SCIENCE · INVESTIGATE AND EXPLAIN

Turn failed requirements into a useful failure log

Separate a failing criterion, its observed symptom and a proposed cause.

Learning outcome: Reproduce a failure with exact candidate/scenario settings and retain alternatives rather than replacing the original evidence.

Starting recap

A candidate contains gain, hardware and correction. One selected candidate is unchanged across its four-scenario suite.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

Standard gain 6 with zero correction passes nominal but fails the delayed tail band despite a passing final temperature.

Open the experiment

Predict

Predict whether one passing endpoint is enough to pass the four tail samples.

Your prediction and reason

Experiment

Select standard gain 6, zero correction and delayed operation. Capture the candidate/scenario and record failed tail rows, symptom, mechanism, alternative cause and proposed test. Compare its other three scenarios without retuning.

Compare failures and constrained design tradeoffs

Worked teaching model · synthetic values · Twelve fixed candidates and four public deterministic cases reuse engineering-device-v1. Keep hardware, gain and correction fixed across each four-case suite. Case pass counts are coverage of supplied conditions, not field reliability, probabilities, independent trials or physical validation. Feasibility requires every supplied criterion; energy and assigned token cost are separate conditional objectives. An empty robust feasible set is a supported result, not permission to relax requirements silently.

Fixed candidate: gain, hardware and correction: Gain 2 W/K; Standard enclosure; subtract 0 degC sensor correction Scenario for conditional tradeoffs: Nominal

Reset keeps your prediction, captures and practice history.

Keep the candidate fixed while changing the test condition

1: gain 2 W/K · Standard enclosure · subtract 0°C. Each matrix row retains one gain, hardware and subtracted correction across all four public scenarios. The selected detail scenario is Nominal. Changing the scenario selector inspects a different condition; it does not retune this candidate.

These are 48 deterministic model combinations, not 48 manufactured devices or independent trials. Passing a fraction of these four selected cases describes only this public suite; it is not a field reliability probability. All outcomes are development evidence with known public exposure.

Compare all twelve candidates across four scenarios

Every supplied criterion is retained. A cell passes only when all four pass.
Fixed candidate	Nominal	Two-sample delay (20 s)	Sensor offset +2 degC	Heater limited to 8 W	Cases meeting all criteria
1: gain 2 W/K · Standard enclosure · subtract 0°C (selected)	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	2 / 4 Not feasible across all four
2: gain 2 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
3: gain 2 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
4: gain 2 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	0 / 4 Not feasible across all four
5: gain 6 W/K · Standard enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
6: gain 6 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
7: gain 6 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
8: gain 6 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
9: gain 12 W/K · Standard enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
10: gain 12 W/K · Standard enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: fail Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
11: gain 12 W/K · Insulated enclosure · subtract 0°C	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four
12: gain 12 W/K · Insulated enclosure · subtract 2°C	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: fail Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: pass Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	Tail 29–31°C at 90–120 s: fail Peak ≤32°C: pass Input ≤2000 J: pass Cost ≤6 tokens: pass	1 / 4 Not feasible across all four

No candidate meets all four scenarios in this finite suite. In particular, the 8 W case fails the finite-time tail requirement even for insulated hardware. Its constant-input equilibrium is 20 + 8/0.5 = 36°C, but its 200 s time constant means the 20°C start reaches only about 27.219°C after 120 s. This is a finite-time service failure, not proof that insulation makes 29°C permanently unreachable. Standard hardware instead has an 8 W equilibrium of 28°C.

