What is the FMECA criticality number Cm?

Cm = (S_eff/10) × (D/10) × λ × N, where S_eff is severity reduced by redundancy (N+1 → ×0.65, 2N → ×0.40), D is detectability (1–10), λ is annual failure rate, and N is installed base. Tier thresholds: VITAL Cm ≥ 0.5; ESSENTIAL 0.1–0.5; DESIRABLE < 0.1. Source: MIL-STD-1629A.

What is the newsvendor critical ratio?

CR = Cu / (Cu + Co), where Cu is the under-stock (stockout) cost per event and Co = carrying_rate × unit_cost × part_life_years is the over-stock cost over the part's service life. Q* is the smallest integer where P(X ≤ Q*) ≥ CR under Poisson(μ_LT) for slow movers (μ_LT < 5) or Normal for fast movers.

Why does the engine switch between Poisson and Normal distributions?

M&E spare parts are typically slow movers (mean demand during lead time μ_LT 200). For fast movers (μ_LT ≥ 5), Normal is a close match and computationally stable. The switchover threshold DATA.spares.poissonThresholdMuLt = 5.

What does the METRIC model add over a single-location newsvendor?

METRIC (Sherbrooke 1968) is a two-echelon model that optimises stock across a regional hub and N sites jointly. It accounts for the depot's outstanding-orders queue: effective site lead time = base hub-to-site time + expected backorders at hub ÷ (N × λ). Marginal analysis then allocates each additional unit to the echelon where the fill-rate gain per dollar is greatest — producing a lower total investment than independent site-level stocking.

Home / DC Solutions / Technical Manuals / Critical Spares Engine

Technical Manual · Spares & Obsolescence

Critical Spares Engine — Methodology & Formulas

Every input, equation, constant, output, and reference behind the Critical Spares Engine. Seven analytical modules — FMECA criticality, readiness gauge, newsvendor optimal stock, METRIC/MEIO two-echelon hub positioning, supplier risk index, DMSMS last-time-buy economics, and Kraljic sourcing strategy — are executed deterministically by RZEngine.models.spares in rz-engine.js. No random values except in the explicitly flagged Monte-Carlo block.

Engine RZEngine v2.5+ models.spares Basis MIL-STD-1629A · Sherbrooke METRIC · Acklam Φ⁻¹ Modules 8 Outputs 20+

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01 Purpose & engineering basis

Data-center M&E equipment failures cost tens of thousands of dollars per hour in downtime. The Critical Spares Engine answers five planning questions: how critical is each spare part, how many should be held on site and at a regional hub, when and how many to buy before a part is discontinued, which supplier relationships carry the most supply risk, and what sourcing strategy is appropriate for each commodity.

The engine is grounded in four interlocking bodies of theory. FMECA (MIL-STD-1629A) provides the criticality framework — severity, detectability, and occurrence combine into a Risk Priority Number that tiers parts into VITAL / ESSENTIAL / DESIRABLE. Newsvendor theory (the critical-fractile model, Whitin 1955 / Porteus 1990) provides the cost-minimising stock level Q* balancing over-stock and under-stock costs. METRIC and MEIO (Sherbrooke 1968; Axsäter VARI-METRIC; Clark-Scarf 1960) extend this to multi-echelon hub-and-spoke networks where marginal analysis allocates stock across hub and sites jointly. DMSMS (Diminishing Manufacturing Sources and Material Shortages, SD-22) governs the last-time-buy and requalification decision when a part reaches end-of-life.

02 Inputs

Inputs across the eight modules. The commodity selector auto-fills λ, installed base, severity, lead time, unit cost, and understock cost with realistic DC M&E industry defaults; all fields are editable to actual fleet data.

