Trade study example: a weighted decision matrix with sensitivity analysis

What a trade study is, and when to run one

A trade study is a structured comparison of alternative solutions to one design question, against criteria that come from what the system has to do. Its output is not only a choice but a record: which options were considered, how they were judged, how sure the result is, and why the team picked what it picked. ISO/IEC/IEEE 15288 places this work in its decision management process, and the INCOSEInternational Council on Systems Engineering The professional society for systems engineering. It publishes the Systems Engineering Handbook. Systems Engineering Handbook describes the same pattern under decision analysis.

Run a trade study when a decision has these traits:

• Several credible options. If one option clearly wins on everything that matters, write down why and move on.
• Competing criteria. The fastest option is the heaviest and the hungriest for power; the cheapest one may not be enough. A trade study makes the exchange rate between criteria explicit.
• Consequences that are expensive to undo. Architecture choices, technology selections, make-or-buy decisions and major interfaces are typical.
• Someone will ask later. A reviewer, a customer or the engineer who inherits the design will want to know why. The study is the answer.

A trade study does not replace engineering judgment. It organizes judgment so that others can see it, challenge it and repeat it.

The example: choosing the CubeSat EO-1 downlink band

The example is the trade study inside the CubeSat EO-1 project, the small Earth-observation satellite that the MBSE example project walks through from mission need to verification. Every name, number and identifier below comes from that model, so the study can be followed in the same project.

EO-1 images crops from orbit and sends the pictures down to partner ground stations. Before the preliminary design review (PDRPreliminary Design Review A milestone review that confirms the preliminary design meets the requirements and is ready for detailed design.), the team had to choose the radio band for the payload downlink. The study is TR-1 Downlink Band Selection, and it feeds the decision DEC-1 Select Payload Downlink Band. These parts of the model bear on it:

Step 1: define the decision, list the alternatives, screen

Write the decision as a question with a scope: Which radio band will carry the payload downlink? A precise question keeps the study from drifting into neighboring decisions, such as which ground stations to contract or which antenna to fly.

Then list the alternatives, wide at first. The study carries three:

1. 1.5.2 S-band Transmitter: 2.2 GHz, 10 Mbps, the baseline design.
2. ALT-X X-band Transmitter: 8.2 GHz with a patch array, 50 Mbps.
3. ALT-KA Ka-band Transmitter: 26 GHz with a horn antenna, 150 Mbps.

Screen before you score. Requirements that every option must meet are pass/fail gates, not weighted criteria. Requirement 5.1 sets the rate at 10 Mbps. (Its text names the S-band transmitter because the requirement was written against the chosen design; as a screen it is the 10 Mbps rate.) All three bands meet it, so all three go forward. To show what a gate does, take a fourth idea that a first workshop might raise and that the demo does not contain: send the payload data over the UHFUltra High Frequency Radio frequencies from 300 MHz to 3 GHz, often used for spacecraft command links. transceiver the spacecraft already carries. At 9.6 kbps (Requirement 5.2) it misses 10 Mbps by a factor of about a thousand, so it leaves the study here, with that reason recorded. If you let a non-compliant option into the matrix, high scores for mass, power and cost could hide the fact that it cannot do the job.

Know which limits are gates. The Ka-band unit weighs 0.6 kg, more than the whole communications allocation of 0.55 kg. An allocation is the team's own design choice and can be rebalanced, so here it stays in the scoring as the Mass criterion rather than as a gate. If the limit were a customer requirement, Ka-band would leave at this step.

Step 2: derive the criteria from requirements, measures and risks

A criterion measures how well an alternative does something the stakeholders care about. Good criteria trace to a requirement, a measure or a risk, discriminate between the alternatives, and are independent of one another. The study uses six:

Two of the criteria are ratings rather than measurements. Write down what the ends of each scale mean before rating, as the descriptions above do, so that a 6 means the same to every rater.

Check the set for overlap. Ground station availability and licensing schedule both depend on how crowded and regulated a band is; they stay separate here because one asks whether stations exist and the other whether permission will arrive in time. Mass and power draw both grow with transmitter size, but they draw on different budgets. Write each boundary down so nobody merges or splits criteria later to move the result.

