Question 6 of 7: Design for Manufacturing and Design for Assembly Used Together

Question 6: Design for Manufacturing and Design for Assembly Used Together (15 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.

Part A — How the two are used together. Design for Assembly attacks the number of parts and the difficulty of putting them together; Design for Manufacturing attacks the cost of each part given the process that will make it. They are used together in a fixed order, and the order is the whole method: DFA first, DFM second. The reason is that DFA changes the part count, and every DFM decision is made about a specific part — so optimising the manufacture of a part that DFA is about to eliminate is wasted work, and worse, it creates an advocate for keeping it.

The joint procedure, as Boothroyd, Dewhurst and Knight set it out, is: analyse the existing or proposed assembly and compute the DFA index; challenge every part against the three retention criteria (does it move relative to its neighbours, must it be of a different material for a fundamental reason, must it be separable for assembly or service?); eliminate or combine every part that fails all three; re-analyse; and only then select the process and refine the geometry of the parts that remain, using process-specific DFM rules — draft angles, uniform wall thickness, tool access, avoidance of secondary operations.

The combination is more than additive, and it is worth being explicit about why. Removing a part removes not only its own piece cost but its assembly operation, its tooling, its inspection, its part number, its purchase order, its inventory and its opportunity to be assembled incorrectly. It also removes an interface, and interfaces are where tolerance stacks accumulate and where field failures concentrate. Then, on the reduced part count, DFM has more to work with: the parts that remain are larger and carry more function, which is exactly the condition under which a high-tooling, low-variable-cost process such as die casting or injection moulding becomes viable. DFA thus creates the conditions in which DFM's biggest wins become available.

Quantifying the joint effect. Given. A baseline product of 47 parts with a total manual assembly time of 396 s, of which a theoretical minimum of 12 parts is justified by the retention criteria; a standard ideal handling and insertion time of 3 s per part; a fully burdened assembly labour rate of CAD 42 per hour; and an annual volume of 250 000 units. Find. The DFA index before and after a redesign that reaches 23 parts and 198 s, and the resulting annual saving.

1. Compute the design efficiency before and after. The Boothroyd DFA index is $$\alpha=\frac{N_{\min}\,t_a}{t_{\text{total}}}$$ so $$\begin{aligned} \alpha_{\text{before}}&=\frac{12\times3}{396}=0.0909 \\ \alpha_{\text{after}}&=\frac{12\times3}{198}=\boxed{0.1818} \end{aligned}$$ The efficiency doubles, from 9.1 % to 18.2 % — still low in absolute terms, which is normal, since the index is a comparative instrument rather than a score to be maximised.
2. Convert to money. Assembly labour per unit falls from $396/3600\times42=\text{CAD }4.62$ to $198/3600\times42=\text{CAD }2.31$, a saving of CAD 2.31 per unit, or $$\Delta C = 2.31\times250\,000=\boxed{\text{CAD }577\,500\ \text{per year}}$$ in direct assembly labour alone, before counting the 24 part numbers removed from purchasing, inventory and inspection.
3. Show the factory-level step change. With two shifts of 7.5 hours the available time is 54 000 s per day against a demand of 1 000 units, so the takt time is $$\begin{aligned} \tau&=\frac{54\,000}{1\,000}=54\ \text{s} \\ \text{stations}&=\left\lceil\frac{t_{\text{total}}}{\tau}\right\rceil \end{aligned}$$ giving $\lceil396/54\rceil=8$ stations before and $\lceil198/54\rceil=4$ after. The line halves, which releases floor space, four sets of fixtures and four operators per shift — a saving that does not appear in the per-unit labour figure at all.
4. Note the yield benefit nobody claimed. If each station passes 99.5 % of units, rolled throughput yield is $0.995^{n}$, so halving the station count raises end-to-end yield from $0.995^{8}=0.9607$ to $0.995^{4}=0.9802$, a gain of 1.95 percentage points obtained purely by removing opportunities to make a mistake. The DFA index never claimed this, and on a 250 000-unit programme it is worth more than the labour saving.

Part B — Three improvements that satisfy both objectives. Each of the three below reduces assembly effort and reduces the cost of making the parts, which is the test the question sets.