Field	Symbol	Unit	Default	Meaning
Annual failure rate `c1_lambda`	`λ`	failures/yr	0.25	Expected failures per unit per year = 1 / MTBF_years. Typical DC M&E range: 0.04–0.25.
Installed base `c1_installed`	`N`	units	4	Count of this equipment type at the site. Scales fleet failure rate and fleet demand.
Severity `c1_severity`	`S`	1–10	8	Consequence if failure reaches the operation. 1 = negligible; 9 = full site outage; 10 = safety. Per MIL-STD-1629A scale.
Detectability `c1_detectability`	`D`	1–10	6	Difficulty of detecting failure before outage. 1 = alarm-monitored; 10 = sudden no warning. Higher = harder to catch.
Redundancy `c1_redundancy`	`r`	enum	N+1	System redundancy: N / N+1 / 2N. Reduces effective severity by factors 1.0 / 0.65 / 0.40.
Qualified alternates `c1_alternates`	`a`	count	1	Number of approved substitute suppliers. Alternate factor = 1 / max(1, a); raises supply exposure when sole-sourced.
Unit cost `s_unit_cost`	`C_u`	USD	4 500	Procurement cost per spare unit (list price or contract rate).
Understock cost `s_understk_cost`	`C_u`	USD/event	85 000	Financial exposure per stockout event — downtime cost, emergency freight, expedite premium.
Carrying cost rate `s_carry_rate`	`r_c`	%/yr	25	Annual holding cost as fraction of unit value: capital (~10%), storage (~4%), insurance (~2%), obsolescence (~9%).
Part life `s_part_life`	`L_p`	yr	8	Expected service life of the spare before obsolescence or physical degradation. Sets Co time horizon.
Annual demand mean `s_demand_mu`	`μ_A`	units/yr	1.0	Mean demand per year across the fleet = λ × N. Sigma defaults to μ × 0.6.
Lead time (mean) `s_lt_weeks`	`LT`	weeks	16	Supplier replenishment lead time from PO to delivery.
Lead time sigma `s_lt_sigma`	`σ_LT`	weeks	4	Standard deviation of lead time — captures supplier variability and logistics uncertainty.
Target fill rate `s_fill_rate`	`FR`	%	99	Fraction of demand events fulfilled immediately from stock. Drives safety stock SS = z(FR) × σ_demand_during_LT.
Hub inputs `h_*`	—	various	see tool	Number of sites (4), part types (6), OEM lead time (20 wk), hub-to-site lead time (0.5 wk), budget ($200 K).
DMSMS inputs `ltb_*`	—	various	see tool	Years to EOL, annual demand, unit cost, holding rate, criticality, alternate qualification cost, requalification cost.

03 Calculation methodology

Eight modules in sequence. Function anchors map to RZEngine.models.spares.* in rz-engine.js and to the matching calc*() in spares-readiness-calculator.html.

M1 — FMECA Criticality & RPN

S_eff = S × redFactor (redFactor: N=1.00, N+1=0.65, 2N=0.40) Cm = (S_eff/10) × (D/10) × λ × N RPN = S_eff × D × min(10, λ×10) [capped at 1000] Fleet failures/yr = λ × N Alternate factor = 1 / max(1, a) Tier: VITAL Cm≥0.5 · ESSENTIAL 0.1≤Cm<0.5 · DESIRABLE Cm<0.1 In calcCriticality(). Cm is the MIL-STD-1629A criticality number normalised to an annual annualised basis. RPN is analogous to FMEA = Severity × Occurrence × Detection. MIL-STD-1629A · STANDARD

M2 — Spare Readiness Gauge

PO confidence = 1.0 if (PO + commit + on-time) else 0.5 (unconfirmed) or 0.3 (late commit) Confirmed supply = on-hand + PO_qty × PO_confidence Readiness % = min(100, confirmed_supply / required × 100) Date slack (days) = need_date − commit_date Status: GREEN readiness≥100% and slack≥7d · YELLOW ≥80% · RED <80% or commit late In calcReadiness(). No engine kernel call — arithmetic on procurement data. DC O&M PRACTICE · PROPRIETARY

M3 — Newsvendor Optimal Stock (critical-fractile)