Step 3: set the weights, and know their pitfalls

Weights state how much each criterion matters relative to the others. Set them with the stakeholders before anyone enters the alternatives' values. The study uses integer weights:

Normalizing (dividing each weight by the total) makes the weights sum to 1, so the weighted score stays on the same 0–10 scale as the criterion scores, whatever raw numbers the team chose.

Common weighting pitfalls:

• False precision. A weight of 0.237 suggests a confidence nobody has. Coarse weights plus a sensitivity analysis are more honest.
• Too many criteria. With fifteen criteria, each gets a few percent and none can change the result. Five to eight is usually enough; merge or drop the rest.
• Weights that hide a requirement. A mandatory requirement with weight 1 can be outvoted. Mandatory items belong in screening, as Requirement 5.1 did in step 1.
• Weights set after the scores. Once the team has seen the numbers, every weight change is suspected of steering the answer, often rightly.

Structured methods such as pairwise comparison (each criterion against each other one) can help a group agree on weights. They do not remove the judgment; they make it traceable.

Step 4: scoring scales and normalization

The raw values have different units: megabits per second, kilograms, watts, dollars, ratings. To add them up, each raw value becomes a score on a common scale, here 0 to 10. The study uses two methods.

Linear scale between a worst and a best value. The worst value scores 0, the best scores 10, values in between are interpolated, and values outside are clamped. For a lower-is-better criterion the worst value is the higher one.

score = 10 × (value − worst) / (best − worst), clamped to 0…10

Direct rating. Ground station availability and licensing schedule are already 1–10 ratings, so the rating is the score.

The anchors carry judgment, and this study shows both kinds:

• Fixed anchors (Data Rate). The scale starts at the TPM-3 threshold and stops at 60 Mbps, so Ka-band's 150 Mbps scores the same 10 as 60 Mbps would. That cap is a statement that the mission cannot use more rate, and it matters: on a scale anchored to the entered values (8 → 150 Mbps) X-band's 50 Mbps would score 2.96 instead of 8.08, and its weighted score would drop from 6.13 to 4.94. Note also that S-band meets Requirement 5.1 yet scores only 0.38 for rate. The criterion rewards rate beyond the requirement, so its weight is really a bet on whether the mission will need more data later.
• Anchors from the range (Mass, Power Draw, Recurring Cost). The study leaves these anchors blank, so the tool uses the lowest and highest entered values. That is quick, but it stretches small differences: 0.28 kg separates the lightest and heaviest unit, and that gap gets the full 10 points. Range anchors also move whenever an alternative is added or dropped, which changes the other alternatives' scores. Where a requirement or allocation gives a limit, anchor to it instead.

A linear scale assumes every unit of improvement is worth the same. Where it is not, a stepped scale (thresholds) or a curved value function fits better. Keep it simple until the sensitivity analysis says the shape matters.

Step 5: the weighted decision matrix

The values for each alternative, from the model's characteristics and the team's ratings:

Converted to scores with the scales above. Take X-band's power draw as an example: 10 × (5.8 − 9.5) / (3.4 − 9.5) = 10 × 3.7 / 6.1 = 6.07.

The weighted score is the sum of each score times its normalized weight. For S-band, with the weights to four places:

0.2308 × 0.385 + 0.0769 × 10 + 0.1538 × 10 + 0.2308 × 9 + 0.1538 × 8 + 0.1538 × 10
= 0.089 + 0.769 + 1.538 + 2.077 + 1.231 + 1.538
= 7.24

Rounding bites here: with the three-place weights from the table (0.231, 0.077, 0.154) the same sum comes to 7.25. The weights add to 1.001 after rounding, and the error lands in the second decimal.

Check it a second way, with the raw weights. Multiply by the integer weights, add, and divide by their sum, 13. No rounded weight enters the calculation:

S-band:  (3×0.385 + 1×10.00 + 2×10.00 + 3×9 + 2×8 + 2×10.00) / 13 = 94.15 / 13 = 7.24
X-band:  (3×8.077 + 1×5.357 + 2×6.066 + 3×5 + 2×6 + 2×5.455)  / 13 = 79.63 / 13 = 6.13
Ka-band: (3×10.00 + 1×0     + 2×0     + 3×2 + 2×4 + 2×0)      / 13 = 44.00 / 13 = 3.38

And a third, coarser view: the Pugh matrix. With S-band as the datum, mark each other alternative better (+), the same (0) or worse (−) per criterion. X-band and Ka-band are each better on one criterion (data rate) and worse on five, so both net −4. Weighting the marks gives 3/13 − 10/13 = −0.54 for each: worse than the datum. The Pugh view cannot separate X-band from Ka-band, but it agrees with the matrix on the leader, and it makes the shape of the trade plain: one strong advantage against five disadvantages.

