Weighted decision matrix
Compare options against weighted criteria, with scoring scales, must-have gates, sensitivity to the weights and a ranked result.
Manufacturing, fab and supplyFree to useHow it worksSourcesWhere it helps
Fills the inputs below with typical figures. Replace any of them with your own.
- Best option
- Option A
- 3.700 out of 5; 0.100 ahead of Option B
- Options in the running
- 3 of 3
- No option is knocked out
- Most sensitive weight
- Cost
- The leader is overtaken by Option B if its share moves from 30.0% to 33.3%, a weight of 3.5
- With equal weights
- Option A
- Same leader as with your weights
Sign in to save your inputs and come back to them later.
Options that miss a must-have are shown last and are not ranked.
- Option A3.700rank 1
- Option B3.600rank 2
- Option C3.500rank 3
Show the data as a table
| Item | Total |
|---|---|
| Option A | 3.700 |
| Option B | 3.600 |
| Option C | 3.500 |
Each criterion's share of the weight times the option's score on it. The bars add up to the total.
- Performance2.000weight share 50.0%
- Cost0.900weight share 30.0%
- Risk0.800weight share 20.0%
Show the data as a table
| Item | Contribution |
|---|---|
| Performance | 2.000 |
| Cost | 0.900 |
| Risk | 0.800 |
| Rank | Option | Status | Total (out of 5) | Share of the best possible | Rank with equal weights |
|---|---|---|---|---|---|
| 1 | Option A | In the running | 3.700 | 74.0% | 1 |
| 2 | Option B | In the running | 3.600 | 72.0% | 1 |
| 3 | Option C | In the running | 3.500 | 70.0% | 3 |
| Criterion | Weight share | Option A | Option B | Option C |
|---|---|---|---|---|
| Performance | 50.0% | 2.000 | 1.500 | 2.500 |
| Cost | 30.0% | 0.900 | 1.500 | 0.600 |
| Risk | 20.0% | 0.800 | 0.600 | 0.400 |
| Total | 3.700 | 3.600 | 3.500 |
| Criterion | Weight now (share) | Weight that changes the winner (share) | Change in share | Overtaken by |
|---|---|---|---|---|
| Performance | 5 (50.0%) | 4 (44.4%) | −5.6 points | Option B |
| Cost | 3 (30.0%) | 3.5 (33.3%) | +3.3 points | Option B |
| Risk | 2 (20.0%) | 1 (11.1%) | −8.9 points | Option C |
- Option A (solid line, circles)
- Option B (dashed line, squares)
- Option C (dotted line, triangles)
Show the data as a table
| Share of the weight on Performance (%) | Option A | Option B | Option C |
|---|---|---|---|
| 0% | 3.4 | 4.2 | 2 |
| 5% | 3.43 | 4.14 | 2.15 |
| 10% | 3.46 | 4.08 | 2.3 |
| 15% | 3.49 | 4.02 | 2.45 |
| 20% | 3.52 | 3.96 | 2.6 |
| 25% | 3.55 | 3.9 | 2.75 |
| 30% | 3.58 | 3.84 | 2.9 |
| 35% | 3.61 | 3.78 | 3.05 |
| 40% | 3.64 | 3.72 | 3.2 |
| 45% | 3.67 | 3.66 | 3.35 |
| 50% | 3.7 | 3.6 | 3.5 |
| 55% | 3.73 | 3.54 | 3.65 |
| 60% | 3.76 | 3.48 | 3.8 |
| 65% | 3.79 | 3.42 | 3.95 |
| 70% | 3.82 | 3.36 | 4.1 |
| 75% | 3.85 | 3.3 | 4.25 |
| 80% | 3.88 | 3.24 | 4.4 |
| 85% | 3.91 | 3.18 | 4.55 |
| 90% | 3.94 | 3.12 | 4.7 |
| 95% | 3.97 | 3.06 | 4.85 |
| 100% | 4 | 3 | 5 |
How it works
A decision matrix compares options against the criteria that matter, with a weight for each criterion. This tool scores each option by a weighted sum of scores or raw values, or by a Pugh comparison against a baseline, drops options that miss a must-have, ranks the rest, shows what each criterion contributes, and finds how far each weight could move before the winner changes.
