🧩 Spacecraft Reliability & Redundancy Calculator

Series chain with per-unit MTBF & redundancy scheme · system reliability at mission time

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Series Units

One row per function in the series chain. Blank/zero MTBF rows are ignored. All schemes assume exponential (random) failures and perfect switching.

串联链中每个功能一行；MTBF 留空/为 0 忽略。各方案均假设指数（随机）失效与理想切换。

UnitMTBF (yr)SchemeR(t)

Mission

Results

System reliability R(t)
–
System failure probability
– %
Weakest link
–
Units in chain
–
–
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📖 How to use

  1. List the functions that must all work (series chain) with each unit's MTBF and redundancy scheme.列出必须全部正常的功能（串联链），填每个单机的 MTBF 与冗余方案。
  2. Cold standby beats hot standby on paper (the spare doesn't age) but needs detection + switching; 2-of-3 voting adds fault detection for computers.冷备份账面优于热备份（备份件不老化）但依赖故障检测与切换；2/3 表决还能提供故障定位，常用于计算机。
  3. The weakest link column shows where redundancy buys the most — upgrade the lowest R(t) unit first.最薄弱环节指明冗余投资方向——优先加强 R(t) 最低的单机。
  4. Real budgets add wear-out items (wheels, batteries), common-cause factors and switch reliability — treat this as the first-order skeleton.真实预算还需计入损耗型器件（动量轮、电池）、共因失效与切换开关可靠度——本页为一阶骨架。

Reliability mathematics

Exponential unit: R = e^(−t/MTBF). Schemes: hot duplex 1−(1−R)²; cold duplex (ideal switch) e^(−λt)(1+λt); 2-of-3 voting 3R²−2R³. Series system: R_sys = Π R_i.

Note the 2-of-3 subtlety: it is less reliable than a single unit for very long missions (three chances to fail, needs two alive) — its value is masking and detection, not endurance. Cold standby roughly doubles the effective life of the weakest units.

All computation runs locally in your browser.

可靠性数学

指数单机：R = e^(−t/MTBF)。方案：热双机 1−(1−R)²；冷双机（理想切换）e^(−λt)(1+λt)；三取二表决 3R²−2R³。串联系统：R_系统 = Π R_i。

注意三取二的微妙之处：任务很长时它反而低于单机（三个失效机会、需两个存活）——其价值在于故障屏蔽与检测，不在寿命。冷备份大致可将薄弱单机的等效寿命翻倍。

全部计算在你的浏览器本地完成。