Question 1 of 7: Improving the functional and non-functional aspects of a product

Question 1: Improving the functional and non-functional aspects of a product (40 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Product selected: (i) the office chair. The chair is the most instructive of the three because it is the only one whose performance is defined against a population rather than against a single task: a kitchen table is sized by convention and a bicycle is fitted to its rider at purchase, whereas an office chair must adjust itself to whoever sits in it. That makes its functional performance measurable in a way the other two are not, which is exactly what part A asks for.

The new market segment chosen for part B is the hybrid home worker in a small Canadian dwelling — a person who works two or three days a week from a condominium or a shared room, buys the chair themselves at a retail price point rather than receiving it through a corporate furniture programme, assembles it alone from a flat box, and keeps it in a room that is also a living space. Every design decision below traces to one of those five facts, and the design direction is held constant from A through E as the question requires.

Part A — Functional versus non-functional aspects, and how each is quantified

Functional aspects are what the product does: the transformations of force, motion, energy and information it must deliver for the user to complete the task. For an office chair they are the support of the seated body at a height and posture matched to the work surface, the transfer of the occupant load safely into the floor, the adjustment of that geometry by the occupant while seated, and mobility across the floor. A functional aspect is recognised by a simple test: it can be stated as a physical quantity with a unit, and a candidate design either meets it or does not.

Non-functional aspects are the qualities the product must possess while it performs those functions — the attributes that govern whether the product is chosen, kept, maintained and eventually disposed of. For the chair they are appearance and the impression of quality, acoustic and visual intrusion into a shared room, physical footprint, the effort of unboxing and assembly, serviceability, durability over a warranty period, environmental burden, and price. These are not "soft" requirements. The engineering distinction is not measurable versus unmeasurable — it is that a functional requirement is measured on the product with an instrument, whereas a non-functional requirement is often measured on a sample of people or over a life cycle, and therefore carries a sampling plan and a confidence interval rather than a single reading.

The way to quantify each, then, is to attach to every aspect a metric, a measuring method and a target. The table below is the working list used for the rest of this answer.

The first row is the one that carries the design, so it is worth doing properly rather than asserting. "The chair adjusts" is not a specification; the number of people it adjusts to is.

Given. Shod popliteal height (the vertical distance from the floor to the underside of the thigh at the knee, with a 25 mm shoe allowance) for the Canadian adult working population: women $\mu = 420$ mm, $\sigma = 26$ mm; men $\mu = 455$ mm, $\sigma = 28$ mm; an even split by sex. A standard class-4 pneumatic column offers 100 mm of stroke.

Find. The seat-height range the chair must offer, and the fraction of the target population a single 100 mm stroke can accommodate.

