--- title: "Weighted decision matrix for drive selection" subject: "Machine Design I" chapter: 1 key: "semester_6/machine_design_i:weighted-decision-matrix-drive" source: https://www.bctengineer.com/q/semester_6/machine_design_i/weighted-decision-matrix-drive site: BCT Engineering --- # Weighted decision matrix for drive selection Machine Design I · Chapter 1: Design Process - Asked in: year not given, 6 marks - Video: [The Weighted Scoring Decision Matrix - Explanation and Step-by-Step Guide](https://www.youtube.com/watch?v=hUlB8lkfw9Q) — airfocus by Lucid - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/machine_design_i/weighted-decision-matrix-drive - Whole chapter: https://www.bctengineer.com/md/semester_6/machine_design_i/chapter-1 ## Question A conveyor needs a speed-reduction drive, and four alternatives are to be evaluated: A (V-belt drive), B (chain drive), C (separate gearbox) and D (integral gear-motor). The criteria weights are: initial cost 5, reliability 4, ease of maintenance 3, compactness 2. The ratings given by the design team (scale 1 to 10, 10 best) in the order [cost, reliability, maintenance, compactness] are: A = [7, 8, 9, 6], B = [8, 6, 7, 7], C = [9, 5, 6, 7], D = [6, 8, 5, 9]. (a) Use a weighted decision matrix to rank the alternatives and state the best choice. (b) State two limitations of this method of evaluating alternatives. ## Short answer Multiplying ratings by weights gives scores: A 106, B 99, C 97, D 95. Best choice is V-belt drive (A). Limitations: subjective weights/ratings can change ranking, and linear addition may hide a very poor rating on a critical criterion. ## Answer A **weighted decision matrix** multiplies the rating of each alternative on every criterion by the weight of that criterion, and the totals are compared. #### (a) Ranking Weights: cost 5, reliability 4, maintenance 3, compactness 2 (sum = 14). Maximum possible score = 10 x 14 = 140. Score of A $= 5(7) + 4(8) + 3(9) + 2(6) = 35 + 32 + 27 + 12 = 106$ Score of B $= 5(8) + 4(6) + 3(7) + 2(7) = 40 + 24 + 21 + 14 = 99$ Score of C $= 5(9) + 4(5) + 3(6) + 2(7) = 45 + 20 + 18 + 14 = 97$ Score of D $= 5(6) + 4(8) + 3(5) + 2(9) = 30 + 32 + 15 + 18 = 95$ | Alternative | Cost x5 | Reliab. x4 | Maint. x3 | Compact x2 | Total | Share of max | |---|---|---|---|---|---|---| | A V-belt | 35 | 32 | 27 | 12 | 106 | 0.76 | | B Chain | 40 | 24 | 21 | 14 | 99 | 0.71 | | C Gearbox | 45 | 20 | 18 | 14 | 97 | 0.69 | | D Gear-motor | 30 | 32 | 15 | 18 | 95 | 0.68 | Ranking: A > B > C > D. **Answer: Alternative A (V-belt drive) is the best choice with a score of 106 out of 140.** #### (b) Limitations - The ratings and weights are subjective; a small change in weights can change the ranking (here B, C and D are within 4 points). - The method treats the criteria as independent and adds them linearly, so a very poor rating on one critical criterion (for example safety) can be hidden by high ratings elsewhere. Important constraints must be checked separately as pass/fail. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the score of an alternative found in a weighted decision matrix? A. Sum of (rating x criterion weight) over all criteria B. Sum of the ratings only C. Product of all the ratings D. Highest single rating of the alternative Answer: A. Each rating is multiplied by its weight and the products are added. (Key point: Method) 2. What is the weighted score of the V-belt drive A = [7,8,9,6] with weights [5,4,3,2]? A. 99 B. 106 C. 97 D. 112 Answer: B. 5(7)+4(8)+3(9)+2(6) = 35+32+27+12 = 106. (Key point: Score of A) 3. Which alternative ranks best and what is the order? A. B (chain); B > A > C > D B. C (gearbox); C > B > A > D C. A (V-belt); A > B > C > D D. D (gear-motor); D > A > B > C Answer: C. Scores are A 106, B 99, C 97, D 95. (Key point: Best choice) 4. Why can a weighted decision matrix mislead? A. It cannot handle more than two criteria B. It always favours the cheapest option C. It gives the same total for every alternative D. Ratings and weights are subjective, and a very poor rating on a critical criterion can be hidden by high ratings elsewhere Answer: D. Subjectivity and linear addition are its main limits; critical constraints should be checked as pass/fail. (Key point: Limitation) ## Related in Machine Design I - [Roller chain drive: length, speed and factor of safety](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aroller-chain-drive-selection) — Machine Design I, chapter 8 - [Tension ratio of a flat belt drive](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Abelt-tension-ratio-derivation) — Machine Design I, chapter 8 - [Needs, goals, constraints and criteria](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aproblem-statement-needs-goals-constraints) — Machine Design I, chapter 4 - [Number of V-belts for a motor drive](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Av-belt-number-of-belts) — Machine Design I, chapter 8 - [Compound gear train speeds, torques and tooth forces](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Acompound-gear-train-forces) — Machine Design I, chapter 9 - [Open flat belt power and cross belt length](https://www.bctengineer.com/question.md?key=semester_6%2Fmachine_design_i%3Aopen-flat-belt-power-and-length) — Machine Design I, chapter 8 ## Related in other subjects - [Gear ratios of a four-speed car](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aautomobile-gear-ratio-selection) — Machine Design II, chapter 5 - [Belt conveyor load inertia and accelerating torque](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Abelt-conveyor-inertia-accelerating-torque) — Utilization of Electrical Energy, chapter 2, asked 2× - [Six-speed machine tool gearbox design](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Amachine-tool-speed-ladder-gear) — Machine Design II, chapter 5 - [Belt conveyor (2.2 m/s) load inertia and torque](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Abelt-conveyor-2-2ms-inertia-torque) — Utilization of Electrical Energy, chapter 2