Question 1 of 7: Improving a Design for Manufacturability

Question 1: Improving a Design for Manufacturability (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 hair dryer (option i). It is the right vehicle for a manufacturability question because it is a genuine high-volume consumer product — the programme assumed here is 400,000 units per year over a three-year model life — in which the factory cost is dominated by piece-part count and assembly labour rather than by material. A coffee maker carries a water circuit and a heater-plus-carafe interface that drag the answer into thermal design; a computer desk is a low-volume flat-pack whose manufacturability question is really a packaging and fastener question. The hair dryer keeps the focus where the examiner asks for it: overall shape, main feature functionality, how the major components interact, and the material, manufacturing, use and disposal consequences of changing them.

Part A — Two general ways to assess manufacturability, and how to get the data

Manufacturability is not a property a drawing either has or lacks; it is a measured distance between the design as drawn and the cheapest design that would still satisfy the requirements. Two families of method measure that distance, and they answer different questions.

Method 1 — structured design-for-assembly (DFA) analysis. This is the Boothroyd–Dewhurst procedure. Every piece part in the assembly is examined against three questions asked in sequence: does it move relative to all other parts already assembled; must it be of a different material for a fundamental reason such as insulation, conduction or elasticity; and must it be separate to allow assembly or service access. A part that fails all three is a theoretical candidate for elimination. Each part is then given a standard handling time and a standard insertion time drawn from the Boothroyd tables, indexed by size, symmetry, nesting tendency and the difficulty of the insertion. The output is a single dimensionless score, the design efficiency

$$\alpha_{\text{DFA}}=\frac{N_{\min}\,t_a}{t_{\text{total}}}$$

in which $N_{\min}$ is the theoretical minimum part count, $t_a$ is the ideal assembly time for an easy-to-handle, easy-to-insert part (conventionally 3 s), and $t_{\text{total}}$ is the estimated total assembly time. The score is between 0 and 1 and is deliberately harsh — consumer assemblies typically score 0.05 to 0.15 — because its purpose is to make the gap visible rather than to flatter the design. Its strength is that it is objective, repeatable between analysts, and computable from a concept sketch long before any tooling money is committed. Its weakness is that it sees assembly only: it will happily recommend a single moulded part whose tool is unaffordable.

Method 2 — process-based should-cost modelling. Here the candidate design is costed directly against the manufacturing routes that could make it. Each route is reduced to a fixed charge that is independent of volume (tooling, fixtures, programming, qualification) and a variable charge that recurs on every unit (material, cycle time, direct labour, energy, scrap), so that unit cost falls with volume as

$$c(n)=\frac{T}{n}+u$$

where $T$ is the amortised fixed cost, $u$ is the variable cost per unit and $n$ is the volume over which $T$ is written off. Comparing two routes gives the break-even volume $n^{*}=(T_2-T_1)/(u_1-u_2)$, which is the number the business actually needs. The strength of this method is that it speaks the language of the decision — dollars against volume — and it captures material and process choices that DFA cannot see. Its weakness is that it is only as good as its cost data, and that data does not exist inside the design office.

Selected method: process-based should-cost modelling, because Part B asks for changes justified by cost and productivity, and because it is the method whose data collection is least obvious. Establishing feasibility and cost data proceeds in five steps.

1. Fix the functional requirement and the annual volume before anything else. A process is never feasible in the abstract: it is feasible for a stated geometry, tolerance, surface finish, material and rate. Writing down "400,000 units per year, ABS/PC housing, class A visible surface, wall 1.8–2.4 mm, no visible sink" is what turns a shopping list of processes into a shortlist.
2. Screen processes on physical capability, not on price. Use process capability charts (Ashby’s process-attribute charts, or Kalpakjian’s tables) to eliminate any route that cannot hold the section thickness, the tolerance or the rate. Injection moulding, structural foam and gas-assist moulding survive for the housing; die casting does not, because the product must be double-insulated. This step is free and it removes most of the candidates.
3. Obtain fixed-cost data from tooling quotations, not from memory. Send the concept geometry to two or three toolmakers as a request for budgetary quotation, stating cavity count, expected tool life in shots and the required texture. Budgetary tool quotations are normally free, are returned in one to two weeks, and are accurate to roughly ±15 per cent — ample for a route comparison.
4. Build the variable cost from first principles and check it against a supplier. Material cost follows from the shot weight and the resin price; machine cost follows from the estimated cycle time and the published hourly rate for the required clamp tonnage; assembly labour follows from the Boothroyd time standards multiplied by the fully burdened labour rate, here $38 per hour. Then ask an existing supplier to quote the current part, and reconcile the difference — a should-cost model that cannot reproduce a price you already pay is not yet calibrated.
5. Close the loop with a capability trial on the risky feature only. One single-cavity prototype tool, or a machined equivalent, run for a short capability study on the one feature that the model says is marginal. This converts the largest remaining assumption into measured data for a small fraction of the production tooling cost.