1. State the ergonomic rule that turns anatomy into a dimension. The seat pan should be set so that the thigh is supported without pressure behind the knee and the foot rests flat, which means seat height equals shod popliteal height. The chair must therefore span from the shortest user it intends to fit to the tallest: $$h_{\min} = \mu_W - 1.645\,\sigma_W = 420 - 1.645(26) = 377.2\ \text{mm}$$$$h_{\max} = \mu_M + 1.645\,\sigma_M = 455 + 1.645(28) = 501.1\ \text{mm}$$
2. Convert that span into a stroke requirement. Subtracting the two gives the adjustment range that a fifth-percentile woman to ninety-fifth-percentile man design must provide: $$\boxed{\Delta h = 501.1 - 377.2 = 123.8\ \text{mm}}$$ A single 100 mm class-4 column is 23.8 mm short of that before any other consideration.
3. Quantify what the standard column actually achieves. Accommodation is the probability that a randomly drawn user falls inside the offered window $[h,\ h+S]$, taken over the mixed population: $$P(h,S) = \tfrac{1}{2}\left[\Phi\!\left(\tfrac{h+S-\mu_W}{\sigma_W}\right) - \Phi\!\left(\tfrac{h-\mu_W}{\sigma_W}\right)\right] + \tfrac{1}{2}\left[\Phi\!\left(\tfrac{h+S-\mu_M}{\sigma_M}\right) - \Phi\!\left(\tfrac{h-\mu_M}{\sigma_M}\right)\right]$$ Maximising over the placement $h$ for $S = 100$ mm gives a best window of 387.5 mm to 487.5 mm and $\boxed{P = 87.9\ \%}$. A window pitched high at 415-515 mm, which is what a chair designed around a nominal male user looks like, collapses to $74.2\ \%$.
4. Solve the inverse problem: how much stroke does a stated accommodation cost? Repeating the maximisation while solving for $S$ gives 105.7 mm for 90 per cent, 124.7 mm for 95 per cent and 161.0 mm for 99 per cent. The 130 mm stroke that is available as a catalogue class-4 column, placed at 375-505 mm, returns $$\boxed{P = 95.9\ \%}$$ and is therefore the smallest standard part that meets a defensible target.
5. Check the last increment against the geometry, not against the catalogue. Ninety-nine per cent accommodation needs a window of 358.8 mm to 519.7 mm. The lowest seat height the architecture can reach is fixed by the castor, base hub, mechanism and cushion stack at about 370 mm, so 11.2 mm of that window is geometrically unreachable no matter how much stroke is purchased. The parameter route is closed, and 99 per cent accommodation would require a concept change — a lower mechanism or a supplied footrest — not a longer cylinder. This result is used again in part E.

Non-functional aspects are quantified with the same discipline, but the sample is people rather than parts. If perceived quality is to be steered by design rather than by opinion, the panel must be large enough that a change is distinguishable from noise. For a seven-point scale with an observed spread of $\sigma = 1.20$ scale points and a required confidence-interval half-width of $E = 0.25$ points at 95 per cent confidence:

That single number converts "it should look better" into a testable proposition, and it is the reason the appearance target in part D is written as a score with an interval rather than as an adjective.

Part B — Three functional and three non-functional design ideas for the new segment

The segment is the hybrid home worker. Each idea below names the segment fact it answers, so that part D has something concrete to convert.

Functional improvements.

F1. Extend the height adjustment to 375-505 mm using a 130 mm class-4 column. In a corporate setting a facilities team specifies a chair against an assessed population and can stock two column heights. The home buyer gets one chair, chosen online, and has no ergonomist. The chair must therefore carry the accommodation itself, and part A shows exactly what that costs: 30 mm more stroke lifts accommodation from 87.9 to 95.9 per cent. This is the single largest functional gain available, and it is a purchased-part change rather than a redesign.

F2. Collapse three separate controls into one paddle operable one-handed while seated, at no more than 22.2 N. Field observation of home users consistently finds chairs left in their factory setting because the controls are under the seat, unlabelled and stiff. An adjustment that is not made delivers none of the benefit of F1. Capping the actuation force at the CSA B651 accessible-control ceiling of 22.2 N and reducing three levers to one paddle with a moulded, tactile icon makes the adjustment discoverable and is also, as part C shows, the change that pays for itself on the assembly line.

F3. Add a forward seat tilt of 4 degrees for work at fixed-height home surfaces. Home desks are dining tables, kitchen islands and repurposed consoles; they are not height adjustable and they are frequently too high. A chair that can pitch the pelvis forward, used towards the top of its height range, lets the user work at a surface that cannot itself be changed. This is a functional change because it is a stated range of motion with a measurable angle, not a styling choice.

Non-functional improvements.

N1. A domestic material and colour palette, targeted at a measured perceived-quality score. The chair sits in a living room, and a black mesh task chair reads as office equipment there. A woven upholstery in muted colourways with a soft-touch polymer surface finish is aimed at a mean score of at least 5.2 out of 7 on the "belongs in my home" scale, measured on the panel of 89 sized in part A. The point of stating a score and an interval is that it can be refuted; "warmer styling" cannot.

