Question 1 of 7: Improving Productivity Through Product Design — a PC Case

Question 1: Improving Productivity Through Product Design — a PC Case (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: the PC case (item i). It is chosen deliberately. A PC case is a sheet-metal and moulded-polymer assembly whose factory cost is dominated by part count and assembly labour rather than by raw material, so the productivity levers are visible and computable; and it is sold into a market where the customer can see the difference between a case that services without a screwdriver and one that does not, so the numerator of the productivity ratio is available too. Throughout this answer the ratio is read the way the question frames it: output is the marketable product actually shipped, input is every resource consumed to ship it — materials, energy, capital services and labour.

Given. The baseline is a mid-tower case built to an incumbent design and assembled on a manual line. The figures below are the programme data used for the whole of Question 1.

Find. A design direction for the case, carried consistently through parts A to E, that demonstrably raises output per unit of input; and, for part C, the size of that improvement expressed in the ratio the question supplies.

Approach. Generate the four ideas against the two halves of the ratio separately (three that shrink the denominator, one that grows the numerator), develop the largest of them into an architecture, then quantify it with the Boothroyd design-for-assembly index, a takt-time line balance, and labour and multifactor productivity at constant prices before converting the result into specifications and prioritising them.

Part A — Four ideas for improving productivity through design

The simple ratio invites four distinct kinds of design action, and it is worth separating them because they do not compete for the same resources and they do not all pay back on the same timescale.

Idea 1 — eliminate the threaded fastener from the assembly bench. The baseline case carries 24 rivets and 32 screws. Every one of them is a part to purchase, present, orient and drive, and none of them is a feature the customer values. Replacing them with integral snap features, lanced-and-formed standoffs, a spring slide latch and a roll-formed welded chassis attacks the largest single block of assembly content.

Idea 2 — change the process route for the chassis. Five stamped panels joined by rivets on the bench become one roll-formed section resistance-welded in the press line. This does not make the joining disappear; it moves it upstream to a machine that does it in seconds rather than to an operator who does it in minutes. The honest accounting of that move is done in part C, because it raises the piece price of the chassis while collapsing its assembly content.

Idea 3 — make the remaining assembly automatable. Vertical, straight-line insertion with self-locating features and no re-orientation of the workpiece is what allows a station to be automated later without a redesign. Automation substitutes capital for labour in the denominator; designing for it costs almost nothing at the concept stage and is effectively unavailable afterwards.

Idea 4 — raise the numerator, not only shrink the denominator. Two levers do this. Quality: a shorter line has fewer opportunities to build a defect, so more of what is started is sold. Platform architecture: one chassis carrying three market variants amortises one tooling investment over three times the volume and lets the firm sell into three price points from one engineering effort. This is the idea Canadian productivity commentary most often misses — the national gap is not mainly a story about people working less hard, it is a story about capital intensity, slow diffusion of new methods into smaller firms, and a product mix with modest value added. All three are design problems.

Part B — The detailed design that captures Idea 1

Idea 1 is developed, with Idea 2 carried alongside it because the fastener count and the chassis process route cannot honestly be separated. The redesign is a tool-less case:

• Chassis. One roll-formed and in-line resistance-welded section replaces five panels and 24 rivets. The motherboard standoffs are lanced and formed directly out of the tray, so nine brass standoffs disappear as parts rather than being replaced.
• Drive mounting. The two screwed cages become an integral shelf pressed into the chassis plus two moulded caddies with cantilever snap arms; eight cage screws go.
• Expansion slots. Seven individual brackets and their screws become one ganged, re-usable cover retained by a single moulded catch.
• Side panels. Four thumbscrews become an integral spring slide latch. The panel is still a separate, removable part — it must be, for service — but its retention is now a feature of the panel, not a bag of hardware.
• Front end. Snap-fit bezel, magnetic dust filter, snap-in fan frame (four fan screws removed), and one keyed connector for the front I/O harness in place of a loose plug set.

The theoretical minimum part count is unchanged at seven: one chassis, two service panels, a bezel in a different material, a removable filter, a purchased fan module and an electrical harness. That is the point of the redesign — it does not invent a cleverer minimum, it removes the 69 parts that were never justified by the Boothroyd criteria in the first place.

Part C — The impact on the productivity relationship

The redesign is now costed against the ratio the question supplies. The chain runs from the design-for-assembly index, through the line balance it permits, to labour and multifactor productivity, and finally to the yield effect on saleable output.

