservative convention, not a law. Measure it with control charts (next chapter, SPC), don't blindly plug in the number.
一句话In One Line
1.5σ 漂移的本质,是承认一件朴素的事实:没有任何过程能永远精准居中。
校准那一刻的完美(短期),不是客户日复一日拿到的产出(长期)。摩托罗拉把分布整体平移 1.5σ,
再去数越界的尾巴,于是 6 − 1.5 = 4.5σ 的尾部 ≈ 3.4 DPMO。所以这个图腾数字的真身是:
「以短期能力命名(6σ),按长期表现计费(4.5σ)」。
理解了这一点,你就不会再把 3.4 当成精确的物理常数 —— 它是一个让全公司朝同一方向努力的、刻意保守的工程约定。
The point of the 1.5σ shift is to admit one honest fact: no process stays perfectly centered forever.
The perfection of the calibration moment (short-term) isn't what the customer receives day after day (long-term). Motorola simply shifts the distribution by 1.5σ
and counts the tail again — so the tail of 6 − 1.5 = 4.5σ ≈ 3.4 DPMO. The real meaning of the totem number is this:
"named in short-term capability (6σ), billed in long-term performance (4.5σ)".
Once you see that, you stop treating 3.4 as a precise physical constant — it's a deliberately conservative engineering convention designed to point the whole company at the same goal.
常见误用Common Mistakes
把 1.5σ 当成普适物理常数硬套。它是经验通约,真实漂移因过程而异,须用控制图实测。
Treating 1.5σ as a universal physical constant. It's an empirical convention. Real drift is process-specific — measure it with control charts.
报告时混用短期 / 长期 σ 水平。必须注明含不含漂移,否则结论相差 1.5σ 量级。
Mixing short-term and long-term σ levels in the same report. Always state whether the figure includes the shift — otherwise conclusions can be off by roughly 1.5σ.
把 3.4 DPMO 当成「零缺陷」。它是百万分之 3.4,仍有缺陷;追求更高要看缺陷的经济后果。
Calling 3.4 DPMO "zero defects". It's 3.4 per million — defects still happen. Whether to chase higher depends on the economic cost of each failure.