1. Consolidate six sheet-metal brackets and fourteen fasteners into one die-cast structural bracket. On the assembly side, twenty parts and their twenty handling and insertion operations become one. On the manufacturing side, the question is whether the tooling is justified. Given. The fabricated route costs CAD 6 000 in tooling and CAD 8.40 per unit; the die-cast route costs CAD 78 000 in tooling and CAD 3.15 per unit. Find. The volume above which die casting is cheaper. With $c(n)=T/n+u$, the two routes cross where $$n^{*}=\frac{T_2-T_1}{u_1-u_2}=\frac{78\,000-6\,000}{8.40-3.15} =\boxed{13\,714\ \text{units}}$$ At the programme volume of 250 000 units per year the die casting costs CAD 3.46 against CAD 8.42, so the consolidation saves CAD 4.96 per unit on the parts as well as removing nineteen assembly operations. Figure 6.1 shows the crossing; note that the decision is unambiguous only because the programme volume is eighteen times the break-even, and a 40 000-unit programme would need a much more careful answer.
2. Replace threaded fasteners with integral snap fits and self-locating features. For assembly, a snap fit is inserted in one motion with no separate part, no torque control, no thread-locking compound and no risk of a missing or cross-threaded screw. For manufacture, the snap feature is formed in the same moulding or casting operation as the wall it belongs to and costs essentially nothing, whereas each threaded boss requires a drilled and tapped hole or an insert. Adding a chamfered lead-in and an asymmetric locating boss at the same time makes the part self-locating and self-aligning, which removes the fixture the station would otherwise need — a DFM saving obtained through a DFA feature.
3. Make the assembly one-directional, layered and mistake-proof about a single base part. Design so that every part is added from above onto a stable base, so that no part can be fitted the wrong way round (asymmetric locating features, or fully symmetric ones where orientation genuinely does not matter), and so that no part must be held while another is fitted. On the assembly side this removes re-orientation, holding fixtures and the entire class of orientation errors. On the manufacturing side, one-directional assembly implies one-directional access, which is precisely the geometry that allows single-parting-line tooling with no side actions in the moulds and castings, and single-setup machining on the machined parts — the single largest lever on piece cost in both processes.

Part C — A strategy for consistently achieving both in a facility that designs and manufactures its own products. The vertically-integrated case is the favourable one, because the firm keeps the savings it creates and can see the consequences of its own design decisions on its own floor. The strategy has six elements.

1. Make manufacturing engineering a member of the design team from the concept phase, not a reviewer of finished drawings. The person who will own the process must be able to influence the architecture while the architecture is still soft. In an integrated facility this costs nothing but organisational will, and it is the single highest-return element of the strategy.
2. Set numerical DFMA targets in the product specification and gate against them. A required DFA index, a maximum part count, a maximum assembly time and a should-cost per unit, entered in the same specification as the functional requirements and reviewed at each gate. Targets that are not in the specification are aspirations, and aspirations lose to schedule pressure every time.
3. Capture the factory's actual capability in a living design-rule set. Minimum wall thickness, achievable tolerance by process and feature size, standard hole sizes, available press tonnages and bed sizes, preferred fasteners and standard tooling — published as a design manual and, better, embedded in the CAD system as checkable rules. This is the mechanism by which one plant's hard-won knowledge stops being one experienced engineer's memory.
4. Aggressively standardise parts and processes across the product range. A managed preferred-parts library, a small approved fastener set and common platforms across models raise the volume on each remaining part number, which moves every part rightwards along its own $c(n)=T/n+u$ curve, and reduce the tooling and changeover burden on the floor. This is the element that most often falls to individual designers' preference and most needs central enforcement.
5. Close the feedback loop from the floor to the design office with data. Track assembly times by station, first-pass yield, rework and scrap by cause, and warranty returns by part, and report them back to the design team against the design decisions that produced them. In a firm that both designs and manufactures, this loop is a structural advantage that a firm outsourcing its manufacture simply cannot have — and it is astonishing how often it is left unbuilt.
6. Institutionalise the method, and measure whether it is working. Train designers in DFMA analysis and give them the software; require a documented DFMA study, with a before-and-after index, as a mandatory gate deliverable; run structured cross-functional workshops on new assemblies; and track the portfolio DFA index and part count over time as a management metric. Recognise and reward part elimination explicitly, because the natural incentives run the other way — adding a part solves an engineer's immediate problem, while removing one is somebody else's saving.