Exercises: Life cycle, metrology and quality control

These phases of a product's life cycle are jumbled: (a) use and maintenance, (b) manufacturing, (c) end of life (recycling or disposal), (d) design, (e) distribution and sales. Put them in order and explain in one sentence what happens in each.

Explain what metrology is and name two common measuring instruments in a technology workshop, indicating what quantity each measures and in which unit.

A shaft must measure $20 \pm 0{,}1\ \text{mm}$, meaning any measurement between $19{,}9\ \text{mm}$ and $20{,}1\ \text{mm}$ is acceptable. In the figure, the measurements of three parts (A, B and C) have been represented on the tolerance line, as shown in the figure.

State which parts are accepted and which are rejected, and explain what it means for a part to be 'out of tolerance'.

Quality is not just "that the product works". Explain what it means for a product to "meet specifications" and give an example of a measurable specification for a reusable bottle (capacity, leak-tightness, drop resistance...).

Explain what a manufacturing defect is and describe three possible defects in a wooden table (in its dimensions, in its finish and in its stability), indicating which one you consider most serious and why.

Vernier calipers are a common instrument in the workshop. Explain what physical quantity they measure, to what approximate precision they operate (tenths of a millimetre) and what you would use them for when verifying a newly manufactured part.

Explain what product traceability is and why food packaging carries a batch number. What does this number allow to be done when a problem is detected in a batch?

At the end of a product's useful life, there are several options: repair, reuse, recycle or dispose of. Order them from most to least sustainable and explain the difference between reusing and recycling, giving an example of each.

Explain what a technical standard is (for example, an ISO or UNE standard) and why manufacturers are interested in complying with it. Give an example of an everyday product whose safety or compatibility depends on a standard.

Distinguish between quality control (detecting defective products) and continuous improvement (preventing defects from occurring in the first place). Give an example of each concept in a bicycle factory and explain why the second strategy usually proves cheaper in the long run.

A shaft must measure $25 \pm 0{,}2\ \text{mm}$. Measuring five parts yields the following measurements: $25{,}1\ \text{mm}$, $24{,}7\ \text{mm}$, $25{,}2\ \text{mm}$, $24{,}9\ \text{mm}$ and $25{,}3\ \text{mm}$. Calculate the acceptable range of measurements and state which parts pass quality control and which do not, justifying each case.

To check $20 \pm 0{,}1\ \text{mm}$ shafts in series production, a "go/no-go" gauge is used: it has one end calibrated at $20{,}1\ \text{mm}$, through which the shaft MUST pass, and another at $19{,}9\ \text{mm}$, through which it must NOT pass. Explain how this gauge is used, what advantage it has in production compared with measuring each shaft with a caliper, and what information is lost with it.

A control chart records the mean diameter of shafts produced in eight batches, with the central line (CL) and upper and lower control limits (UCL, LCL), as shown in the figure.

(a) State which batch falls outside the control limits. (b) Explain what it means for a process to be 'out of control' and how this differs from normal variation between batches. (c) Propose two immediate actions for the company to take (regarding the machine and the parts from that batch).

The ISO 9001 standard certifies quality management systems. Explain in your own words what is actually certified (the company's processes, not each individual product) and what confidence this certification provides to customers purchasing from that company.

Recalling a defective product from the market costs much more than having detected it in the factory. Break down the costs of non-quality in this scenario (reverse logistics, customer service, brand image, potential penalties) and compare them with the cost of having prevented the defect.

Some parts are inspected one by one (100% inspection) and others by sampling (only a few from each batch are checked). Explain when each strategy is appropriate and justify it with two examples: hardware screws and car seatbelt pretensioners.

A telecommunications company claims in its advertising campaign that its new model is "50% more sustainable" because its packaging is made of recycled cardboard and the charger has been removed from the box. Average data from a Life Cycle Assessment (LCA) for this type of handset reveals the following greenhouse gas emissions breakdown: raw material extraction and component manufacturing: 78%; transport and distribution: 4%; use and recharging over two years: 16%; end of life and waste treatment: 2%.

