Every ECLSS component (CO₂-scrubber cartridges, O₂ valve seals, water-loop filters…) that reaches a spacecraft must first pass a manufacturing quality gate. Testing every single unit is often destructive or too slow, so QA engineers inspect a random sample of size n drawn from each production lot and accept or reject the whole lot based on how many defects turn up — an "acceptance sampling plan" (n, c).
Decision rule: count defects d in the sample
d ≤ c → ACCEPT the lot (ship the rest)
d > c → REJECT the lot (100% rework/scrap)
P(accept | p, n, c) = Σ_{k=0}^{c} C(n,k) · p^k · (1-p)^(n-k)
This binomial sum is the lot's operating-characteristic (OC) curve: for a given plan (n, c) it plots the probability the lot gets accepted as a function of the true fraction defective p. A steep curve near the target defect rate means the plan discriminates sharply between good and bad lots; a shallow curve means good lots get rejected (producer's risk) or bad lots slip through (consumer's risk) too often.
- True defect rate p — sets the hidden manufacturing quality of the next lot (unknown to the inspector, exactly like real production variance).
- Sample size n / acceptance number c — the sampling plan itself; increasing n steepens the OC curve, increasing c shifts it right (more tolerant).
- Draw Sample & Inspect — pulls n units at random without replacement, reveals each as good (green) or defective (red), and applies the decision rule live.
- Drag to pan, scroll/pinch to zoom — the lot grid below is a flat 2D layout of all 200 units; zoom in to read individual unit states.
This is the same statistical logic behind MIL-STD-105 / ANSI-ASQ Z1.4 sampling plans used across aerospace hardware acceptance, adapted here to a life-support component lot.