N2. Reduce the base to 560 mm diameter and hold castor noise below 42 dB(A) at 1 m. A 680 mm five-star base sweeps a 0.36 m² circle that a condominium cannot spare, and hard castors on laminate flooring are both audible in the room and picked up by a video-call microphone. Both are non-functional in the strict sense — the chair works either way — and both are decisive in a shared living space. Note that shrinking the base is constrained by the BIFMA X5.1 stability test, which is a hard limit, not a preference; see part E.

N3. Ten-minute tool-free assembly, at least 45 per cent post-consumer recycled content, and separation to material streams in under 8 minutes. The home buyer assembles the chair alone on a floor, so the out-of-box experience is the first and strongest quality impression the product will ever make; and this segment buys on stated environmental credentials. Snap-in castors, a captive-fastener mechanism and a base moulded from a single recyclable polymer serve all three targets at once, which is why they are grouped as one idea.

Part C — Impact of the part B changes on the manufacturing process and cost

The six changes fall into three quite different categories of manufacturing consequence, and it is worth separating them before any arithmetic. F1 is a purchased-part substitution: a longer column is a catalogue item, so it changes the bill of materials and the length of the telescoping shroud but touches no process. F2 and N3 are assembly-content changes: they remove parts and operations from the line. N2 is a process-route change, because a smaller base that still passes the stability test invites a different material and therefore a different process. Each is quantified in turn.

Given. Baseline chair: 54 parts, total assembly work content 648 s, theoretical minimum part count 15. Redesigned chair after F2 and N3: 31 parts, 396 s, same minimum of 15. Programme volume 60 000 chairs per year over 250 working days on one 7.5 h shift at 90 per cent availability; burdened labour CAD 41.00/h. Base options: die-cast A380 aluminium, tooling CAD 46 000 and piece cost CAD 21.40; injection-moulded PA6-GF30, tooling CAD 88 000 and piece cost CAD 9.60.

Find. The change in the Boothroyd design-for-assembly index, the number of assembly stations the line needs before and after, the annual labour cost difference, and the break-even volume for the base process change.

Approach. Score the assembly with the DFA index, convert work content into stations through the takt time (which is where the money actually is, because a plant pays for operators and not for seconds), then compare the two base processes on the standard two-term cost model.