- Set the options, criteria and weights. List up to eight options and up to twelve criteria. Give each criterion a weight for how much it matters and, for raw values, a direction. The weights are turned into shares of their total, so only their ratios matter.
share of criterion j = weight j / sum of all weights - Apply the must-have gates. A must-have is a threshold that an option has to meet to stay in the comparison, whatever it scores elsewhere. An option that misses one is marked out and not ranked. In the score methods and Pugh the threshold is a minimum score or mark; for raw values it follows the direction, so a lower-is-better criterion has a maximum. An empty value cannot show that a threshold is met, so it fails the gate.
- Score each option on each criterion. In the score methods you enter a score from 1 to 5 or 1 to 10, with the best at the top. With raw values the tool scales each criterion for you: either from the worst option (0) to the best (1), or as a ratio to the best option. Scaling each criterion on its own makes quantities in different units comparable. A criterion on which every option has the same value scores 1 for all and so does not change the order.
worst to best: score = (x − worst) / (best − worst); ratio to best: score = x / best when higher is better, or best / x when lower is better - Add up the weighted scores. The total for an option is the sum, over the criteria, of the share times the score. Each term is that criterion's contribution, so the contributions add up to the total and show where an option wins or loses. The tool also totals with equal weights, so you can see whether the weights decide the result.
total i = sum over j of (share j x score ij) - Compare with a baseline (Pugh). In a Pugh matrix one option is the baseline, usually the incumbent or a reference design. Every other option is marked plus, 0 or minus on each criterion for being better than, the same as or worse than the baseline. The plain count adds the marks (a plus counts 1 and a minus counts −1); the weighted version multiplies each mark by the criterion's share. It ranks by direction of difference, so it suits an early screen before scores can be defended.
net marks = number of plus − number of minus; weighted net = sum over j of (share j x mark j) - Rank. Options that pass every gate are ranked by total, highest first. Equal totals share a rank.
- Find the weight change that would change the winner. For each criterion, the tool moves its weight share from 0 to 1 while the other shares keep their proportions, and finds where the leader would be overtaken. Each total is a straight line in that share, so the crossing point with each rival has a closed form; the nearest one is reported, as a share and as the equivalent raw weight. A criterion with no crossing in 0 to 1 cannot change the winner by its weight alone.
rest i = (total i − share x score i) / (1 − share); total i at share q = rest i + q x (score i − rest i); crossing q = (rest W − rest K) / ((rest W − score W) − (rest K − score K)) for leader W and rival K - Sweep one weight. The line chart plots the totals of the leading options as one chosen criterion's share runs from 0% to 100%. Where two lines cross, the order changes.
Assumptions
- Criteria are treated as independent, so the weighted sum can add them. Two criteria that measure the same thing count that thing twice.
- Scores on a 1 to 5 or 1 to 10 scale are ordinal judgements treated as numbers; the method adds them as if the steps between scores were equal.
- Scaling raw values from worst to best depends on the options in the comparison: adding or removing an option can change the scaled scores of the others. Options knocked out by a gate still set the scale.
- The sensitivity moves one weight at a time and keeps the others in proportion. It does not test changes to scores or several weights together.
- The example presets use invented figures. Replace them with quotes, measurements and your own judgement.
Limits and warnings
- A weighted sum can let a high score on one criterion hide a poor one on another. Use a must-have for anything that cannot be traded off.
- The ranking is only as good as the weights and scores. Close totals are not a decision: use the margin, the sensitivity and the equal-weight check before relying on the winner.
- The ratio method needs values above 0, and a ratio can reward a small absolute gain on a small number. The worst-to-best method does not have that problem but exaggerates small gaps when options are close.
- The Pugh methods keep only the direction of each difference, not its size.
- The tool does not model risk, uncertainty in the scores or time. For decisions with probabilities or cash flows use a decision tree or a cost model.
Sources
The methods and default figures rest on these public sources. The wording here is our own; read the source for its full text.
- Total Design: Integrated Methods for Successful Product Engineering, Addison-Wesley (Stuart Pugh), 1991. The origin of the Pugh matrix: concepts compared with a datum by plus, same and minus. Catalogue records give 1990 or 1991; this follows the 1991 Addison-Wesley edition.
- Improve Hiring Success with Kepner-Tregoe Decision Analysis (opens in a new tab), Kepner-Tregoe, Inc., February 2021. The split between must-haves, which remove options, and weighted wants, which rank the rest.