1. Compute the design-for-assembly index for both architectures. The Boothroyd index measures how much of the assembly content is theoretically necessary: $$\alpha_{DFA}=\frac{N_{min}\,t_a}{t_{total}}$$ where $N_{min}$ is the theoretical minimum part count, $t_a$ the ideal handling-plus-insertion time of 3.0 s, and $t_{total}$ the actual assembly content. Substituting the baseline $N_{min}=7$, $t_{total}=431.5\ \text{s}$ and then the redesign value $t_{total}=84.0\ \text{s}$, $$\begin{aligned} \alpha_{base}&=\frac{7\times 3.0}{431.5}=0.0487\\ \alpha_{new}&=\frac{7\times 3.0}{84.0}=0.2500\\ &\boxed{\alpha_{DFA}:\ 4.87\ \%\ \longrightarrow\ 25.0\ \%} \end{aligned}$$ The part count falls 86.8 per cent and the assembly content 80.5 per cent, but the index is the number that matters because it is dimensionless: it says the baseline spent 95 per cent of its assembly effort on work that a perfect design would not have required.
2. Convert the assembly content into a line balance. The number of stations is set by the takt time, not by the assembly content directly: $$\tau=\frac{\text{available time per day}}{\text{daily demand}} =\frac{2\times 7.5\times 3600}{240{,}000/250}=\frac{54{,}000}{960}=56.25\ \text{s}$$ and the station count is the ceiling of the content divided by it, $s=\lceil t_{total}/\tau\rceil$. The baseline gives $\lceil 431.5/56.25\rceil=\lceil 7.67\rceil=8$ stations; the redesign gives $\lceil 84.0/56.25\rceil=\lceil 1.49\rceil=2$. This step behaviour is the single most useful fact in the whole question and part E turns on it.
Figure 1.2 — Assembly stations are a step function of unit content, stations = ceil(t_total / tau). Specification overruns are free inside a tread and expensive across a riser, which is what makes the factory cost function, not the specification table, the right thing to prioritise against.
3. Labour productivity. With eight stations over two shifts the line consumes $H=8\times 2\times 7.5=120$ labour-hours per day against 960 units, so $$LP=\frac{Q}{H}=\frac{960}{120}=8.00\ \text{units per labour-hour}$$ Two stations consume 30 labour-hours per day, giving 32.00 units per labour-hour — a factor of four. That figure is true and it is also misleading on its own, which is exactly why the next step is necessary.

Direct assembly labour is a small share of what the factory actually consumes. Quoting the four-fold gain and stopping there is the commonest error in productivity arguments; the honest measure divides the same output by all the inputs.

4. Multifactor productivity at constant prices. $$MFP=\frac{Q\,p_0}{H r+M+E+K}$$ with output held at the pre-change transfer price $p_0=\text{CAD }42.00$ so that the measure cannot be flattered by a price change. Annual output value is $240{,}000\times 42.00=\text{CAD }10{,}080{,}000$ in both cases. On the input side the labour bill falls from CAD 840,000 to CAD 210,000; materials fall from CAD 22.40 to CAD 20.665 per unit (56 fasteners, nine standoffs, seven brackets and two cages removed, against a chassis piece price up CAD 1.35 for the larger progressive die and in-line welding, plus caddies, latch and magnetic filter); energy rises from CAD 0.85 to CAD 0.92 per unit because the press line now does the joining; and capital services rise from CAD 620,000 to CAD 805,000. Total input falls from CAD 7,040,000 to CAD 6,195,400, so $$MFP:\ 1.4318\ \longrightarrow\ 1.6270, \qquad \boxed{\Delta MFP=+13.6\ \%}$$

That contrast — four-fold on labour, thirteen and a half per cent on everything together — is the substantive answer to the premise of the question. Roughly a third of the labour saving is bought back by the capital and energy required to move the joining upstream, and that is not a failure of the design; it is what raising capital intensity looks like on a profit-and-loss account.

5. The numerator: yield. Rolled throughput yield multiplies across stations, $RTY=y^{s}$, so at $y=0.985$ the baseline returns $0.985^{8}=0.8861$ and the redesign $0.985^{2}=0.9702$. Saleable output per unit started therefore rises by $0.9702/0.8861=1.0949$, a further 9.5 per cent that the assembly index never claimed. Compounding it with the multifactor gain, $$1.1363\times 1.0949=1.2442,\qquad \boxed{\text{overall productivity }+24.4\ \%}$$ Removing six stations removes six chances to build a defect — a benefit of part-count reduction that appears in the numerator, not the denominator.
6. The numerator: platform amortisation. Tooling is a fixed charge spread over volume, $c_{tool}(n)=T/n$. The redesign's press tooling of CAD 1,850,000 carried by one model at 240,000 units per year is CAD 7.71 per unit; carried by three market variants sharing the chassis, 720,000 units, it is CAD 2.57 per unit. The design decision that makes this available — a common chassis envelope with variant-specific bezels — costs nothing at the concept stage and cannot be retrofitted.

