01 · STAGE
关键阶段 Critical stages
只把业务成功真正依赖的检索、决策、工具、校验等节点列入链。 Include retrieval, decision, tool, validation, and other nodes the business outcome truly depends on.
01 · 先从日常问题开始
01 · Start with an everyday question
四道工序每道都说“我有 95% 成功率”，整件产品最后还能有 95% 吗？ Four stages each claim 95% success. Does the finished outcome still succeed 95% of the time?
02 拖各阶段 p，再加一个必经节点 Drag Each Stage p, Then Add a Required Node
总可靠率实时连乘 live reliability product
端到端可靠率 R
End-to-end reliability R
—
Π pᵢ
必经阶段数 n
Required stages n
4
chain length
最弱阶段
Weakest stage
—
first hardening target
03 总可靠率由四类信息组成 Four Inputs Define End-to-End Reliability
把变化映射到零件 Map change to parts02 · P
单阶段成功率 Stage success rate
每个 p 必须有固定分母和同一成功定义，不能拿局部印象代替。 Every p needs a fixed denominator and one success definition, not local impressions.
03 · PRODUCT
连乘 Product
当各关键阶段都必须成功时，总可靠率是阶段成功率的乘积。 When every critical stage must succeed, total reliability is the product of stage success rates.
04 · DEPEND
依赖边界 Dependency boundary
若阶段相关，简单独立连乘只是近似，必须显式说明假设。 If stages are correlated, simple independent multiplication is only an approximation and must state that assumption.
04 最小公式：各阶段都成功才算端到端成功 Minimal Formula: Every Stage Must Succeed
R = Π pᵢ ≈ pⁿ
R = ∏i=1n pi
若 p 相同：R ≈ pn
若 p 相同：R ≈ pn
拖任一 p，会按乘积直接改变 R；新增一个 97%
节点也会让总可靠率继续下降。这里采用阶段独立的教学近似。
Dragging any p changes R through the product. Adding even a 97%
node lowers total reliability. This lab uses an independence
approximation for teaching.
固定每阶段分母
Fix stage denominators
局部成功可比较
local rates become comparable
沿业务链连乘
Multiply along the chain
所有关键站都必须成功
all critical stages must pass
定位最弱节点
Find the weakest node
Harness 针对性加固
harden with the Harness
05 边界实验：六个 90% 节点 Boundary Test: Six 90% Nodes
主动制造失败 Create a failure每站看似不错，总链只剩约一半 Each stage looks decent while the chain falls near half
把链扩到六个节点并全部设为 90%。单点分数仍是“九成”，但端到端可靠率只有 53.1%。 Expand to six nodes and set each to 90%. Every local score still looks strong, yet end-to-end reliability is only 53.1%.
尚未执行。先操作上方主交互。
Not run yet. Use the main interaction above first.
✗ 每阶段 95%，总流程也是 95%。
Every stage is 95%, so the whole flow is 95%.
→ ✓ 关键阶段都要成功时，总率按乘积下降。
When all stages must pass, total rate falls by
multiplication.
✗ 加一个高分节点不会影响可靠率。
Adding a high-scoring node does not affect
reliability.
→ ✓ 任何小于 100% 的必经节点都会降低乘积。
Any required node below 100% lowers the product.
✗ 连乘公式适用于所有相关失效。
Simple multiplication fits every correlated
failure.
→ ✓ 阶段独立是近似假设，相关性要另建模。
Independence is an approximation; model correlation
separately.
06 · 一句话带走
06 · One line to keep