What does DPU / RTY / FTY · The Hidden Factory Exposed · LSS.WIKI explain?

A 10-step line where every step reports a tidy 95% yield, yet chained together the rolled throughput yield (RTY = 0.95¹⁰ ≈ 60%) collapses — that's the Hidden…

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DPU / RTY / FTY · The Hidden Factory Exposed

产线控制台Line Console

工序数量 NNumber of steps N 10

工序越多 → RTY 衰减越狠 More steps → RTY decays harder

各工序统一 FTYUniform FTY per step 95%

每道工序的首次合格率(不算返工) First-time pass rate per step (rework not counted)

FTY = e^(−DPU),故 DPU = −ln(FTY);RTY = FTY 的 N 次方 FTY = e^(−DPU), so DPU = −ln(FTY); RTY = FTY raised to the N-th power

RTY 滚动合格率RTY (Rolled Throughput Yield)

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一次就全程无缺陷的比例 Share of units that clear every step defect-free on the first try

隐藏工厂损失Hidden Factory loss

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途中至少出一次缺陷的比例 Share of units that hit at least one defect along the way

累计 DPU(全线)Total DPU (whole line)

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每件产品平均缺陷数 = N × DPU Average defects per unit = N × DPU

故事 · 那座没人愿意承认的「隐藏工厂」 Story · The "Hidden Factory" Nobody Will Admit To

传统的"最终良率(FTY 单点)"只看产品走出大门时合不合格,却把过程中产生、又被返工修掉的缺陷统统藏了起来。质量先驱们把这套"专门用来返修自家缺陷"的隐形产线称作「隐藏工厂」(Hidden Factory) —— 它不出现在任何排产表上, 却实实在在消耗着人力、设备和时间。RTY(Rolling Throughput Yield,滚动合格率)正是为戳破它而生: 它问的不是"最后好不好",而是"从头到尾一次就做对的产品有几成"。把各工序 FTY 连乘,那些被返工掩盖的损失瞬间无所遁形。这也是六西格玛"第一次就把事情做对"信条的量化基石。 Traditional "final yield" looks only at whether a unit passes when it leaves the building — it quietly hides every defect that was created mid-process and then reworked away. Quality pioneers gave that invisible "rework-our-own-mistakes" line a name: the Hidden Factory. It never shows up on a production schedule, yet it eats real labor, real machine time, and real cycle time. RTY (Rolled Throughput Yield) exists to call its bluff. It doesn't ask "is the final unit OK?"; it asks "what fraction of units made it through without a single first-time defect anywhere?" Multiply the step-by-step FTYs together and every reworked loss instantly comes out of hiding. This is the quantitative backbone of the Six Sigma mantra: do it right the first time.

1 1000 件产品,过一关丢一点 1,000 Units In — Each Gate Shaves a Bit Off

RTY 0%

2 单工序看着高,连乘起来暴跌 Each Step Looks Tall — Multiplied, It Crashes

单工序 FTY 一根高高的柱子,全程 RTY 却矮一大截。差距 = 隐藏工厂。FTY 每降一点,RTY 因连乘被放大成断崖 —— 这就是"木桶不是看最短板,而是所有板相乘"。 Single-step FTY stands tall; end-to-end RTY sits a lot shorter. The gap is the Hidden Factory. Every tick down in FTY gets amplified by the chain into a cliff — the bucket isn't the shortest stave, it's all the staves multiplied.

3 现实里的 RTY 与隐藏工厂 RTY and the Hidden Factory in the Real World

滚动合格率:多工序产品的真实良率不是最后一关的合格率,而是各工序 FTY 的连乘。 Rolled throughput yield: the real yield of a multi-step product isn't the final-gate pass rate — it's the product of every step's FTY.

隐藏工厂:返工 / 返修 / 复检消耗的产能,账面看不见,RTY 一算就现形。 Hidden factory: the capacity burned by rework, repair, and re-inspection never shows up in the ledger — but RTY drags it straight out.

多工序累积:工序越多、单步 FTY 越低,RTY 跌得越快,长流程尤其要警惕。 Multi-step compounding: more steps and a lower per-step FTY make RTY plummet faster. Long processes deserve extra suspicion.

返工损失:第一次做对最便宜;RTY 把"返工成本"翻译成全员都懂的良率语言。 Cost of rework: getting it right the first time is always cheapest. RTY translates "rework cost" into yield language everyone on the floor already understands.

一句话In One Line

DPU 数的是"平均每件有几个缺陷"。假设缺陷按泊松分布随机出现,那么"一个缺陷都没有"的概率正是 FTY = e^(−DPU) —— 这就是首次合格率的真身。把每道工序独立的 FTY 连乘, 得到 RTY = ∏ FTYᵢ:要一次走完全程,必须每一关都首次通过。关键在连乘:0.95 自乘 10 次只剩 0.60,这种指数级衰减正是"单步看着没事、整体却崩盘"的根源。所以 RTY 逼着我们换视角:质量不是某一关的事,而是整条链一次做对的概率 —— 隐藏工厂,就藏在那个被忽略的乘号里。 DPU counts the average number of defects per unit. If defects arrive as a Poisson process, the probability of seeing zero defects is exactly FTY = e^(−DPU) — that's the true face of first-time yield. Multiply the independent FTYs across every step and you get RTY = ∏ FTYᵢ: to clear the whole line in one pass, every gate has to pass the first time. The crux is the product: 0.95 raised to the 10th power is only 0.60. That exponential decay is exactly why "every step looks fine, the whole line collapses." RTY forces a shift in perspective: quality isn't owned by any single gate — it's the probability that the whole chain works on the first try. The Hidden Factory lives in that ignored multiplication sign.

常见误用Common Mistakes

用最终良率冒充真实良率。最终良率含返工,掩盖隐藏工厂;多工序须用 RTY 看"首次做对"。 Passing off final yield as true yield. Final yield silently includes rework and hides the Hidden Factory. For multi-step lines, use RTY to measure true first-time success.

把各工序 FTY 相加而非相乘。RTY 是连乘,不是平均也不是求和;连乘才反映"关关都过"。 Adding or averaging step FTYs instead of multiplying. RTY is a product, not a sum or an average. Only multiplication captures "must pass every gate."

忽略工序间的相关性。∏FTY 假设工序独立,若上游缺陷诱发下游,须额外建模。 Ignoring correlation between steps. ∏FTY assumes steps are independent. If an upstream defect drives downstream failure, you need a richer model on top.