Selected candidate: separate requirements in each condition

Same candidate, same initial temperature and 120 s horizon; scenario changes are explicit
Scenario	Tail samples at 90, 100, 110, 120 s (°C)	Peak (°C)	Applied input (J)	Assigned cost	All criteria
Nominal	29.359, 29.542, 29.673, 29.766 Pass	29.766 at 120 s Pass	1821.035 Pass	3 tokens Pass	Pass
Two-sample delay (20 s)	30.341, 30.359, 30.294, 30.201 Pass	30.359 at 100 s Pass	1922.517 Pass	3 tokens Pass	Pass
Sensor offset +2 degC	28.187, 28.324, 28.422, 28.492 Fail	28.492 at 120 s Pass	1607.588 Pass	3 tokens Pass	Fail
Heater limited to 8 W	24.747, 25.057, 25.337, 25.590 Fail	25.590 at 120 s Pass	960.000 Pass	3 tokens Pass	Fail

Temperature judgments use full precision, not rounded display values. Held-input exact one-node intervals are monotonic toward their interval equilibria, so endpoint samples bound their peaks and the intervening tail temperatures here. This is not a general claim about physical temperature fields. A passing energy budget cannot compensate for a failed temperature requirement.

Cost and input energy within one feasible scenario

For Nominal, feasible means meeting all four supplied requirements. The comparison then minimizes only assigned token cost and applied heater energy. A candidate is nondominated if no other feasible candidate is no worse on both and strictly better on at least one. Equal pairs do not dominate each other. This conditional comparison excludes other priorities and is not a universal best design.

Feasible candidates only · fixed axes: cost 3–5 tokens, input 0–2400 J

Circles: feasible pairs. Outer squares: nondominated pairs. Identical or nearby points can overlap; the table retains every candidate. Points outside the fixed scale are omitted with a notice, never moved onto the boundary.

Nominal: retain rejected candidates and their failed criteria alongside the feasible comparison
Candidate	Cost (tokens)	Applied input (J)	Failed criteria	Cost–energy status
1: gain 2 W/K · Standard enclosure · subtract 0°C	3	1821.035488	None	Feasible and nondominated
2: gain 2 W/K · Standard enclosure · subtract 2°C	3	2012.930200	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
3: gain 2 W/K · Insulated enclosure · subtract 0°C	5	1624.624719	Tail 29–31°C at 90–120 s	Excluded: infeasible
4: gain 2 W/K · Insulated enclosure · subtract 2°C	5	1809.091605	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible
5: gain 6 W/K · Standard enclosure · subtract 0°C	3	1887.808894	None	Feasible, dominated on cost/energy
6: gain 6 W/K · Standard enclosure · subtract 2°C	3	2130.915020	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
7: gain 6 W/K · Insulated enclosure · subtract 0°C	5	1558.581071	None	Feasible, dominated on cost/energy
8: gain 6 W/K · Insulated enclosure · subtract 2°C	5	1790.699641	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible
9: gain 12 W/K · Standard enclosure · subtract 0°C	3	1893.370525	None	Feasible, dominated on cost/energy
10: gain 12 W/K · Standard enclosure · subtract 2°C	3	2153.177644	Tail 29–31°C at 90–120 s; Input ≤2000 J	Excluded: infeasible
11: gain 12 W/K · Insulated enclosure · subtract 0°C	5	1515.220813	None	Feasible and nondominated
12: gain 12 W/K · Insulated enclosure · subtract 2°C	5	1757.975786	Tail 29–31°C at 90–120 s; Peak ≤32°C	Excluded: infeasible

Selected run: all thirteen true states

1: gain 2 W/K · Standard enclosure · subtract 0°C · Nominal
Time (s)	True temperature (°C)
0	20.000000
10	21.903252
20	23.625385
30	25.183636
40	26.558649
50	27.541112
60	28.243095
70	28.744670
80	29.103051
90	29.359119
100	29.542083
110	29.672812
120	29.766220

Selected run: all twelve observation, command and energy receipts

Commands occur at 0–110 s; 120 s is the final state, not a new observation command. The delayed scenario requests t − 20 s. Negative requested times use the held initial state at effective time 0, not a measured prehistory. Raw indication adds the scenario bias to the selected true observation; corrected indication subtracts the candidate correction of 0°C. A nonzero correction is not automatically appropriate in an unbiased scenario.