- Weight stability intervals for multi-criteria decision analysis using the weighted sum model (opens in a new tab), Expert Systems with Applications 296, 128460 (O'Shea, Deeney, Triantaphyllou, Diaz-Balteiro and Tarim), 15 January 2026. Why the sensitivity of a ranking to its weights matters, and the idea of the range of a weight over which the ranking holds.
- Weighted sum method in the analysis of multicriterial decisions: pro et contra (opens in a new tab), Business Informatics 7(3), pages 41 to 48 (V. Podinovski and M. Potapov), 2013. A critical review of the weighted sum: constant weights, ordinal scales treated as numbers and dependence on the other options.
Where it helps
The lifecycle stages this tool serves: 10 stages in 7 lifecycles.
More manufacturing, fab and supply tools
Method notev1Formula, ranges, sources and limits
Scores options against weighted criteria by a weighted sum of scores or scaled raw values, or by a Pugh comparison against a baseline, applies must-have gates, ranks the options and finds how far the weights could move before the winner changes.
Formula
share of criterion j = weight j / sum of all weights; worst to best: score = (x − worst) / (best − worst); ratio to best: score = x / best when higher is better, or best / x when lower is better; total i = sum over j of (share j x score ij); net marks = number of plus − number of minus; weighted net = sum over j of (share j x mark j); rest i = (total i − share x score i) / (1 − share); total i at share q = rest i + q x (score i − rest i); crossing q = (rest W − rest K) / ((rest W − score W) − (rest K − score K)) for leader W and rival K
| Input | Unit | Range it holds for | Comes from |
|---|---|---|---|
| Scoring method | choice | wsum5, wsum10, minmax, ratio, pugh, pughw | Your figure |
| Baseline option for the Pugh methods | option number | 1 to 8 | Your figure |
| Criterion for the weight sweep | criterion number | 1 to 12 | Your figure |
Outputs: Winning option (option number); Total of the winning option (score); Total of the runner-up (score); Margin of the winner over the runner-up (score); Options that pass every must-have (count).
Assumptions
- Criteria are treated as independent, so the weighted sum can add them. Two criteria that measure the same thing count that thing twice.
- Scores on a 1 to 5 or 1 to 10 scale are ordinal judgements treated as numbers; the method adds them as if the steps between scores were equal.
- Scaling raw values from worst to best depends on the options in the comparison: adding or removing an option can change the scaled scores of the others. Options knocked out by a gate still set the scale.
- The sensitivity moves one weight at a time and keeps the others in proportion. It does not test changes to scores or several weights together.
- The example presets use invented figures. Replace them with quotes, measurements and your own judgement.
Uncertainty: The arithmetic is exact. The ranking is only as reliable as the weights and the scores, which are judgements; read a small margin together with the sensitivity and the equal-weight check.
Known limits
- A weighted sum can let a high score on one criterion hide a poor one on another. Use a must-have for anything that cannot be traded off.
- The ranking is only as good as the weights and scores. Close totals are not a decision: use the margin, the sensitivity and the equal-weight check before relying on the winner.
- The ratio method needs values above 0, and a ratio can reward a small absolute gain on a small number. The worst-to-best method does not have that problem but exaggerates small gaps when options are close.
- The Pugh methods keep only the direction of each difference, not its size.
- The tool does not model risk, uncertainty in the scores or time. For decisions with probabilities or cash flows use a decision tree or a cost model.
Where the method comes from
The Hub's own decision matrix: the weighted sum model with must-have gates in the manner of Kepner-Tregoe, a Pugh comparison against a baseline, and a closed-form search for the weight at which the leader is overtaken.
Reference example, checked by test: Worked example in this method note: three options scored 1 to 5 on performance (weight 5; scores 4, 3, 5), cost (weight 3; scores 3, 5, 2) and risk (weight 2; scores 4, 3, 2). Shares are 0.5, 0.3 and 0.2, so the totals are 4 x 0.5 + 3 x 0.3 + 4 x 0.2 = 3.7 for Option A, and 3.6 and 3.5 for Options B and C. Option A leads Option B by 0.1. Winning option 1; Total of the winning option 3.7; Total of the runner-up 3.6; Margin of the winner over the runner-up 0.1; Options that pass every must-have 3.
Versions
- v1 (2026-10-25): First version, built from the tool idea.
Terms on this page
- Reference design
- A complete, tested example implementation, comprising schematics, board layout, BOM and software, published by a chip supplier to shorten a customer's development.
Tell us what you're after and leave your email: we'll connect you with the right person on the Hub.