Appendix

Velocity was our research engine for every number we could not measure ourselves. We ran 20+ Velocity research prompts across a dozen chats and logged each one (prompt, answer, what we used, what we pushed back on) in docs/research/velocity.md.

Where Velocity could not answer (e.g. a national rate of surprise failures, cabinets per plant), we say so and label the number an assumption.

A part uses whatever evidence it has. More sources → tighter remaining-life range and higher confidence (high ±15%, medium ±30%, low ±50%).

How many parts come with a known install date? No survey measures it directly, so we combined the Velocity estimates: From Velocity · Manufacturing Maintenance Data Adoption

P(install record) = P(CMMS) × [ P(part level) × completeness  +  P(machine level) × P(part is original) × completeness ]
                  = 0.60     × [ 0.15 × 0.7                +  0.85 × 0.6 × 0.7 ]
                  ≈ 28%   (6% part-level records + 21% machine-level records)

Also from the same chat: drives exposing fan/capacitor life 10/25/45%; PLCs networked with diagnostics 50/70/85%; plants that routinely use those diagnostics 5/12/25%. That gap (data inside the hardware, unread) is why the Cabinet Monitor reads it.

Each photo is read by Claude (claude-sonnet-5-5) into manufacturer, part number, serial, date code, plus an explicit list of anything unclear. Readings are cached so the demo runs offline.

Design rules from that research: an identifier with any ambiguous character is unverified; never silently correct a serial or series letter; low-confidence reads go to a person. Appraisers may rely on AI-collected data but keep responsibility (USPAP Advisory Opinion 41, April 2026). From Velocity · Vision feasibility

Health = 100 × the chance the part survives the next 12 months, from a Weibull proportional-hazards survival model (the reliability-engineering standard).

effective age  a = life_used × rated_life
life_used      = self-reported (fan/capacitor life from the drive)            if available
               = age × heat_factor / rated_life                               otherwise
heat_factor    = 2 ^ ((T − T_ref) / 10)      (life halves per +10 °C; half of today's excess counted for the past)
hazard mult. m = exp( ln(20) × anomaly_severity ) × (1 + 0.3 × faults_12m)     (faults capped at 5)
η = 1.1 × rated_life,  β = 3

health        = 100 × exp( −m × ((a + 1)^β − a^β) / η^β )          floored at 1
remaining life = (a^β + η^β × ln 2 / m)^(1/β) − a                    (conditional median)
range          = ± 15% / 30% / 50%  for high / medium / low confidence

Rated life comes from the manufacturer manual / knowledge base. T_ref: drives 55 °C, PLCs/HMIs 45 °C, power supplies 50 °C. Order-by dates use the health model's conservative remaining life (below).

Each monitored part learns its own normal over 30 days, then every daily summary is checked by standard statistical process control:

expected temp:  (T − ambient) = a + c × load        (least squares on the 30-day baseline)
residual r      = actual − expected
EWMA            z_t = 0.2 r_t + 0.8 z_{t−1};  alarm beyond 3σ limits        → sudden shifts (failing fan)
CUSUM           S_t = max(0, S_{t−1} + r_t/σ − 0.5);  alarm at S > 5        → slow drift (aging capacitors)
trend           slope of r over time, t-test;  alarm at > 1 °C/month, t > 3 → warming
peers           robust z vs same-model parts (median / MAD);  alarm at |z| > 3
motor current   Mahalanobis distance on RMS/load + sideband energy;  alarm at > 3
severity        1 − exp(−(stat − alarm)/alarm) per detector;  anomaly_severity = max (0–1)
judged on the last 7 days

Toledo line-stopper drive with a failing fan (planted, simulated sensor data): EWMA crosses its limit the week the step starts. Measured false-alarm rate: ~1 in 40 monitored parts.

Downtime is the number plants feel. We count it two ways, and only for spare rescues we actually found (a line-stopping part whose spare sits at a sister plant). Never scaled up to the whole plant, never in the fee.

hours down without spare = min(lead time to buy one, outage cap 10–25 operating days) × operating hours/day
hours down with spare    = transfer (1–2 days) + swap (2–8 h)
at stake (one failure)   = (hours without − hours with) × line $/hour × share of output never made up (40–80%)

OUTPUT PROTECTED   = Σ at stake                                  (Toledo: $622k, 668 h of stoppage)
DOWNTIME AVOIDED   = Σ P(fails within 3 yrs) × at stake, discounted at 10%, per year   (Toledo: ~$77k/yr, $12–205k)
EXPOSURE / YEAR    = P(fail this year) × hours down × $/hour × unrecovered share        (line-stopper table)

P(fail this year)  = 1 − health/100     (the part's own health score: age, heat, sensor anomalies, faults)
                   = age table below     (only for parts with no health evidence)

Fallback failure odds by age, for parts with no health score: 0–10 yrs 2–5%/yr, 10–20 yrs 4–8%, 20+ yrs 6–10% From Velocity · money thread #4. Transfer time and cost From Velocity · #20 sister-plant transfer. Line $/hour from plant revenue and operating hours From Velocity · #1 plant baseline.