Held input for each 10 s interval; positive ambient energy is outward
Step / interval (s)	True start → end (°C)	Requested / effective observation (s)	Raw / subtracted correction / corrected (°C)	Error (K)	Requested / applied (W)	Clipping	Input (J)	Stored change (J)	To ambient (J)	Residual (J)
0: 0–10	20.000000 → 21.903252	0 / 0	20.000000 / 0 / 20.000000	10.000000	30.000000 / 20.000000	Upper	200.000000	190.325164	9.674836	0.00e+0
1: 10–20	21.903252 → 23.625385	10 / 10	21.903252 / 0 / 21.903252	8.096748	26.193497 / 20.000000	Upper	200.000000	172.213330	27.786670	0.00e+0
2: 20–30	23.625385 → 25.183636	20 / 20	23.625385 / 0 / 23.625385	6.374615	22.749230 / 20.000000	Upper	200.000000	155.825065	44.174935	0.00e+0
3: 30–40	25.183636 → 26.558649	30 / 30	25.183636 / 0 / 25.183636	4.816364	19.632729 / 19.632729	None	196.327288	137.501302	58.825986	0.00e+0
4: 40–50	26.558649 → 27.541112	40 / 40	26.558649 / 0 / 26.558649	3.441351	16.882703 / 16.882703	None	168.827028	98.246365	70.580663	0.00e+0
5: 50–60	27.541112 → 28.243095	50 / 50	27.541112 / 0 / 27.541112	2.458888	14.917775 / 14.917775	None	149.177755	70.198232	78.979523	0.00e+0
6: 60–70	28.243095 → 28.744670	60 / 60	28.243095 / 0 / 28.243095	1.756905	13.513811 / 13.513811	None	135.138108	50.157497	84.980612	0.00e+0
7: 70–80	28.744670 → 29.103051	70 / 70	28.744670 / 0 / 28.744670	1.255330	12.510661 / 12.510661	None	125.106609	35.838146	89.268463	0.00e+0
8: 80–90	29.103051 → 29.359119	80 / 80	29.103051 / 0 / 29.103051	0.896949	11.793898 / 11.793898	None	117.938980	25.606795	92.332185	0.00e+0
9: 90–100	29.359119 → 29.542083	90 / 90	29.359119 / 0 / 29.359119	0.640881	11.281762 / 11.281762	None	112.817621	18.296369	94.521252	0.00e+0
10: 100–110	29.542083 → 29.672812	100 / 100	29.542083 / 0 / 29.542083	0.457917	10.915835 / 10.915835	None	109.158347	13.072980	96.085368	0.00e+0
11: 110–120	29.672812 → 29.766220	110 / 110	29.672812 / 0 / 29.672812	0.327188	10.654375 / 10.654375	None	106.543751	9.340804	97.202947	0.00e+0

Whole-run balance: 1821.035488 J applied input = 976.622047 J stored change + 844.413440 J signed ambient transfer. Residual -3.41e-13 J. Display rounding can create a small apparent discrepancy.

Original fictional one-node device and assigned costs. Uniform temperature, constant heat capacity/conductance/ambient, held heater input and exact exponential propagation within each sample. No spatial gradient, evaporation, radiation law, random noise, active cooling, integral control or physical safety/efficiency/reliability certification. Public cases are exposed teaching practice. The 2000 J requirement is an acceptance criterion, not an automatic cutoff. Token cost is fictional; heater input is not a measured wall-plug consumption. No averaging of these indicators repairs a failed requirement.

Your investigation: predict the scenarios a fixed candidate will fail, inspect its receipts and retain a failure explanation. Compare a second candidate without changing the criteria. Explain one tradeoff and one condition outside this finite public suite before recommending a design.

Selected fixed candidate meets all criteria in 2 of 4 supplied public cases. Nominal: all requirements met.

Selected case: 1821.035 J applied heater energy; 3 assigned tokens. 5 feasible candidates in this scenario; 2 nondominated on cost and energy. This case count is not field reliability. Changing correction between scenarios would define different candidates.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Record what failed before naming its cause

A failure log connects a requirement with evidence and a proposed next step. “The controller is bad” identifies neither the violated requirement nor the condition that produced it. Begin with a particular candidate: standard enclosure, gain 6 W/K, correction 0°C. Keep those three choices fixed while comparing nominal and delayed operation.

