SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish scenario coverage from field reliability

Interpret a fixed public suite without inventing probabilities or independent replications.

Learning outcome: Report bounded pass counts, preserve common assumptions and identify evidence needed for a reliability estimate.

Starting recap

The matrix has twelve candidates and four deterministic scenarios, not forty-eight sampled physical devices.

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

Try

Standard gain 2 with zero correction passes nominal and delayed, but fails offset and limited operation.

Open the experiment

Predict

Predict whether repeating those four runs changes the number of distinct conditions covered.

Your prediction and reason

Experiment

Capture one fixed candidate and classify all four cases. Compare the selected-suite summary with the full matrix. State the denominator and retain failures instead of swapping candidates per scenario.

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

State the denominator before stating a percentage

Select standard hardware, gain 2 W/K and zero correction. This candidate passes nominal and delayed operation, but fails the offset and limited scenarios. It passes two of four supplied cases, or 50% of this suite. That arithmetic is useful when the denominator is clear. It is not a 50% probability that a physical product will work.

The four conditions are deliberately chosen deterministic tests. They were not randomly sampled from a population of users, environments or devices, and no occurrence frequencies were supplied. Equal space in the matrix does not mean equal likelihood in actual use. A suite pass fraction describes coverage of these particular conditions and requirements.

Keep one candidate fixed

The selected candidate contains gain, hardware and correction. All three remain fixed across the four-case summary. It would be misleading to use correction 0°C in nominal operation and correction 2°C in the offset case, then report those passes as one fixed candidate’s performance. Such adaptation would require its own rule for detecting bias and choosing a correction. The present candidate does not contain that rule.

Inspect the full 48-combination matrix. Five candidates pass nominal, one passes delayed, six pass offset and none passes the limited scenario. Adding those counts gives 12 passing combinations, but 12/48 is still a property of a deliberately constructed matrix. It is neither a field reliability estimate nor the success probability of a selected design. Different rows correspond to different candidates, so the aggregate answers a different question from a fixed candidate’s two-of-four result.

Write both denominators in your notebook: four scenarios for one candidate, and 48 candidate/scenario combinations for the matrix. Explain why mixing them can make a weak claim look stronger without supplying new evidence.

Repetition is not a new condition

Capture the selected recipe and repeat its evaluation. The same pure model and inputs return the same outputs. That can demonstrate reproducibility and help find transcription mistakes. It does not produce another independently manufactured unit or another sample from an operating population. Ten replays of four cases do not create forty distinct conditions.

All cases share assumptions: one uniform temperature, fixed heat capacity and conductance, the same 120-second horizon and exact held-input propagation. If those assumptions omit an important process, every row can share that weakness. Passing several rows therefore does not rule out common model inadequacy. Nor can the four pass/fail outcomes be multiplied as independent probabilities; no such probabilistic model is present.

NIST’s reliability discussion explains that actual failure observations matter when estimating reliability and that extrapolating from stresses requires a model. This exercise is narrower still: its cases are synthetic, so it supplies no empirical lifetime or failure-rate data to fit.

Treat an empty feasible intersection honestly

No candidate passes all four supplied scenarios. The limited case prevents an all-four pass among these twelve candidates. This is an exhaustive result only for the stated finite candidate set and criteria. It does not prove that every imaginable enclosure, actuator, correction method or operating rule is incapable of satisfying an expanded design brief.

The supported response is to state the failed requirement and consider what new design freedom or revised requirement would need investigation. Do not silently lower the standard after seeing failure, and do not promise that an unmodeled change will succeed. A larger heater, a different time horizon or a revised thermal system would need explicit assumptions and new calculations.

Transfer: compare different suites

A paper team reports eight passes in ten selected conditions; another reports three passes in four different conditions. Calculate both fractions. Can the percentages alone establish which physical product is more reliable? Name information needed for a meaningful comparison.

Check the suite-denominator transfer

The fractions are 80% and 75%. The suites differ, so the percentages alone cannot rank field reliability. You would need common failure definitions, comparable test conditions and relevant sampling or operating-frequency evidence, plus a justified model for any extrapolation. The ten and four cases are hypothetical public practice, not additional measurements in the widget.

Conclude with a scoped statement such as “This fixed candidate passes these two named cases and fails these two under the supplied criteria.” Return to controls and replication if repeated readings and independent units are still unclear. Continue to design tradeoffs to choose among feasible candidates without mistaking preference for probability.

Apply

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

Explain why 2/4 is descriptive suite coverage, why scenario probabilities are unknown and why no all-four pass is not universal impossibility.

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: Turn failed requirements into a useful failure log Next: Compare feasible designs before ranking preferences

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