SCIENCE · INVESTIGATE AND EXPLAIN

Compare feasible designs before ranking preferences

Use scenario-specific cost and energy comparisons without hiding failed constraints.

Learning outcome: Identify nondominated feasible candidates and explain why a two-objective comparison does not select a universal best design.

Starting recap

A candidate is feasible only if all supplied criteria pass in the chosen scenario; tokens and joules are different objectives.

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Try

Nominal standard gain 2 zero correction costs 3 tokens and uses 1821.035 J; insulated gain 12 zero correction costs 5 and uses 1515.221 J.

Open the experiment

Predict

Predict whether either of those nominal candidates is no worse in both cost and energy.

Your prediction and reason

Experiment

Select nominal and inspect feasible candidates and the cost-energy comparison. Capture the two nondominated choices, calculate their energy difference, then switch scenario to delayed and retain changed feasibility.

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

Apply hard constraints before comparing preferences

A design with attractive energy use may still violate temperature requirements. Begin by selecting the nominal scenario and inspecting which candidates pass all supplied criteria: the four tail temperatures must be 29–31°C, peak no higher than 32°C, input energy no more than 2,000 J and cost no more than six tokens. Only then compare preferences among feasible designs.

The suite has five nominal feasible candidates. Their resource costs are fictional tokens, and their energy totals are modeled heater inputs over 120 seconds. Neither quantity is an actual purchase price, electricity bill or full lifecycle impact. Keep the units separate; adding tokens to joules without an explicitly chosen weighting rule creates an unexplained score.

Explain dominance with two concrete candidates

Within the nominal feasible set, the cost-energy comparison leaves two nondominated choices: standard hardware, gain 2, correction 0; and insulated hardware, gain 12, correction 0. A candidate dominates another in these two objectives if it is no worse in both and strictly better in at least one. Nondominated means no other feasible candidate improves one objective without worsening the other; it does not mean universally optimal.

The standard choice costs 3 tokens and uses about 1,821.035 J. The insulated choice costs 5 tokens and uses about 1,515.221 J. The insulated option uses approximately 305.815 J less while costing two additional tokens. The standard option is cheaper within the invented resource scale but uses more heater input. Neither dominates the other.

At the same standard-hardware cost, nominal gains 6 and 12 use more energy than gain 2 while still passing the specified temperature criteria. They are therefore dominated in this two-objective comparison. That statement does not erase their closer final tracking: final error is simply not a separate minimized objective in the cost-energy plot once feasibility has been checked.

A frontier belongs to its conditions

Capture the two nominal choices and write a preference rule before choosing one. For example, “Minimize tokens among feasible candidates” favors standard gain 2. “Minimize modeled input energy among feasible candidates” favors insulated gain 12. Those are chosen objectives, not scientific facts about what every stakeholder should value.

Now select delayed operation without silently changing the definition of a candidate. Only standard gain 2 with zero correction passes all supplied criteria in that scenario. A candidate’s nominal position on the cost-energy frontier does not establish delayed-case feasibility. The selected four-scenario suite is useful for seeing the broader limits of a promising nominal choice.

NASA’s system-design discussion connects alternatives and trade studies with requirements and decision criteria. This original exercise follows that reasoning pattern with supplied numbers; it does not claim a complete economic, social or environmental assessment of an actual product.

Resist a tempting calibration shortcut

Some candidates pass the +2°C offset scenario by subtracting the supplied two-degree correction. But correction remains fixed across the selected candidate’s entire suite. Applying it in an unbiased scenario changes the indicated temperature in the wrong direction. A candidate that succeeds when a correction happens to match a known bias does not automatically include a real calibration procedure or a method for detecting when bias changes.

One uncorrected insulated low-gain candidate also passes the offset scenario through the combined effects of hardware and controller. That coincidence is not evidence that its sensor is accurate. Distinguish meeting a temperature requirement in one case from correctly measuring the underlying state. The mechanism and the metrology need their own evidence.

Transfer: introduce a declared token ceiling

On paper, restrict nominal candidates to at most four tokens while retaining every original thermal and energy criterion. Which of the two nominal nondominated candidates remains eligible? If instead the ceiling is five and input energy is the sole preference among feasible candidates, which would be chosen? State one limit shared by both conclusions.

Check the preference-and-constraint transfer

With at most four tokens, the five-token insulated candidate is excluded and the three-token standard candidate remains eligible. With a five-token ceiling and minimum energy as the declared preference, insulated gain 12 correction 0 is chosen from the nominal feasible set. Both decisions depend on the stipulated nominal model and criteria; neither establishes all-scenario robustness, an actual price advantage or a physical product recommendation.

Keep the preference rule with the result so another learner can reproduce the decision. Return to design requirements for constraints versus preferences, then continue to unfamiliar failure to plan evidence beyond the known matrix.

Apply

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

State which priorities would justify a choice and why nominal Pareto membership cannot establish all-scenario robustness.

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: Distinguish scenario coverage from field reliability Next: Plan evidence for an unfamiliar failure

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