CapEx in year Y   = Σ replacement cost of control parts expected to reach end of life in Y  (+ migration engineering if discontinued)
replacement cost  = market price from trusted listings, else type fallback;  migration = engineering hours × integrator rate
failure date      = today + health model's conservative remaining life   (else install year + typical life)
order-by          = failure date − lead time − 14-day buffer

Component prices and migration labor From Velocity · #16 prices + migration labor; emergency vs planned cost From Velocity · #5; lead times for new PLCs 10–24 wks From Velocity · market validation.

Recommended order: a spare already on a shelf in the portfolio (reserve it, ~7 days) → the manufacturer or an authorized distributor (for discontinued parts: the official successor) → refurbishers and marketplaces, flagged as counterfeit risk.

Marketplace prices: 42 real listings hand-collected for the demo parts, plus real distributor offers. Lifecycle status comes from manufacturer pages and distributor records (source URL + date on every knowledge-base row). From Velocity · PLC/drive/HMI lifecycle check

Read-only to plant equipment, own cellular link (not on the plant network), no inbound ports. Before quoting: qualify the clamps, confirm camera field of view in a real cabinet, test LTE-M inside a closed steel cabinet. Diagram source: docs/plan/hardware/cabinet-monitor-diagram.tex (TikZ).

We charge for what the customer can count, not for what we say they saved. Never a share of savings: savings can't be audited, so a share of them would make us the judge of our own fee (mentor feedback).

Toledo pays ~$9.7k a year against ~$48.6k of auditable savings: paid back in ~2.4 months. Cost to serve a plant: $0.3–1.8k a year. Tier amounts come from Brandon's money model (xray/pricing.py); pilots test willingness to pay.

Revenue per PE portfolio (slide 9: $1–4M a year). A typical mid-market PE portfolio: 10–20 companies, 30–100 plants.

registry      = plants × ~$5.9k (demo-plant average)                       = $0.2–0.6M / yr
sensors       = plants × ~60 line-stopper cabinets × $50 / point / month     = $36k per plant / yr   (illustrative; price to set)
total         = 30 plants × ($5.9k + $36k) ≈ $1.3M   …   100 plants ≈ $4.2M   → $1–4M / yr
market        = 25,800 US plants with 100+ employees (Census CBP 2022): registry alone $7.6M / yr at 5%, $152M at all

The $50 / point / month sensor price is an assumption for illustration (comparable monitoring sells for ~$900 per machine per year From Velocity · unit economics). Without sensors one portfolio is ~$0.2–0.6M a year.

The savings model stays as the customer's business case (payback), not as the price formula. Comparable monitoring sells for ~$900 per machine per year From Velocity · unit economics.

Sensor data in the demo is simulated in the exact format the device would send; plants are fictional; part numbers, lifecycle data and listings are real.

What it is: unplanned downtime costs the world's 500 largest companies about $1.4 trillion a year, 11% of their revenue (Siemens, The True Cost of Downtime, 2024). From Velocity · Manufacturing Equipment Risk Costs

How to say it: it is a cost to the largest companies, not the size of a market, and not specific to mid-market plants. For smaller firms, the same Velocity research found 52% of smaller US manufacturers put an hour of downtime at $50k or more, and 44% have an equipment interruption every month.

What it is: one real plant audit published by Siemens (2025): 699 of 843 automation assets, from 17 manufacturers, were discontinued or end-of-life. From Velocity · Manufacturing Equipment Risk Costs

Why we don't headline it: it is one plant, from a vendor that sells upgrades, not a national rate. Siemens' other published audits found 35% (3,686 filling/packaging assets), 59% (914 process assets) and 60% (388 utility assets). From Velocity · Manufacturing Equipment Risk Costs

What we claim: a large share of the automation in older plants is past its supported life, often a third to most of it. Our own demo portfolio, built on real part numbers and lifecycle data, has 32% of critical parts discontinued or end-of-life. No survey measures a national rate, so we never quote one.