The suite offers twelve candidates, combining three gains, two hardware choices and two corrections. Each is evaluated under the same four public scenarios: nominal, 20-second sensing delay, +2°C sensor offset and an 8 W heater limit. Selecting a different scenario does not authorize a different correction or gain when claiming performance of one candidate across the suite. The full matrix contains 48 deterministic combinations, not 48 measured prototypes.

Distinguish requirement, symptom and explanation

For the selected delayed case, temperatures at 90, 100, 110 and 120 seconds are approximately 31.474, 31.295, 30.593 and 29.695°C. The requirement is 29–31°C at every one of those samples. The symptom is therefore two upper-band violations. The passing final temperature does not cancel the earlier failures. Peak remains below 32°C, input energy below 2,000 J and cost below six tokens; those are separate entries in the log.

A proposed explanation is that old sensor information keeps the applied heating too high after the true state has risen. That mechanism is consistent with the delayed-case receipts. It is different from the observation itself. In actual equipment, alternative explanations might include a sensor offset or a changed thermal boundary; they would need distinguishing evidence. Here the scenario deliberately supplies the cause, so the activity practices reasoning rather than discovering an unknown real fault.

Create a log with columns for candidate/version, scenario, requirement, failing value/time, mechanism hypothesis, alternative explanation and proposed retest. Include units. Record “31.474°C at 90 s exceeds 31°C,” rather than merely marking a red cell. A table reader should understand the failure without relying on color.

Reproduce before revising

Capture the selected recipe and explain its 120-second horizon, 20°C start and ambient, fixed standard hardware and correction. Inspect the same case again to check that the result can be reconstructed. Reproducing a deterministic result confirms the recipe was applied consistently; it does not add a new physical specimen or independent failure observation.

Next compare gain 2 while retaining standard hardware, zero correction and the delayed scenario. Its tail samples all lie in the band. That is a candidate revision, not a correction to the original failed record. Keep both captures and explain the changed input. Return to controller redesign for the detailed tradeoff, including the small increase in energy for this successful delayed-case revision.

NASA’s verification guidance connects compliance evidence with stated requirements and test conditions. The original log here supports a bounded model comparison; it does not validate intended physical use, provide a field failure rate or certify safety.

Recognize distinct kinds of heating failure

Switch the standard candidate to the 8 W limited scenario. Every allowed gain has the same applied-power trace and ends near 25.590°C. Its constant-maximum-input equilibrium is only 28°C, below the 29°C lower requirement. Increasing gain cannot fix that capacity shortfall under the stated standard-plant boundary.

For insulated hardware, the same 8 W input has equilibrium 36°C, yet reaches only about 27.219°C at 120 seconds. This is still a failure of the stated deadline, but not proof that 29°C is permanently unattainable. The lower conductance also changes the time constant. Preserve this distinction in the cause column instead of grouping every cool endpoint as “heater can never reach target.”

Transfer: repair an incomplete failure report

A paper report says, “The insulated limited case failed because its equilibrium is below target.” Use conductance 0.5 W/K, ambient 20°C and constant input 8 W to check that sentence. Rewrite it without claiming a new widget run or changing the deadline.

Check the failure-description transfer

Equilibrium is 20 + 8/0.5 = 36°C, so the stated explanation is wrong. The run fails because its actual temperatures during the specified 90–120 s window remain below 29°C; its final value is about 27.219°C. A steady limit above target does not establish performance by a deadline. The corrected report preserves the failure while changing the causal interpretation.

Keep the original report beside the correction. Continue to reliability claims to explain what a suite of such logs can and cannot establish.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain which observed statement supports the failure and which causal statement still depends on the stipulated model.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Revise a controller while retaining its failure Next: Distinguish scenario coverage from field reliability

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