Batch, tolerance and shelf life

Break-even. Each process costs C(n) = F + v·n: a fixed cost F (tooling, programming, set-up) and a cost per part v. Two processes cost the same at n = (F_A − F_B) ÷ (v_B − v_A). The book’s invented clip — printed and finished by hand at £0 + £6.00 against an £8,000 aluminium mould at £0.80 — breaks even at about 1,540 parts. Add up to six processes; the chart runs from 1 to 10,000 parts on a log axis, as total cost or cost per part, and lists every crossover and the cheapest process over each range. Add invented middle methods puts in CNC and silicone-mould casting with made-up figures for shape only. Cost is not the whole comparison: for a cleaned, re-used item the break-even on suitability may come long before the break-even on cost.

Tolerance stack-up. Parts in a chain, each with a nominal size, a ± tolerance and whether it adds or subtracts. Worst case is ±Σt; the statistical (root sum of squares) estimate is ±√Σt². Four parts at ±0.1 mm give ±0.4 and ±0.2 mm (chapter 14); question 13’s ±0.05 mm gives ±0.2 and ±0.1 mm. Enter what the chain allows to compare.

Cp and Cpk. Paste measurements of one dimension — ten consecutive parts is the chapter 14 exercise — and the limits. Cp = (USL − LSL) ÷ 6σ, Cpk = min(USL − μ, μ − LSL) ÷ 3σ with the sample standard deviation. Cpk = 1.0 means the process just fits; 1.33 or more is a common target. An approximate 95 % interval for Cpk (Bissell, 1990) shows how little ten parts can tell you. Anything that is not a number is reported, not skipped. The histogram shows the measurements, a fitted normal curve and the tolerance band.

Surface roughness. Typical Ra by process (appendix C, chapter 14) on a log scale against the ~0.8 µm Ra that hygienic-design guidance commonly targets for product-contact surfaces and a ~1 µm bacterium. Add your own measured Ra.

Accelerated ageing. ASTM F1980 (accelerated ageing of sterile barrier systems and medical devices) uses AAF = Q₁₀ raised to the power (T_AA − T_RT) ÷ 10; the test time is the real time divided by AAF. With Q₁₀ = 2, 55 °C against 25 °C gives AAF = 8, so a year takes about 46 days (chapter 2); the chapter 2 exercise — two years at 25 °C — takes about 129 days at 50 °C and 64.5 days at 60 °C. Enter the lowest transition of your materials (a glass transition, a melting point) to have ageing temperatures at or above it flagged: such a test simulates something that never happens in service.

Related: statistics (more on distributions and tests), print tolerances and fits, filament and print cost, tissues, materials and temperature, levers, moment arms and contact.

Share link (under the title) copies a URL that reopens this tool with your processes, parts, measurements and ageing set-up. Each tab has its own address: #tolerance, #capability, #roughness or #ageing opens that tab.