Part D — Converting the design ideas into realistic engineering specifications

A design idea becomes an engineering specification when it acquires a measurable quantity, a target value with a tolerance or a limit, and a named method of verification. The conversion is done by asking, of each idea in part B, what physical variable would have to move for the idea to have worked, and what would have to remain true for the product still to be acceptable. The first question produces the target specifications; the second produces the constraints that the redesign must not break, and those are the ones most often lost.

Two remarks about realism, since the question asks for realistic specifications. First, a target is only realistic if someone can say how it will be measured before the design is frozen; "easy to service" is an aspiration, "side panel removed in under eight seconds without tools by twenty untrained users" is a specification. Second, the specification set must contain the constraints that the change puts at risk, not merely the benefits it promises. Removing four thumbscrews and a continuous screwed seam is an assembly improvement and an electromagnetic regression, which is why the compliance line is in the table at all — and it is the line that fails.

Part E — Establishing priorities when not all specifications can be met

Priorities are established in three passes, in a fixed order, because the passes are not commensurable and mixing them is how design teams talk themselves into shipping non-compliant products.

Pass 1 — hard gates. Regulatory, safety and contractual requirements are not weighted against anything; they are entry conditions. If a candidate design cannot meet ICES-003 Class B or CSA/UL 62368-1, the design is not a lower-scoring option, it is not an option. In this redesign the gate is genuinely threatened, and the arithmetic shows why the parameter route is closed:

1. Test whether the tool-less seam can be made compliant by adjustment alone. Shielding effectiveness of a slot is $$SE=20\log_{10}\!\left(\frac{\lambda}{2L}\right)$$ where $L$ is the longest unbonded dimension. At 1 GHz, $\lambda=299.8\ \text{mm}$. The 180 mm unbonded slide-latch seam gives $SE=-1.6\ \text{dB}$, i.e. no shielding at all. Breaking it with spring finger stock at 12 mm pitch gives 21.9 dB, and at 3 mm pitch 34.0 dB. Setting the requirement $SE\ge 40\ \text{dB}$ and solving for the slot length, $$L\le\frac{\lambda}{2\times 10^{40/20}}=\frac{299.8}{200}=1.50\ \text{mm}$$ A 1.5 mm contact pitch is not manufacturable as discrete fingers, so $$\boxed{\text{no pitch adjustment reaches the requirement; the concept must change}}$$ The resolution is geometric, not parametric: make the panel seam a lapped joint, with overlapping conductive surfaces held in contact by the preload the latch already applies. The latch stops being a fastener replacement and becomes the shield contact.

Pass 2 — the discontinuities in the factory cost function. Only after the gates does cost enter, and it enters as a step function rather than a smooth penalty. From part C the takt is 56.25 s and two stations absorb any assembly content up to 112.50 s. The lapped-seam fix adds a conductive gasket and 9.5 s of assembly, taking the content to 93.5 s — still two stations, so the fix is free. Had the same fix cost 31 s, the content would be 115.0 s, the line would need a third station, and the annual cost would be a discrete CAD 105,000 (2 shifts × 7.5 h × 250 days × CAD 28.00). Prioritising against the smooth targets in the specification table would have treated those two outcomes as similar. They are not.

Pass 3 — weighted priority for what remains. Only the specifications that survive both passes and still conflict are scored, with the weights fixed and recorded before the ratings are entered, and with a sensitivity pass run afterwards. The remaining conflict here is small: part count lands at 11 against a target of 12 after the gasket is added, so it passes; airflow tightens because the lapped seam closes a leakage path, which is a benefit; and the only genuine shortfall is chassis torsional stiffness, at 112 N·m per degree against 120, recovered by a formed swage in the tray at no assembly cost. When a shortfall cannot be recovered, the weighted score decides the trade — but the sensitivity pass must be honest about it: if a plausible re-weighting inverts the ranking, the matrix has not decided anything and the decision must be escalated to a gate that can see the market consequence.