Part B — Three manufacturability improvements driven by the cost model

The baseline hair dryer is a 32-piece assembly with an estimated total assembly time of 196 s. Applying the three Boothroyd questions to the bill of materials leaves eight parts that must exist as separate items: the rotor-and-fan group, the heating element (nichrome, a fundamentally different material), the housing, the folding handle (relative motion), two switch actuators (relative motion), the mains cord, and the removable rear grille (service access for lint cleaning). Everything else — screws, retainers, brackets, harnesses — is a candidate for elimination.

Given. Baseline assembly:

Find. The DFA index before and after redesign, the unit and annual cost saved, and the volume at which the extra tooling the redesign needs is repaid.

1. Score the baseline design. The design efficiency is $$\alpha_{\text{DFA,0}}=\frac{N_{\min}t_a}{t_{\text{total},0}}=\frac{8\times 3}{196}=0.1224$$ so $\boxed{\alpha_{\text{DFA,0}}=12.2\ \text{per cent}}$. Twelve per cent is unremarkable for a consumer appliance, but the absolute gap is the useful reading: 172 s of the 196 s is spent on parts that a perfect design would not contain.
2. Improvement 1 — replace the eight-screw housing joint with a snap-fit spine and two structural screws. The two moulded housing halves are currently closed with eight self-tapping screws, each costing about 9 s of driving, torque-verification and rework exposure. Moulding a continuous cantilever-hook spine along the parting line, and retaining only the two screws that carry the handle hinge reaction, removes six parts and 54 s. It also removes six torque-controlled operations, which is where most of the assembly rework on this product originates.
3. Improvement 2 — insert-mould the heater terminals into a single mica-carrier sub-assembly with a bayonet mount. The element currently arrives as a mica former, a nichrome coil, two crimped terminals, an insulator ring, a retainer and three screws. Insert-moulding the terminals into the carrier and replacing the retainer and its screws with a quarter-turn bayonet on the housing removes seven parts and 30 s, and it makes the creepage and clearance distances a moulded-in geometric feature rather than an assembly-dependent one, which is worth more than the labour saving when the unit is submitted for certification.
4. Improvement 3 — replace the discrete wire harness with a stamped lead frame and a keyed connector. Two flying harnesses and their crimp-and-route operations become one stamped lead frame that drops into moulded channels in one axis. This removes two parts and 20 s, and the asymmetric key makes the connection impossible to fit the wrong way round — a poka-yoke that removes a latent safety defect rather than merely a cost.
5. Score the redesigned assembly. The three changes remove $6+7+2=15$ parts and $54+30+20=104$ seconds, leaving $N=17$ parts and $t_{\text{total}}=92\ \text{s}$. The theoretical minimum is unchanged at eight, because no function was removed, so $$\alpha_{\text{DFA,1}}=\frac{8\times 3}{92}=0.2609$$ giving $\boxed{\alpha_{\text{DFA,1}}=26.1\ \text{per cent}}$, a factor of 2.13 improvement on the baseline. Note that the index improved because the denominator fell, not because the numerator rose — that is the correct signature of a part-count reduction.
6. Convert the time saving into money. At $38/3600=0.010556$ CAD per second, the assembly labour falls from $196\times 0.010556=2.069$ to $92\times 0.010556=0.971$ CAD per unit, a saving of 1.098 CAD. The fifteen deleted parts are worth a further 0.34 CAD of purchased material and handling, so the total is $$\Delta c = 1.098 + 0.340 = 1.438\ \text{CAD per unit}$$ which over 400,000 units per year is $\boxed{575{,}100\ \text{CAD per year}}$.
7. Check that the change pays for its own tooling. The snap-fit spine, the bayonet feature and the insert-moulded carrier together require 86,000 CAD of new and modified tooling. The break-even volume is $$n_{\text{pay}}=\frac{86{,}000}{1.438}=59{,}800\ \text{units}$$ or $\boxed{1.8\ \text{months of production}}$ at the planned rate. A payback inside one quarter, on a three-year model life, is the answer that makes the engineering case a business case.