1. Score the baseline and the redesign on the DFA index. Boothroyd's index compares the work content actually required with the work content of a theoretically perfect assembly, in which only the parts that must exist are each handled and inserted in an ideal 3 s: $$\alpha_{\mathrm{DFA}} = \frac{N_{\min}\,t_a}{t_{\text{total}}}$$ with $N_{\min}$ the number of parts surviving the three minimum-part tests and $t_a = 3$ s. For the baseline chair, $\alpha = (15 \times 3)/648 = 0.0694$, and for the redesign $\alpha = (15 \times 3)/396 = 0.1136$.
2. Read what the index is saying. The index rises from $\boxed{6.9\ \% \rightarrow 11.4\ \%}$ because the numerator is unchanged — the chair still needs the same 15 functionally necessary parts — while the denominator falls. In other words the whole gain comes from removing parts that never had to exist and from making the survivors easier to handle and insert. Part count falls 42.6 per cent (54 to 31) and work content falls 38.9 per cent (648 s to 396 s).
3. Convert work content into stations through the takt time. Takt is the rate the line must beat: $$\tau = \frac{\text{available time}}{\text{demand}} = \frac{7.5 \times 3600 \times 0.90}{60\,000/250} = \frac{24\,300}{240} = 101.25\ \text{s}$$ The number of stations is the work content divided by takt, rounded up, because an operator cannot be bought in fractions: $$m = \left\lceil \frac{t_{\text{total}}}{\tau} \right\rceil$$
4. Evaluate the step for each design. The baseline needs $\lceil 648/101.25 \rceil = \lceil 6.40 \rceil = 7$ stations; the redesign needs $\lceil 396/101.25 \rceil = \lceil 3.91 \rceil = 4$. $$\boxed{7\ \text{stations} \rightarrow 4\ \text{stations}}$$ The slack before the next step is $4 \times 101.25 - 396 = 9.0$ s, a figure part E needs.
5. Price the station reduction, which is the real saving. Each operator works $250 \times 7.5 = 1875$ h per year, so $$\Delta C_{\text{labour}} = (7-4) \times 1875 \times 41.00 = \boxed{\text{CAD } 230\,625\ \text{per year}}$$ The per-unit view understates this: the work content saved is $252\ \text{s} \times \text{CAD } 41.00/3600 = \text{CAD } 2.87$ per chair, or CAD 172 200 a year, and the difference between the two figures is the idle time the plant was paying for anyway. Stations, not seconds, are what appear on the cost sheet.
6. Compare the two base processes on the two-term cost model. Any tooled process carries a one-off tooling charge amortised over volume plus a variable piece cost: $$c(n) = \frac{T}{n} + u$$ Setting the two equal gives the break-even volume $$n^{*} = \frac{T_2 - T_1}{u_1 - u_2} = \frac{88\,000 - 46\,000}{21.40 - 9.60} = \frac{42\,000}{11.80} = \boxed{3\,560\ \text{units}}$$
7. Place the programme against that break-even. At 60 000 chairs a year the moulded base is nearly seventeen times past break-even, and the first-year benefit is $60\,000 \times 11.80 - 42\,000 = \text{CAD } 666\,000$; per unit the cost falls from CAD 22.17 to CAD 11.07. The moulded base is also what makes N3's recycled content and single-material separation achievable, so one process decision serves two of the six ideas.
8. State the constraint the arithmetic cannot see. The polymer base must still pass the ANSI/BIFMA X5.1 base and drop tests at the reduced 560 mm diameter demanded by N2. That is a screening constraint, not a criterion: if it fails, no break-even volume resurrects the candidate. The programme cost of that risk is a qualification test series and a glass-content trial, which is charged against the change and revisited in part E.

Part D — Converting high-level design ideas into realistic engineering specifications

A design idea becomes an engineering specification when four things are attached to it: a metric that is a physical or statistical quantity, a target value with a limit (a number and whether it is a maximum, a minimum or a band), a verification method naming the test and the acceptance criterion, and a classification as a demand or a wish. The last of these is the step most often skipped and the one that makes part E possible: in Pahl and Beitz's requirements list a demand must be met for the design to be acceptable at all, while a wish is to be maximised subject to the demands. Only wishes can be traded.

The conversion is not a translation exercise; it is where the idea is tested for realism. Three discipline rules keep it honest. First, every target must be traceable to evidence — either a measurement on the user population, a standard, or a competitor teardown — because a number invented to sound ambitious will be traded away at the first review. Second, the target must be stated at the level at which it can be verified: "comfortable" is not verifiable, "seat height adjustable over 375-505 mm" is. Third, the specification must record the reason for the value, so that a later trade-off knows what it is spending.

The cost target deserves the same treatment as any other. Working back from the market price rather than forward from a cost estimate is what makes it binding:

Given. Target retail price CAD 349, retail margin 42 per cent, required manufacturer gross margin 35 per cent. Find. The allowable factory cost.

Everything the chair is going to contain has to fit inside that number, which is precisely why the base process decision in part C mattered: the CAD 11.80 it released is nine per cent of the entire allowable cost and it is what pays for F1, F3 and N1 together.

Part E — Establishing priorities when the specifications cannot all be met

Trade-offs are not a failure of the specification; they are the normal condition of design, and the question is only whether they are made deliberately or by default. The procedure below is the one used on this chair, in order, and it is deliberately arranged so that the cheap and objective filters run before the expensive and subjective ones.

