What is the FMECA RPN formula?

RPN = Severity × Occurrence × Detection, each rated 1–10. Severity reflects mission impact; Occurrence reflects failure likelihood given historical MTBF data (IEEE 493, CIGRE, OREDA); Detection reflects the probability that monitoring or inspection will miss the fault. Per MIL-STD-1629A, RPN ≥ 200 triggers mandatory corrective action.

How is Weibull reliability used in this advisor?

Weibull two-parameter reliability R(t) = exp(−(t/η)^β) models the survival probability of a component at mission time t, where η is the characteristic life (63.2% failure point) and β is the shape parameter (β 1 = wear-out). The advisor uses published β and η values from Telcordia SR-332 and IEEE 493 to rank components by projected reliability at the next planned outage window.

Is this a live ML model or a concept/demo?

This is a concept and illustrative demonstration. The 109 fault modes and 834 Knowledge Graph rows are synthesised from published research (Lin & Ompusunggu 2026) and the RZ FMECA seed dataset. The ML advisor pathway is described as a proposed architecture — no live Random Forest or graph-inference model is deployed on this page. All numerical outputs are deterministic calculations from the FMECA formulas and reliability databooks, not predictions from a trained model.

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Technical Manual · Predictive Maintenance

AI Engineering Maintenance — Methodology & Formulas

Every input, equation, constant, output, and reference behind the AI Engineering Maintenance advisor concept. The advisor synthesises FMECA risk-priority scoring, Weibull reliability modelling, and spares-readiness analysis across 109 fault modes and 20 DC asset families — grounded in Lin & Ompusunggu (2026) and the RZ FMECA seed dataset. This is an illustrative concept and pre-design aid, not a deployed ML model.

Concept FMECA + KG + ML-advisor Fault modes 109 KG rows 834 Asset families 20 Basis Lin & Ompusunggu (2026)

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01 Purpose & engineering basis

The AI Engineering Maintenance advisor is a concept demonstration of a prescriptive maintenance system for data-centre engineered assets. It answers three design questions: which fault modes carry the highest risk-priority, what is the projected reliability at the next outage window, and is the spares inventory adequate given lead-time and current stock.

Basis of design follows Lin & Ompusunggu (2026), Intelligent Advisor System for Prescriptive Maintenance of Engineered Assets Using FMECA, Knowledge Graph and Machine Learning (IET Artificial Intelligence for Engineering, doi:10.1049/aie2.70019). The paper proposes a four-layer architecture: (1) FMECA fault-mode database, (2) Neo4j Knowledge Graph linking assets → faults → actions → effects → mechanisms, (3) a Random Forest ML classifier trained on historical work-order data, and (4) a rule-based NLP interface for technician queries. This manual documents layers 1–2 and the underlying reliability mathematics.

Concept / Demo notice: The 109 fault modes and 834 KG rows described here are synthesised from the Lin & Ompusunggu (2026) framework and the RZ FMECA seed dataset (RZ Research Team, 2026-05-23). No live Random Forest model or Neo4j graph is deployed in the current advisor implementation. All numerical outputs in the tool are deterministic, using the FMECA formulas and published reliability databooks below.

02 Inputs

Six inputs across three groups — component identity, part-stock BOM, and lead-time / OEM support. The FMECA SOD scores are drawn from the preloaded 109-fault-mode database; the user may override per site.

Field	Symbol	Unit	Range / default	Meaning
Asset family	`A`	enum	20 families	Selects the FMECA fault-mode block (transformer, switchgear, UPS, etc.).
Severity score	`S`	1–10	Per fault mode	Mission impact if the failure effect is reached. 10 = loss of critical redundancy or human safety.
Occurrence score	`O`	1–10	Derived from MTBF	Likelihood of fault mode within maintenance interval, informed by IEEE 493, CIGRE TB-642, NPRD-2016, OREDA.
Detection score	`D`	1–10	Per monitoring rig	Probability that current controls will fail to detect the fault. 10 = no monitoring, no scheduled inspection.
Current stock qty	`Q_s`	pcs	≥ 0	On-hand inventory of the critical spare part.
Supplier lead time	`L`	days	≥ 0	Procurement lead time from order to delivery, used in spares-readiness and lead-time risk scoring.