L = LT_weeks / 52 (lead time in years) μ_LT = μ_A × L (mean demand during LT) σ_LT = √( L·σ_A² + μ_A²·σ_LT_yr² ) (demand-during-LT sigma) Co = r_c × C_unit × L_p (over-stock cost) CR = C_u / (C_u + Co) (critical ratio) Q* = min k : P(X≤k; Poisson(μ_LT)) ≥ CR [if μ_LT < 5] Q* = max(0, ⌈μ_LT + Φ⁻¹(CR)·σ_LT⌉) [if μ_LT ≥ 5] SS = max(0, ⌈Φ⁻¹(FR) · σ_LT⌉) (safety stock for fill-rate) ROP = ⌈μ_LT + SS⌉ (reorder point) Fill% = P(X≤Q*; Poisson(μ_LT)) or Φ((Q*−μ_LT)/σ_LT) Cost = (Co/L_p)·max(0,Q*−μ_LT) + C_u·μ_A·(1−Fill%) In RZEngine.models.spares.newsvendor(input). Poisson mode auto-selected when μ_LT < DATA.spares.poissonThresholdMuLt = 5. Φ⁻¹ via Acklam (2003): RZEngine.models.spares.normInv(p). Whitin 1955 / Porteus 1990 · ACKLAM 2003

Poisson CDF kernel — slow-mover demand model

P(X≤k; λ) = Σ_{i=0}^{k} e^{−λ} · λ^i / i! (exact partial sum) ≈ Φ((k+0.5−λ)/√λ) (continuity-corrected Normal, only when λ>200) P(X≥1 stockout) = 1 − P(X≤Q*; λ_LT) In RZEngine.models.spares.poissonCdf(k, lambda). Exact partial sum for λ≤200; normal-continuity approximation only beyond. M&E spares are always well below λ=200. ABRAMOWITZ & STEGUN 26.4 · STANDARD

Inverse Normal CDF (Acklam kernel)

Φ⁻¹(p) — Acklam (2003) rational approximation, three-region piecewise |relative error| < 1.15×10⁻⁹ (vs Beasley-Springer-Moro 1977 |e|<4.5×10⁻⁴) Used for: Q* in Normal mode, safety-stock z-score, MEIO fill targets In RZEngine.models.spares.normInv(p). Coefficients in DATA.spares.acklamA/B/C/D, threshold DATA.spares.acklamPLow = 0.02425. Also underpins alarm-management Poisson model. DATA.sources['spares.acklam'] · ACKLAM 2003

M4 — METRIC / MEIO Two-Echelon Hub Positioning

λ_regional = N_sites × λ_site × LT_vendor_yr (Poisson demand at regional hub) B(s, λ) = λ·(1−CDF(s−1,λ)) − s·(1−CDF(s,λ)) (expected backorders at hub stock s) eff_LT_site = LT_hub_to_site + B(s1, λ_reg) / (N_sites × λ_site) λ_site_eff = λ_site × eff_LT_site Fill_site(s1, s2) = P(X≤s2; Poisson(λ_site_eff)) Marginal gain per $ = ΔFill / (unit_cost × holding_pct) Allocate next unit to echelon with higher marginal gain/$ until fill-target reached In calcMEIO() and calcHub(). Implements the Sherbrooke (1968) METRIC insight: hub backorders increase effective site lead time, and marginal analysis allocates each unit optimally across echelons. SHERBROOKE 1968 / AXSÄTER VARI-METRIC · ACADEMIC

M5 — Supplier Risk Index

SRI = Σ w_i × score_i where scores are: OTIF (18%), single-source (16%), financial health (14%), lead-time volatility (14%), geographic concentration (12%), capacity headroom (10%), geopolitical risk (10%), contract status (6%) Tier: CRITICAL SRI≥7.0 · HIGH 5.5–7.0 · MEDIUM 3.5–5.5 · LOW <3.5 In calcSupplierRisk(). OTIF (On-Time In-Full %) is inverted: score = (100 − OTIF%) / 10. Weights sum to 1.00. SUPPLY-CHAIN PRACTICE · PROPRIETARY RUBRIC