(a) Quantitatively refute the company's claim and justify why this action represents an obvious case of greenwashing.

(b) Identify the critical stage (hotspot) of the life cycle and calculate how much the prorated annual impact would be reduced if, through modular design and spare parts availability, the phone's lifespan were doubled from 2 to 4 years.

(c) Propose two specific technical decisions that the design team should adopt in the product conception phase to ensure its repairability and effective recycling at the end of its life.

In a machined production line of steel cylindrical shafts for gearboxes, the critical dimension of the nominal diameter is $25{,}00 \pm 0{,}05\ \text{mm}$. Final inspection detects an $8\ \%$ scrap rate due to out-of-tolerance dimensions. As the quality manager, design a Statistical Process Control (SPC) plan to address the problem at its source:

(a) Define the sampling strategy: appropriate metrological instrument with its minimum precision, subgroup size, and data collection frequency, justifying why a variables control chart ($\bar{X}-R$) is preferable to an attributes chart.

(b) During the first control shift, the following diameter means of five consecutive subgroups are obtained: $25{,}00\ \text{mm}$, $25{,}01\ \text{mm}$, $25{,}02\ \text{mm}$, $25{,}03\ \text{mm}$, and $25{,}04\ \text{mm}$. Although all individual parts are within the tolerance limits, interpret what anomaly this trend reveals in the process and predict what physical machining cause is producing it.

(c) Establish the immediate corrective action and the preventive maintenance measure that must be implemented for the process to regain stability.

An artisan workshop that manufactures custom solid wood kitchen furniture faces a serious problem: $15\ \%$ of the assembled furniture pieces are rejected during the final varnishing and packaging stage due to dimensional errors in the initial cuts or misaligned drill holes. The manager proposes hiring a full-time inspector to thoroughly check each finished piece of furniture before loading it onto the delivery truck.

(a) Relying on the "1-10-100 rule" of the cost of poor quality, justify why the manager's proposal will increase costs instead of solving the workshop's profitability problem.

(b) Design a quality-at-the-source (self-inspection) strategy tailored to this workshop: propose two simple poka-yoke (mistake-proofing) mechanical devices or dimensional checklists that the operators themselves can apply at the cutting and drilling machines.

(c) Explain why in a make-to-order and custom production, statistical control by random sampling is not applicable and what systematic verification criterion should replace it.

In the turning of steel pins, a nominal dimension of $50{,}00 \pm 0{,}20\ \text{mm}$ is specified. A consecutive sample of 10 parts is taken at the end of a work shift, yielding the following diameters in millimeters:

$49{,}90;\ 50{,}15;\ 50{,}30;\ 50{,}05;\ 49{,}80;\ 50{,}10;\ 50{,}25;\ 49{,}75;\ 50{,}00;\ 50{,}35$.

(a) Determine which parts do not meet the design specifications and classify them with reasoning into non-recoverable parts (scrap) and parts that allow rework (re-turning on the lathe).

(b) Calculate the sample mean $\bar{x}$ and the sample range $R$. Compare the sample range with the allowable tolerance interval and interpret whether the main problem with the process lies in a centering error (zero offset) or in excessive intrinsic variability (dispersion).

(c) Knowing that the operation consists of external turning, predict with reasoning how tool tip wear affects the resulting diameter of the parts and what compensation must be introduced into the CNC program to correct it.

The Technology department has two 3D printers (Model A and Model B) for producing student prototypes. Over the last term, the following operating data were recorded after 150 class hours of availability:

• Model A: 60 parts started; 48 valid parts on the first attempt; 3 severe nozzle clogs that required disassembly (cumulative repair and calibration time: 9 h); $1{,}90\ \text{kg}$ of filament consumed to produce $1{,}40\ \text{kg}$ of useful finished parts.