Part C — Impact on the production floor

A design change of this size is not absorbed silently by the factory. The floor consequences follow from one number, the takt time, and they run in both directions — some are the benefit being claimed, and some are costs that must be budgeted.

Given. 400,000 units per year, 250 working days, two shifts, 7.5 productive hours per shift. Find. The takt time, the number of assembly stations before and after, and the resulting line-balance efficiency.

1. Compute the takt time from customer demand. Available time is $250\times 2\times 7.5\times 3600=13{,}500{,}000$ seconds per year, so $$\tau=\frac{13{,}500{,}000}{400{,}000}=33.75\ \text{s per unit}$$ and $\boxed{\tau = 33.75\ \text{s}}$ is the drumbeat every station must meet.
2. Size the line before and after. The minimum station count is $\lceil t_{\text{total}}/\tau\rceil$. Before, $196/33.75=5.81$ gives six stations at a balance efficiency of $196/(6\times 33.75)=96.8$ per cent. After, $92/33.75=2.73$ gives three stations at $92/(3\times 33.75)=90.9$ per cent. So the line goes from $\boxed{6\ \text{stations to }3}$, releasing three operators per shift and six across the two shifts.

Around that headline number sit six further floor effects, three favourable and three that consume the savings if they are not planned for.

Favourable. Floor space falls roughly with station count, and the three released bays absorb the next product introduction without a building change. Work in process falls in proportion to the number of buffers between stations, which shortens the time between making a defect and detecting it — on a two-shift line the practical effect is that a moulding problem is caught the same shift rather than the next day. Training time and operator certification cost fall, because there are fewer distinct operations and because the keyed lead-frame connector removes the one operation that previously required a certified operator.

Costs to budget. The screwdriving stations and their torque controllers become surplus and must be redeployed or written off, and the write-off is a real charge against the project even though it never appears in the unit cost. The snap-fit joint shifts inspection from a torque reading, which is automatic and logged, to a pull-off test, which is destructive and therefore sampled — a new sampling plan and a new gauge are required, and quality engineering must agree the plan before launch. Finally, the balance efficiency fell: with only three stations, a single station running long has nowhere to hide, so the line becomes more sensitive to a slow operator or a jammed feeder, and a small buffer or a floating operator has to be re-introduced. The honest summary is that halving the assembly content is unambiguously good, but a shorter line is a tighter line.

Part D — Converting design ideas into realistic engineering specifications

An improvement idea becomes an engineering specification when it acquires four things it did not have as an idea: a measurable parameter, a target with a tolerance, a verification method that someone can actually perform, and an owner who is accountable for it. "Use snap-fits instead of screws" is a design direction; "the housing joint shall withstand a 90 N pull-off load after five open-and-close cycles, verified on a tensile tester to the sampling plan in QP-114" is a specification. The conversion is a five-step discipline.

1. Trace every specification back to a customer or statutory need. A requirement with no parent is a preference, and preferences are what get traded away in Part E. The trace also fixes the classification — statutory, customer-critical, or internal — which is the input the prioritisation needs.
2. Choose a parameter that is a property of the product, not of the process. Specify retention force, not the number of hooks; specify creepage distance, not the shape of the moulded rib. A process-shaped specification freezes the supplier’s design and destroys the very manufacturability the exercise was trying to buy.
3. Set the target from evidence and the tolerance from capability. The target comes from the physics or from the standard; the tolerance comes from what the chosen process can hold at an acceptable capability index, which is why Part A’s capability trial matters. Setting a tolerance tighter than the process can hold guarantees either scrap or a deviation note, and both are more expensive than the wider tolerance would have been.
4. Name the verification method and its acceptance criterion in the same line. Test, analysis, inspection or demonstration — and for a test, the sample size. An unverifiable specification is not a specification; it is an aspiration that will be closed by assertion at the end of the programme.
5. Freeze the set, then manage it under change control. Specifications that drift during detail design are the mechanism by which a validated cost model becomes wrong. Each later change is re-costed through the same should-cost model before it is accepted.