03 Calculation methodology

Five calculation layers: FMECA RPN, MTBF / failure-rate conversion, Weibull reliability, spares readiness, and lead-time risk. All formulas are deterministic; the ML-advisor layer is described as a proposed enhancement.

FMECA Risk Priority Number (RPN)

RPN = S × O × D (dimensionless, range 1–1000) S = Severity (1–10), O = Occurrence (1–10), D = Detection (1–10). Tier-1 action required if RPN ≥ 200; Tier-2 at 100–199; Tier-3 below 100. Per MIL-STD-1629A and IEC 60812 guidelines.MIL-STD-1629A · STANDARD

MTBF and failure rate

λ = 1 / MTBF (failures per operating hour) MTBF = η · Γ(1 + 1/β) (Weibull mean life) λ is the failure rate (constant-hazard assumption, exponential model). For exponential failure, MTBF = 1/λ exactly. For Weibull: Γ is the gamma function; MTBF reduces to 1/λ only when β = 1. Databook sources: NPRD-2016 for electronic/mechanical parts, IEEE Std 493 (Gold Book) for power equipment, CIGRE TB-642 for transformers, OREDA for offshore/process plant.Telcordia SR-332 · STANDARD

Weibull reliability function

R(t) = exp( −(t / η)^β ) (survival probability at mission time t) F(t) = 1 − R(t) (cumulative failure probability) h(t) = (β / η) · (t / η)^(β−1) (hazard rate) η = characteristic life (scale, 63.2% failure point) [hours]. β = shape parameter: β < 1 early-life failures; β ≈ 1 random/exponential; β > 1 wear-out. The advisor ranks components by R(t) at the next planned maintenance interval to prioritise pre-emptive replacement.Weibull (1951) · PUBLISHED

Spares readiness %

Readiness% = (Q_s / Q_min) × 100 [%] Q_min = ceil( N_assets × F(t_interval) + safety-stock ) Q_s = on-hand stock; Q_min = minimum required stock. Q_min uses F(t) to estimate expected demand over the maintenance interval across N_assets installed units, plus a safety-stock factor (typically 1–2 units for critical Tier-1 faults). Readiness% ≥ 100 = fully covered; below 100 = gap.RZ FMECA Seed · INTERNAL

Lead-time risk score

LT_risk = ( L / MTTR_target ) × S (dimensionless) L = supplier lead time [days]; MTTR_target = maximum acceptable mean-time-to-restore [days] (Tier-III default 4 h = 0.17 day; Tier-IV 1 h = 0.042 day); S = severity score. LT_risk > 1 indicates that the procurement lead time exceeds the restoration target — the part must be stocked on-site.RZ FMECA Seed · INTERNAL

ML advisor (proposed architecture)

Proposed: Random Forest classifier → P(action | fault_mode, sensor_vector, work_order_history) Knowledge Graph query: MATCH (a:Asset)-[:HAS_FAULT]->(f)-[:TRIGGERS_ACTION]->(act) WHERE f.rpn > threshold RETURN act The ML layer — as described in Lin & Ompusunggu (2026) — would rank corrective and preventive actions given live sensor inputs and historical CMMS work-order data. The KG Cypher query retrieves the recommended actions from the 834-row graph. This layer is illustrative in the current implementation; the tool returns rule-based FMECA recommendations.Lin & Ompusunggu 2026 · PROPOSED

04 Constants & data provenance

The 109 fault modes across 20 asset families were synthesised by the RZ Research Team (2026-05-23) from the sources listed below. Each fault mode carries a source: tag in the seed CSV. Representative MTBF and SOD templates are reproduced here for transparency.

