What could have been known · one cutoff · no replay

The Missing Denominator

On the night before Challenger launched, the incident flights looked like a scattered warning with no denominator. Restore every inspected prior flight, including the flights with no O-ring distress, and the temperature relationship appears. Then the famous prediction at 31°F reveals a second omission: its uncertainty.

One information cutoffJanuary 27, 1986 at 11:15 p.m. EST. The NASA and Thiokol teleconference ended with a recommendation to launch. This page makes no release-by-release time series.

Operate the omission

Selection is the axis. The left control conditions on the outcome by keeping only flights with distress. The right control restores all 23 usable flight outcomes that cleared the single cutoff.

Flights in view7 / 23

Temperature slope+0.0014

Descriptive p at 31°F20.7%

The incident-only view has selected on damage. Its nearly flat refit is descriptive, not a valid risk model.

No launch date appears on this axis. Figure 2 dates rows by launch or static firing, while damage was learned during later recovery and inspection. Those event dates cannot support an availability replay, so this page does not attempt one.

The whole ledger crosses once

23used flights

1later outcome

12stated exclusions

0undated

Why all 23 are eligible. Every usable earlier flight had flown, been recovered, and been inspected before the January 27 call. The last one, STS-61-C, supplies the conservative availability ceiling for the set: the Presidential Commission records completion of its booster inspection on January 19, 1986. That is eight days before this page's cutoff. The page assigns that one source-backed ceiling to the whole prior-flight ledger. It never treats a launch date as an observation date.

STS-61-C's field and nozzle anomalies were available for the launch-minus-one-day Level III review, but they had not entered the formal problem system. Availability and presentation were different facts.

The full Figure 2 archive has 36 rows: 25 Shuttle flights and 11 development or qualification motors. STS-4 is excluded because its hardware was lost at sea, leaving no usable outcome. The 11 motors are excluded because this model's population is Shuttle flights. STS-51-L's outcome is later than the cutoff. The four buckets balance to 36.

The number that looks precise

Dalal, Fowlkes and Hoadley's retrospective temperature-only model gives a per-ring distress probability of about 0.818 at 31°F. That point is 22°F below the coldest usable observation. Move the target back into the observed range and watch the likelihood interval tighten.

Prediction temperature31°F

Per-ring point estimate

81.8%

95% profile interval: 14.2% to 99.1%

This interval re-optimizes the slope at every fixed candidate probability, then keeps values within a likelihood-ratio distance of 3.841459.

Expected distressed rings

4.91 / 6

interval maps to 0.85 to 5.94 rings

A mean is not a forecast of an integer result. It is six times the fitted per-ring probability.

31°F is 22°F below every usable observation. This is extrapolation, not interpolation.

Two flight-level answers, one free choice

99.9963% At least one distressed ring 1 - (1 - p)⁶, using model 3.2

Uses the six-ring binomial model. It treats the six rings on a flight as independent trials with the same probability.

99.9609% At least one distressed ring logit(P) = 15.042902 - 0.232163t

Uses one binary outcome per flight. It does not require independence among the six rings.

Independence is not a fact recovered from the ledger. It is a modeling choice. Only 30.4% of eligible flights had shown any primary-ring distress, 7 of 23. Both specified logistic models put the 31°F flight-level probability close to one, far above that demonstrated share, while the profile interval says the precise per-ring probability was not knowable from these observations.

The check: recomputed live from the shipped ledger

The browser maximizes the grouped-binomial likelihood over the 23 eligible rows. No displayed fitted result is a stored answer. The published comparison is equation 3.2 of the 1989 paper.

quantity	published	live
intercept	5.085	5.084977
temperature slope	-0.1156	-0.115601
deviance on 21 df	18.086	18.086327
p(31°F), per ring	about 0.818	0.817774
expected rings at 31°F	about 4 to 5	4.906646
profile 95% interval	not reported	0.141852 to 0.990522

Negative control. The same page pipeline is rerun with a planted six-distress flight dated 2099 inside the input array. The firewall must put it in the later bucket, keep it out of the fit, and leave every fitted value unchanged. Status: checking.

Free choices: primary field-joint rings only; erosion or blow-by counted as distress; a linear logit in temperature; six equal-probability independent trials for the binomial reading; likelihood-ratio cutoff 3.841459 for the profile interval; and the complete 23-flight population rather than static motors.

Uncertainties: 31°F lies outside the 53°F to 81°F observed range; the particular regression was retrospective, not a calculation shown to the teleconference; ring outcomes on one flight may be dependent; distress is not catastrophic joint failure; and the exact full-scale sealing behavior at 31°F was unobserved.

Offline reproduction: node research/challenger-o-ring-information-set/verify.mjs

What the check can score, and what it cannot

Control 3 · observed decision

Launch versus delay

Thiokol engineering's frozen rule was not to launch below 53°F. It says delay. Management's actual choice was launch. The observed immediate outcome was loss of Challenger and its seven crew members. Against that immediate observed outcome alone, the delay rule scores better than the actual choice.

This does not identify the unchosen branch. The record cannot tell us when or at what temperature Challenger would have flown after a delay, or what that later flight would have done.

Control 4 · unavailable quantity

The sealing time at 31°F

No previous flight and no available test reproduced the primary and secondary O-rings inside the assembled full-scale field joint at 31°F with the actual putty, joint rotation, and ignition loading together.

Boisjoly testified that he was asked to quantify the timing concern and could not because he had no data. No diligence that night could reveal the realized sealing behavior of that joint.

Apparatus and provenance

Open the 23-flight ledger

flight	joint temp °F	distressed primary rings	selection

The ledger deliberately contains no launch-date field. Every row uses January 19 as a conservative certification that the complete prior-flight set was available before the cutoff.

Source disagreement and model scope

The current NASA HTML transcription of Commission Figure 2 contains errors. This page uses 69°F for STS-3, 70°F for STS-9, and 78°F for STS-41-G, values that agree between Dalal, Fowlkes and Hoadley's Table 1 and the government's 1988 Post-Challenger evaluation. The page counts two primary distressed rings on STS-51-C. The paper's table also notes secondary-ring distress there, but model 3.2 explicitly analyzes primary rings.

The incident-only chart is a reconstruction of the selection rule described by the paper and Commission: flights with zero incidents were omitted. It is not a claim that the seven points were the only engineering evidence discussed that night. The call also covered bench tests, static tests, joint mechanics, putty, and sealing time.

Why this is not a historical prediction

Logistic regression existed in 1986, and the 23-flight ledger was constructible from information available by the cutoff. The exact coding, corrections, model form, diagnostics, and failure-chain analysis in the 1989 paper were retrospective. The live fit shows what this eligible record supports under a declared model. It does not claim anyone on the call possessed the equation or its probability.