M6 — DMSMS / Last-Time-Buy Economics

DMSMS score = f(criticality, years_to_EOL, alternates, requalification_cost) LTB economic qty = ⌈μ_A × remaining_life_yrs × (1 + buffer_pct)⌉ LTB cost = LTB_qty × unit_cost Stockout exposure (no LTB) = μ_A × remaining_yrs × Cu × P(stockout per yr) Decision: BUY if LTB_cost < stockout_exposure + requalification_cost In calcLTB(). Buffer_pct = 15% default for consumption uncertainty. DMSMS tiers follow SD-22 exposure bands: Low / Medium / High / Critical. DMSMS SD-22 · DOD STANDARD

M7 — Kraljic Sourcing Matrix

x-axis: Supply Risk score (1–10) = f(single_source, geo_conc, OTIF, geopolitical, qualified_suppliers) y-axis: Spend Impact score (1–10) = f(criticality, unit_cost, annual_spend) Quadrant: Strategic (high-risk, high-impact) → partnership + dual-source Bottleneck (high-risk, low-impact) → secure supply, safety stock Leverage (low-risk, high-impact) → competitive bidding Non-critical (low-risk, low-impact) → simplify, consolidate In calcKraljic(). Per Kraljic (1983) HBR "Purchasing Must Become Supply Management". KRALJIC 1983 HBR · ACADEMIC

M8 — Monte-Carlo Stress Test

For each trial t = 1 … N_trials (10 000): LT_t ~ Normal(LT_mean, σ_LT) (or Triangular for asymmetric) demand_t ~ Poisson(μ_A × LT_t/52) for slow movers supply_t = stock × supplier_reliability_t stockout_t = demand_t > supply_t P(stockout) = count(stockout_t) / N_trials P5 / P50 / P95 readiness from sorted readiness_t distribution In calcMonteCarlo(). Uses Math.random() (browser CSPRNG) for trial sampling only — all deterministic modules are unaffected. Tornado chart ranks input variable contribution to P(stockout) variance. MONTE-CARLO METHOD · STANDARD

04 Constants & data sources

All numerical constants live in the deep-frozen DATA object with a // source: tag in rz-engine.js. Key blocks:

DATA key	Value / Range	Meaning	Source
`DATA.spares.poissonThresholdMuLt`	5	μ_LT threshold below which Poisson CDF is used instead of Normal for Q*.	Statistical practice
`DATA.spares.acklamPLow`	0.02425	Tail-region threshold for Acklam Φ⁻¹ rational approximation.	Acklam (2003)
`DATA.spares.acklamA/B/C/D`	6+5+6+4 coefficients	Rational polynomial coefficients for three-region Φ⁻¹ approximation. \|relative error\| < 1.15×10⁻⁹.	DATA.sources['spares.acklam']
Redundancy severity factors	N=1.00, N+1=0.65, 2N=0.40	Multiplier applied to raw severity S to obtain S_eff. Reflects probability of second-failure exposure given N+1 or 2N architecture.	DC FMECA engineering practice
VITAL threshold Cm	≥ 0.50	Criticality number above which stockout is unacceptable — STOCK + DUAL-SOURCE decision.	MIL-STD-1629A adapted
ESSENTIAL threshold Cm	0.10 – 0.50	Criticality range requiring stock; single-source acceptable.	MIL-STD-1629A adapted
`DATA.sparesPricing.classes`	8 classes	Unit list-price bands (low/mid/high, USD) for UPS 50 kW module, VRLA string, genset PM kit, genset top-overhaul, chiller compressor, CRAH EC fan kit, PDU MCCB breaker, air filter set.	DATA.sources['sparesPricing']
DMSMS LTB buffer	15%	Consumption uncertainty buffer added to the deterministic LTB quantity. Conservative; adjust upward for higher demand variance parts.	SD-22 engineering practice
Normal CDF coefficients	Abramowitz-Stegun 26.2.17	5-term rational polynomial for normCdf(x); \|error\| ≤ 7.5×10⁻⁸. Used for fill-rate achieved calculation in Normal mode.	Abramowitz & Stegun (1964)