Applying that to the three improvements gives the following specification set. Note that every row names its parent need and its verification, and that two of the targets are set by the Canadian certification standard rather than by the design team.

Two of these deserve comment because they are where inexperienced specifications go wrong. The 90 per cent vertical-insertion target is a manufacturability specification written as a product property: it constrains the geometry so that gravity assists every insertion and no station needs a re-orientation fixture, and it is auditable from the process sheet without any test equipment. The factory-cost row is a specification, not a wish, precisely because its verification method is named — the should-cost model reconciled against a real quotation — which is what stops it becoming the line item everyone agrees to revisit later.

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

Late in a programme it is normal to find that the specification set is over-determined: the cost target, the noise target and the assembly-time target cannot all be held with the money and the time remaining. Prioritising is not a matter of arguing about which target matters most in the abstract. It is a three-stage procedure that first removes the negotiable from the non-negotiable, then ranks what remains by return on the money available, and finally verifies the consequence of each deferral on the factory.

Stage 1 — classify, and take the statutory rows off the table. The dielectric-strength, terminal-position and mis-mating specifications derive from CSA C22.2 No. 60335-2-23 and from the double-insulation construction. They are not tradeable at any price: a product that fails them cannot be sold in Canada, so they are removed from the negotiation before it starts. This single step usually settles a third of the argument, and it also protects the engineer’s professional obligation under the Engineers and Geoscientists Act to hold public safety paramount above cost and schedule.

Stage 2 — rank the remainder by a priority index. For each negotiable specification, record the weight the customer places on it, the normalised shortfall against target, and the marginal unit cost of closing that shortfall. The index

$$\text{PI}=\frac{w\,s}{c}$$

ranks the specifications by customer value bought per dollar spent. It is deliberately a ratio: a heavily weighted specification that is very expensive to close should lose to a lightly weighted one that is nearly free, and the ratio is what makes that visible.

Given. A residual budget of 0.85 CAD per unit and the five negotiable specifications below. Find. Which are funded and which are deferred.

Taking the specifications in descending index order and funding them until the budget runs out buys airflow (0.18), cord length (0.22) and noise (0.42) for a total of 0.82 CAD, leaving 0.03 CAD in hand. Mass is deferred because it is by far the worst value: closing it would consume two thirds of the budget to buy a quarter of one specification.

Stage 3 — verify what each deferral actually costs on the floor, because the index does not know. This is the step that turns a spreadsheet decision into an engineering one, and here it produces a genuinely useful result. The noise specification is closed by adding a lined volute, which adds 6 s of assembly, taking the total from 92 to 98 s and breaching the internal 95 s target that was just deferred. That looks like a contradiction until the takt time from Part C is applied: the station count is

$$\left\lceil \frac{98}{33.75} \right\rceil = \lceil 2.90 \rceil = 3\ \text{stations}$$

which is the same three stations as before, at a balance efficiency that actually improves from 90.9 to 96.8 per cent because the work now divides more evenly. In other words the assembly-time overrun is free: it consumes slack that already existed inside the takt and it changes neither the headcount nor the floor space. The 95 s target was an internal convenience, and the number that mattered all along was 101.25 s, the point at which a fourth station becomes necessary.

The general principle the example illustrates is that manufacturing specifications should be prioritised against the discontinuities in the factory cost function — the point where a station, a shift, a machine or a cavity is added — not against the smooth targets in the specification table. Between discontinuities, an overrun is nearly free; across one, a trivial overrun is very expensive. Ranking by priority index finds the best value, and checking against the discontinuities tells you which of the deferrals you can actually live with.