All three views agree, and the same totals come out of the tool in the screenshots further down. S-band leads X-band by 1.12 points on a 10-point scale; Ka-band is far behind. A lead is still only as good as the weights behind it, which is what the next step tests.

Step 6: sensitivity analysis: how far must a weight move to flip the result

The weights are the least certain inputs in the study. A sensitivity analysis changes one weight at a time, keeps the other weights as they are, and finds the weight at which the leader changes, the rank reversal point. The further a reversal point is from the current weight, the sturdier the decision.

Worked by hand for Data Rate. Let its raw weight be w; the other five stay as they are (total 10). Each alternative's weighted sum is its sum without data rate plus w times its data rate score, and every total is divided by the same 10 + w, so the leader is whoever has the larger sum:

S-band:  (94.15 − 3×0.385) + 0.385w = 93.00 + 0.385w
X-band:  (79.63 − 3×8.077) + 8.077w = 55.40 + 8.077w
Equal when 93.00 + 0.385w = 55.40 + 8.077w  →  w = 37.60 / 7.692 = 4.89
Normalized: 4.89 / (10 + 4.89) = 0.328   (now 3 / 13 = 0.231)

Ka-band: (44.00 − 3×10) + 10w = 14.00 + 10w
Overtakes X-band when 14.00 + 10w = 55.40 + 8.077w  →  w = 21.5, normalized 0.683

A data rate weight of 4.9 instead of 3 hands the lead to X-band; Ka-band leads only when data rate carries more than two thirds of the total weight. The same calculation for every criterion:

The five robust criteria have no reversal at any weight from 0 upward: S-band scores at least as well as both rivals on each of them, so more weight only widens its lead, and with the weight at 0 the remaining criteria still favor it.

How to read it:

• The decision rests on one weight. Only data rate can change the leader. A move of 0.098 in its normalized weight (from 0.231 to 0.328) does it, which is about a 42 % increase. That is not far: a tornado chart with each weight moved by ±50 % shows S-band's lead of 1.12 points growing to 2.44 at the low end and turning into a 0.20-point deficit at the high end.
• The question behind the weight is the data volume. Data rate matters more only if the mission needs to move more data than S-band can carry. That is a question about future collection plans, not about radio bands, and it is the condition the decision record should name.
• The scale matters as much as the weight. As step 4 showed, the 60 Mbps cap and the 8 Mbps floor set X-band's data rate score. Anchor the scale differently and the reversal point moves.
• Robust criteria need less debate. No weight on mass, power, ground stations, licensing or cost changes the leader, so arguments about those weights do not change the decision.

Sensitivity to the weights is one kind of uncertainty. The values are uncertain too (the X-band power draw is an estimate, the ratings are judgments); when they carry ranges rather than single numbers, a Monte Carlo analysis shows how often each alternative wins.

The engineering consequence of the runner-up. The matrix says X-band is second; the model says what choosing it would cost. Its 5.8 W draw is 2.4 W more than S-band's 3.4 W. At PDRPreliminary Design Review A milestone review that confirms the preliminary design meets the requirements and is ready for detailed design., TPM-2 shows 15 % margin on the 28 W orbit-average allocation against a 10 % threshold, and 2.4 W is about 8.6 % of 28 W, so X-band would push the power margin below its threshold. Its 0.45 kg unit leaves 0.01 kg of the 0.55 kg communications allocation once the 0.09 kg UHFUltra High Frequency Radio frequencies from 300 MHz to 3 GHz, often used for spacecraft command links. transceiver is counted. A weight debate that ends in X-band must also reopen the power budget.

Step 7: record the rationale and link it to requirements and risks

The decision record is the part people read years later. It should state:

• the decision question and the alternatives, including the ones screened out and why;
• the criteria with their sources, weights, scales and the assumptions behind them (here: the 60 Mbps cap on data rate; range anchors on mass, power and cost);
• the result, the margin of the lead and the sensitivity findings;
• the choice, who made it and when;
• the conditions under which the decision should be revisited.