Asset family	Fault modes	Key MTBF source	RPN range (seed)
Transformers (oil-filled, dry-type)	5	CIGRE TB-642	72–168
Switchgear (LV/MV)	5	IEEE 493 Gold Book	108–160
UPS (static, rotary, flywheel)	6	IEEE 493; Eaton / Vertiv white papers	90–180
Generators / Gensets	6	NPRD-2016; ISO 8528-11	96–200
Battery systems (VRLA, Li-ion)	6	IEEE 1188; IEC 62619; NFPA 855	80–216
PDU / RPP / Busway	5	IEEE 493; NPRD-2016	60–140
Chillers	6	ASHRAE HVAC Applications; OREDA	80–168
CRAH / CRAC units	5	ASHRAE; Schneider APC field data	72–160
Pumps (CW, condenser, tower)	6	OREDA; Hydraulic Institute	84–180
Cooling towers	5	EPRD-2014; CTI publications	60–140
Liquid cooling (DLC, immersion)	5	ASHRAE TC 9.9; OEM data sheets	72–160
Valves + actuators	5	OREDA; ISA-75	60–120
PLCs / DDC controllers	5	NPRD-2016; IEC 61511	54–150
Sensors	5	NPRD-2016; Telcordia SR-332	36–120
Variable frequency drives (VFDs)	5	IEEE 519; NPRD-2016	72–160
Network equipment (ICS/BMS)	5	Telcordia SR-332	48–120
Pre-action fire systems	5	NFPA 25; FM Global DS 3-7	60–160
Clean-agent suppression	5	NFPA 2001; NFPA 25 (recharge timelines)	72–160
Diesel fuel storage / day tanks	5	EPRD-2014; NFPA 30	48–140
Raised access flooring	3	Owner inspection data; BICSI 002	30–80

KG structure: 834 rows across 8 node/edge types — Component, Fault, Failure, Mechanism, Effect, Action, Step, SOD_RPN. Companion CSV seed files: components, faults, failures, actions, mechanisms, effects, steps, sod_rpn (see docs/research/2026-05-23-fmeca-kg-worldwide-asset-failure-data.md).

NFPA 2001 recharge note: For clean-agent suppression, the OEM support window and recharge lead time are critical to the LT_risk score. Novec 1230 and FM-200 cylinders typically require 24–72 h for recharge by a certified contractor. Spares-readiness analysis should account for whether a spare cylinder set is held on-site or relies on third-party recharge.

05 Outputs

Output	Formula	Unit	Interpretation
RPN	`S × O × D`	1–1000	Tier-1 ≥ 200; Tier-2 100–199; Tier-3 < 100.
Reliability R(t)	`exp(−(t/η)^β)`	%	Survival probability at mission time t; low R(t) drives replacement recommendation.
Failure probability F(t)	`1 − R(t)`	%	Cumulative probability of failure by time t.
Hazard rate h(t)	`(β/η)(t/η)^(β−1)`	failures/hr	Instantaneous risk; rising h(t) signals wear-out regime.
Spares readiness	`(Q_s/Q_min)×100`	%	≥ 100% = adequate; below 100% = procurement gap.
Lead-time risk	`(L/MTTR_target)×S`	dimensionless	> 1 = must stock on-site; ≤ 1 = JIT procurement feasible.
KG action recommendation	Graph query on RPN threshold	text	Corrective or preventive action text from the KG node, with estimated downtime impact.
Priority tier	RPN band	T1/T2/T3	Work-order scheduling priority for the CMMS.

06 Worked example

UPS static inverter — IGBT bridge failure mode. Operating time t = 43,800 h (5 yr at 8,760 h/yr), Weibull β = 1.8 (wear-out regime), η = 87,600 h (10 yr characteristic life), installed units N = 4, MTTR target = 4 h = 0.167 day, lead time L = 21 days, S = 9.