Step one: separate demands from wishes and refuse to trade the demands. The demands in the part D table — BIFMA structural and stability compliance, the 22.2 N control force, the accommodation floor and the CAD 131.57 cost ceiling — are boundaries of the feasible region, not points on a scale. A design that fails the stability test is not a worse design, it is not a design. Running this filter first typically eliminates a third of the candidate packages before anything is scored, at no cost.

Step two: look for specifications that are provably unreachable and change the concept rather than negotiating. Part A produced one: 99 per cent accommodation requires a seat as low as 358.8 mm, and the mechanism stack cannot go below about 370 mm. No amount of stroke closes an 11.2 mm geometric deficit. The correct response is not to relax the target quietly but to change the concept — ship a footrest with the chair, or offer a second short-column variant — and to record that 95.9 per cent is the limit of this architecture. Identifying a closed route early saves the programme from spending review cycles on it.

Step three: weight the wishes before anyone sees the candidates. Fixing the weights first is the whole discipline of the method; weights chosen after the scores are simply a rationalisation of a decision already made. The weights below come from the segment definition: fit dominates because the home buyer has no ergonomist, and appearance ranks second because the chair lives in a shared room.

Given. Three packages that each satisfy every demand but achieve different subsets of the wishes. P1 "fit first" takes the 130 mm column and defers the upholstery upgrade; P2 "look first" takes the premium textile and keeps the 100 mm column; P3 "balanced" takes the 130 mm column and a mid-tier textile but defers the base-diameter reduction. Ratings are on a 1-5 scale. Find. The preferred package, and whether the preference is robust.

1. Score each package. The weighted total is the ordinary linear model $S_j = \sum_i w_i\,r_{ij}$, so for P1 $$S_1 = 0.30(5)+0.20(2)+0.15(4)+0.15(4)+0.10(4)+0.10(4) = 3.90$$ and likewise $S_2 = 3.35$ and $S_3 = 3.80$. On the nominal weights the ranking is $\boxed{P1 > P3 > P2}$.
2. Test whether that ranking survives a defensible change in the weights. A 0.10 shift between the top two criteria is well inside the uncertainty of any weighting workshop, so swap them and rescore: $S_1 = 3.60$, $S_2 = 3.65$, $S_3 = 3.70$. The ranking inverts completely to $\boxed{P3 > P2 > P1}$.
3. Choose on robustness, not on the nominal winner. P1 leads by 0.10 on one set of weights and trails by 0.10 on the other; P3 is first or second on both. Where a sensitivity pass inverts the ranking, the honest conclusion is that the nominal leader is not distinguishable from the runner-up, and the package that is never worse should be taken. P3 is selected.
4. Overlay the discontinuities in the cost function, which the smooth score cannot see. Part C left 9.0 s of slack before the line needs a fifth station. The upholstery change in P3 adds 7 s, so it is free; adding F3's mechanism as well would take the content to $396 + 7 + 14 = 417$ s, past $4\tau = 405$ s, and cost a whole operator at $1875 \times 41.00 = \text{CAD } 76\,875$ a year. F3 is therefore deferred to the next model year, not because it scores badly but because it lands on the wrong side of a step.
5. Confirm the deferred items against the demands one last time. Deferring the base-diameter reduction removes the BIFMA stability requalification from the critical path and protects the CAD 131.57 ceiling; deferring F3 costs 0.2 of a weighted point. Neither deferral touches a demand, which is the test that the trade-off was legitimate.

The general principle the chair illustrates is worth stating plainly, because it is what part E is really asking. Priorities are established by filtering against constraints first, then ranking the remainder against weights that were fixed in advance, then testing that ranking for robustness, and finally checking it against the discontinuities in the factory cost function. The specification table is smooth and the factory is not, and a priority list that ignores the steps will trade away a genuine benefit to buy a target that was free.