起源故事 · Little 的一行证明 Origin Story · Little's One-Line Proof
1961 年,MIT 的 John Little 给出了排队论里一个惊人简洁的结论:稳态系统里,平均在制品数 = 平均到达率 × 平均停留时间。 它不挑分布、不问细节,只要进出平衡就铁律成立 —— 这让它成为精益生产、库存管理、产能规划的万能尺子。 这条法则还有个反直觉的推论:想缩短周期 W,与其拼命加速,不如砍掉在制品 WIP(少排队),因为三者被锁死,降一个就拉低另一个。 配上 OEE(设备综合效率)把"可用、跑得快、做得对"三道折扣连乘,你就能定位产能到底漏在哪。 In 1961, MIT's John Little published a startlingly simple result: in any stable system, average WIP = average arrival rate × average time-in-system. It is distribution-free and assumption-light — as long as long-run inflow equals outflow, the law holds. That is what makes it the universal ruler of lean manufacturing, inventory management and capacity planning. It also carries a counter-intuitive corollary: if you want to shrink lead time W, don't just push the machines harder — shrink WIP instead. The three are locked together, and pulling one down drags the others with it. Pair it with OEE — three discounts (it's running, it's running fast enough, it's making good parts) multiplied together — and you can pinpoint exactly where capacity is leaking.

1 在制品 WIP:系统里同时排着多少工件? Work-in-Process: How Many Units Are Queuing Right Now?

2 OEE 瀑布:100% 产能被三道折扣吃到只剩多少 OEE Waterfall: How Three Discounts Eat 100% Down

从理论满产 100% 出发,可用率扣掉停机损失、性能扣掉速度损失、质量扣掉不良损失,三道连乘 —— 每环看似都不低,连乘后却可能跌破七成。 Start from 100% theoretical capacity. Availability subtracts downtime, Performance subtracts speed loss, Quality subtracts defect loss — three discounts multiplied. Each factor looks healthy on its own, yet the product can easily fall below 70%.

3 现实里的利特尔法则与 OEE Little's Law & OEE in the Real World

在制品控制:限制看板/CONWIP 卡住 WIP 上限,按 W=WIP/λ 直接缩短交付周期。 WIP control: kanban or CONWIP caps WIP at the ceiling, and W = WIP / λ shrinks lead time directly.
产能规划:已知订单到达率 λ 和目标周期 W,反推需要多少缓冲与节拍。 Capacity planning: given order arrival rate λ and a target lead time W, back-solve the buffer and takt you need.
设备诊断:OEE 拆成三因子,一眼看出产能漏在停机、降速还是不良。 Equipment diagnosis: split OEE into three factors and you immediately see whether capacity is leaking through downtime, slow cycles, or defects.
节拍设计:Takt time 与 WIP、周期联动,是单件流与拉动生产的设计基础。 Takt design: takt time, WIP and cycle time move together — the foundation for one-piece flow and pull production.
一句话 In One Line
利特尔法则把库存、节拍、周期三者用一个乘法锁死:WIP、λ、W 任意两个定了,第三个就定了。 所以精益不靠"跑得更快"而靠"少排队"—— 压低 WIP,周期 W 自然缩短。 OEE 则提醒你:设备表面在转,真实产出要打三道折扣,连乘是无情的,三个 90% 连乘只剩 73%。 想提产能,先用 OEE 找到最大损失环节,再用利特尔法则把改善换算成交付周期的缩短 —— 这就是把可靠性数学落到产线节拍上的最后一步。 Little's Law fuses WIP, throughput and lead time into a single product: fix any two of WIP, λ and W, and the third is fixed too. That is why lean does not chase "run faster" — it chases "queue less". Squeeze WIP down and W shrinks on its own. OEE reminds you that a machine which looks busy still owes three discounts, and multiplication is merciless: three 90% factors leave just 73%. To lift capacity, use OEE to find the biggest loss bucket, then use Little's Law to translate that improvement into shorter lead time — the final step that turns reliability math into actual line cadence.
常见误用 Common Mistakes
对不稳定系统硬套 WIP=λ×W。法则只在稳态(长期进出平衡)下成立。 Applying WIP = λ × W to an unstable system. The law only holds in steady state — long-run arrivals must equal long-run departures.
靠堆 WIP 提产出。WIP 越高周期越长,精益反而要压低 WIP。 Piling on WIP to lift throughput. More WIP just means longer lead time — lean does the opposite and drives WIP down.
把三因子相加当 OEE。OEE 是三者相乘,连乘惩罚远比相加狠。 Adding the three factors instead of multiplying them. OEE is a product, not a sum — the multiplicative penalty is far harsher than addition.

利特尔法则与 OEE