RPN: S=9, O=4, D=5 → RPN = 9 × 4 × 5 = 180 → Tier-2 (plan within 30 days).
Weibull R(t): R(43800) = exp(−(43800/87600)^1.8) = exp(−(0.5)^1.8) = exp(−0.2871) = 75.1%
Failure probability: F(43800) = 1 − 0.751 = 24.9%
Expected demand over next year (t = 8,760 h more): F(52560) − F(43800). R(52560) = exp(−(52560/87600)^1.8) = exp(−(0.6)^1.8) = exp(−0.4038) = 66.8%, so incremental F ≈ 8.3% per unit.
Q_min: ceil(4 × 0.083 + 1 safety) = ceil(1.33) = 2 spare IGBT modules needed.
If Q_s = 1: Readiness% = (1/2) × 100 = 50% — gap → raise PO immediately.
Lead-time risk: (21 / 0.167) × 9 = LT_risk = 1132 → must stock on-site (lead time >> MTTR target).
KG recommendation (Tier-2 RPN 180): Schedule IGBT module health-check within 30 days; thermographic scan of power stack; replace if junction temperature deviation > 15 °C from baseline. Estimated downtime: 4–6 h with pre-staged spare.

Engineering reading: The combination of RPN 180 (Tier-2), 24.9% cumulative failure probability, and LT_risk of 1132 makes this component a clear spares-stocking candidate. Waiting for JIT procurement against a 21-day lead time with a 4-hour MTTR target is not viable — the part must be on the shelf before the next planned shutdown.

07 References & standards

MIL-STD-1629A (1980) — Procedures for Performing a Failure Mode, Effects and Criticality Analysis (FMECA): SOD scoring definitions, RPN computation, criticality matrix.
IEC 60812 (2018) — Analysis techniques for system reliability — Procedure for failure mode and effects analysis (FMEA): harmonised SOD scoring for industrial systems.
Telcordia SR-332 Issue 4 (2016) — Reliability Prediction Procedure for Electronic Equipment: Weibull β and η parameters for electronic components, MTBF conversion.
IEEE Std 493-2007 (Gold Book) — IEEE Recommended Practice for the Design of Reliable Industrial and Commercial Power Systems: failure rates for switchgear, breakers, transformers, motors.
CIGRE Technical Brochure 642 (2015) — Transformer Reliability Survey (WG A2.37): 964 major failures across 167,459 transformer-years, bushing / OLTC / winding failure rates.
NPRD-2016 (Quanterion Solutions) — Nonelectronic Parts Reliability Data: mechanical / electromechanical failure rates.
OREDA Handbook (6th Ed., 2015) — Offshore Reliability Data: pumps, valves, instrumentation; proxy for process plant mechanical equipment.
NFPA 2001 (2022) — Clean Agent Fire Extinguishing Systems: cylinder recharge timelines and support-window guidance.
ASHRAE TC 9.9 — Mission Critical Facilities publications: chiller, CRAC/CRAH reliability context.
Weibull W. (1951) — "A Statistical Distribution Function of Wide Applicability", J. Applied Mechanics 18:293–297.
Lin H. & Ompusunggu A. P. (2026) — "Intelligent Advisor System for Prescriptive Maintenance of Engineered Assets Using FMECA, Knowledge Graph and Machine Learning", IET Artificial Intelligence for Engineering, doi:10.1049/aie2.70019.
RZ FMECA Seed Dataset (2026-05-23) — RZ Research Team, FMECA-Knowledge-Graph Seed Data: Worldwide Industrial Asset Failure-Mode Research, internal report + 8 CSV seed files. Located at docs/research/2026-05-23-fmeca-kg-worldwide-asset-failure-data.md.

08 Assumptions & limitations

The FMECA SOD templates and MTBF figures in the seed dataset are representative starting points, not site-calibrated values. Engineers must localise O scores using actual CMMS work-order history and installed-fleet age for each site. Weibull parameters (β, η) are literature-derived; confidence intervals are not propagated through the formulas in the current concept implementation. Spares readiness uses a simplified demand model (Poisson-in-expectation from F(t)); a full multi-echelon inventory optimisation is outside scope. The ML-advisor layer (Random Forest + KG inference) is a proposed architecture from Lin & Ompusunggu (2026) — no live ML model is trained or deployed in the current tool. This manual and the associated tool are an engineering education and pre-design aid; final maintenance strategies must be developed by qualified reliability engineers with site-specific data, and reviewed against the authority having jurisdiction and applicable OEM warranty terms.

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