• Model B: 60 parts started; 42 valid parts on the first attempt; 1 motherboard breakdown (repair time: 18 h); $2{,}60\ \text{kg}$ of filament consumed to produce $1{,}30\ \text{kg}$ of useful parts.

(a) Mathematically define and calculate for each machine three operational quality indicators: First-Time Yield (FTY), Material Scrap Rate (\%), and Technical Availability (\%).

(b) Interpret the results: if the school has a very limited budget for filament but needs to quickly manufacture 20 critical parts for a technology contest with a strict deadline, justify which machine you would select for the batch.

(c) For the machine ruled out in the previous section, formulate a continuous improvement action aimed at mitigating its poorest indicator.

A school needs to install 25 air conditioning units in its classrooms, and the management team is hesitating between two offers:

• Offer A: Low initial cost standard units. Acquisition and installation: $600\ \text{€}$ per unit. Estimated service life: 6 years. Average electrical power consumption: $1{,}60\ \text{kW}$. Maintenance: $40\ \text{€}$ per year per unit.

• Offer B: High-efficiency inverter and eco-designed units. Acquisition and installation: $1100\ \text{€}$ per unit. Estimated service life: 12 years. Average electrical power consumption: $0{,}90\ \text{kW}$. Maintenance: $25\ \text{€}$ per year per unit.

Operating data: 800 hours of use per year per classroom. Average electricity price: $0{,}16\ \text{€/kWh}$.

(a) Calculate the Life Cycle Cost (LCC) for all 25 classrooms combined over a 12-year time horizon (including initial acquisition, replacement if its service life ends, energy, and maintenance).

(b) Determine after how many years of use the accumulated savings offset the higher initial investment of Offer B (simple payback period).

(c) Issue a technical-environmental assessment justifying the final choice based on the calculated economic results and the minimization of environmental impact due to discarded materials and indirect emissions.

The support of a mobile robot consists of a housing into which three rectangular parts $A$, $B$, and $C$ must be inserted in series. The assigned manufacturing dimensions are:

• Width of the housing cavity: $L = 80{,}40 \pm 0{,}15\ \text{mm}$.

• Thickness of part $A$: $a = 20{,}00 \pm 0{,}10\ \text{mm}$.

• Thickness of part $B$: $b = 35{,}00 \pm 0{,}12\ \text{mm}$.

• Thickness of part $C$: $c = 25{,}00 \pm 0{,}08\ \text{mm}$.

For the assembly to work without binding or vibrating, the assembly clearance $J = L - (a + b + c)$ must strictly be between $0{,}05\ \text{mm}$ and $0{,}75\ \text{mm}$.

(a) Perform a tolerance stack-up analysis using the worst-case method and determine the minimum possible clearance ($J_{\min}$) and maximum possible clearance ($J_{\max}$).

(b) Interpret the results: predict whether there is a risk of interference (inability to assemble the parts) or excessive clearance, and indicate under which combination of extreme dimensions failure would occur.

(c) If tightening the machining tolerances of the parts increases the product cost by $40\ \%$, propose an alternative mechanical design solution (without changing the tolerances of $A$, $B$, and $C$) that guarantees the correct fit of the mechanism.

In the technology workshop, $25\ \%$ of the tin-soldered joints in the circuits of robotics projects present functional defects (cold solder joints, short circuits caused by solder bridges, or components coming loose after a few hours of use).

(a) P Phase (Plan): Apply the Ishikawa diagram to identify at least four root causes of the problem grouped according to the 4Ms (Manpower, Materials, Machinery/Tools, and Methods). Based on them, formulate a testable technical working hypothesis.

(b) D Phase (Do) and C Phase (Check): Design a small-scale experimental test plan to validate the hypothesis proposed in the previous phase without stopping the work of the entire group. Define which measurable variable you will record and which quantitative success criterion will determine if the solution is valid.

(c) A Phase (Act): Assuming that the experimental test has reduced the defective solder joint rate to $3\ \%$, propose two specific standardization measures in the workshop to ensure that this improvement does not deteriorate with subsequent cohorts of students.