The demo records DEC-1 as decided for the S-band transmitter on 18 June 2026, with this rationale:

S-band scores highest: every partner station supports it, the license request is filed and the unit costs less. X-band ranks second and wins only if the data rate weight rises well above the other criteria; revisit if the daily volume grows beyond 5 GB.

It names the result, the runner-up, the one weight that can flip it, and a measurable trigger for revisiting. The numbers from step 6 make "well above" exact: a data rate weight of 4.9 against 3 for ground station availability, the next highest.

Then link it:

• Requirements. DEC-1 traces from Requirement 5.1, so a change to the rate requirement flags the decision for review. Tracing it also to TPM-3, TPM-1 and TPM-2 (and through them to Requirement 3.1) connects it to the measures its criteria came from. The requirements traceability guide covers how such links answer "what is affected if this changes".
• Risk. Choosing S-band makes the mission depend on a frequency license. That is RK-4, S-band License Delay: caused by the communications subsystem, mitigated by the task File S-band Frequency License (done), now on watch with the trigger "no license decision by 1 June 2027". The licensing criterion scored S-band 8 because the request was filed; the risk keeps watching the part that is not yet certain. Relate the decision to RK-4 so that if the risk is realized, the record already says which alternative is next.

Common mistakes

• Criteria that double-count. Mass and launch cost, power draw and battery size, licensing and band congestion: when one physical fact feeds two criteria, it gets twice its weight. Define each criterion so that it measures something the others do not, and write the boundary down.
• Scoring to a pre-chosen answer. When the team already has a favorite, criteria, scales and weights drift until it wins. Fix the criteria, weights and scales before entering values, have someone outside the design team review the ratings, and treat a large swing in weights after the first results as a warning sign.
• Weighting a mandatory requirement. Must-meet items are gates. Scoring them lets a non-compliant option win on points.
• Scales anchored to the options. Scaling each criterion to the best and worst option in the table makes small differences look large and makes every score shift when an option is added or dropped. Anchor scales to requirement limits, allocations and meaningful targets.
• Rewarding performance nobody needs. A scale that keeps paying for rate, range or accuracy beyond what the mission can use favors the most capable option for no benefit. Cap the scale where the value stops.
• Reporting the winner without the margin. A 0.2-point lead and a 2-point lead are different decisions. Show the sensitivity result next to the ranking.
• Losing the study. A spreadsheet in someone's folder is not a decision record. Keep the study with the requirements and risks it depends on.

Try it in Holarch

Download the completed decision matrix: CubeSat downlink band trade study (Excel workbook with the scoring and sensitivity formulas), or the same matrix as CSV values with scores and totals. Change a weight or a value in the workbook to see the totals and the data rate reversal point move.

Holarch has trade studies built in: a Decision with its alternatives, weighted criteria with scoring methods, a decision matrix, a Pugh matrix, sensitivity charts and a recorded decision. Its scoring follows the rules on this page (0–10 scores, linear scales between a worst and a best value, weights normalized to sum to 1), and the CubeSat EO-1 demo project contains this study, so the numbers above appear there.

1. Create the demo with Manage Projects → Project Files ▾ → New Demo Project, then open Risk & Decisions → Trade Studies and click Downlink Band Selection.
2. On the Decision Matrix tab, change a Weight or click a Scoring button to change a scale; the scores, the weighted score row and the ranking update as you type. Mass and power draw come from the model's characteristics through Pull Values from Model.
3. Open Pugh Matrix to compare the rivals with the S-band datum.
4. Open Sensitivity and choose a criterion in the Weight Sweep. The Rank Reversal Points table lists the reversal for every criterion and marks the others Robust.
5. To run a study of your own, click + New Trade Study, add alternatives with + New, criteria with + Criterion, and finish with Record Decision…. The Decision's status becomes Decided.

The steps in detail are in Run a trade study and record the decision; every tab and export is described under Trade Studies.

Where to go next

• Risk and decisions in Holarch: the risk register, risk matrix, trade studies and decision records.
• Risk & Decisions docs: the full reference for trade studies, sensitivity and recorded decisions.
• Budgets & TPMs docs: the mass and power budgets and the TPMsTechnical Performance Measure A key technical parameter, such as mass or power, tracked over time against its target and threshold. a trade study draws on.