Commodity	Typical λ (failures/yr)	Typical unit cost	Typical LT (weeks)	FMECA severity default
UPS 50 kW power module	0.20 – 0.30	$25 K – $60 K	12 – 20	9 (N config)
UPS VRLA battery string	0.12 – 0.20	$8 K – $15 K	4 – 8	8
Genset annual PM kit	1.00	$5 K – $15 K	2 – 4	5
Genset top overhaul	0.10 – 0.15	$60 K – $150 K	16 – 24	9
Chiller centrifugal compressor	0.10 – 0.20	$80 K – $250 K	20 – 32	9 (N config)
CRAH EC/VFD fan retrofit kit	0.15 – 0.25	$8 K – $20 K	6 – 12	6
PDU/MCCB breaker (DC-grade)	0.05 – 0.10	$1 K – $5 K	2 – 6	7
CRAH G4 filter set	3.00 (annual change)	$1.5 K – $4 K	1 – 3	3

Pricing bands sourced from: Schneider/APC Galaxy VS module class (public list), criticalpowerbatterysolutions.com VRLA TCO 2026, OnPoint/Secondwatt genset maintenance guides 2026, and industrial MCCB distributor ranges. All bands are SCREENING level — not quotation or contract prices. See DATA.sources['sparesPricing'].

05 Outputs

Output	Symbol / Formula	Unit	Interpretation
Criticality tier	Cm threshold	VITAL / ESSENTIAL / DESIRABLE	Primary stocking decision: VITAL → STOCK + DUAL-SOURCE; ESSENTIAL → STOCK; DESIRABLE → don't stock.
Risk Priority Number	RPN = S_eff × D × min(10, λ×10)	1 – 1000	FMECA composite risk score. >100 indicates VITAL-tier stocking pressure.
Fleet failures / yr	λ × N	events/yr	Expected annual failure events across the installed fleet — the demand signal for stock sizing.
Readiness %	confirmed_supply / required × 100	%	Current coverage of the stated requirement. GREEN ≥ 100%; YELLOW 80–100%; RED < 80%.
Optimal stock Q*	Newsvendor critical-fractile	units	Cost-minimising stock level balancing Cu and Co over the part life.
Safety stock SS	⌈Φ⁻¹(FR) × σ_LT⌉	units	Buffer above mean LT demand needed to achieve the fill-rate target FR.
Reorder point ROP	⌈μ_LT + SS⌉	units	On-hand inventory level at which a replenishment order should be placed.
Critical ratio CR	Cu / (Cu + Co)	0 – 1	Fractile of the demand distribution to stock against. CR > 0.9 typically signals VITAL classification.
Fill rate achieved	P(X ≤ Q*; Poisson(μ_LT))	%	Fraction of demand events met from stock at Q*. Compare to target FR.
Annual cost at Q*	(Co/L_p)·excess + Cu·μ_A·(1−Fill%)	USD/yr	Total carrying + expected-stockout cost at the optimal stock level.
P5 / P50 / P95 readiness	Monte-Carlo percentiles	%	Stochastic readiness distribution across 10 000 scenarios. P5 = worst-case 5th percentile.
P(stockout)	MC fraction of trials with stockout	%	Target < 5% for VITAL parts. Driven by lead-time jitter, demand variability, supplier reliability.
Expected downtime cost	P(stockout) × Cu × μ_A × horizon_yrs	USD	Expected financial exposure from stockout events over the planning horizon.
Hub s1 / Site s2 stock	MEIO marginal analysis	units	Optimal allocation of units across hub and sites to reach the fleet-readiness target at minimum cost.
Fleet readiness	P(X ≤ s2; Poisson(λ_site_eff))	%	Fraction of fleet assets serviceable within MTTR given the current hub allocation.
Supplier Risk Index (SRI)	Weighted 8-factor score	0 – 10	CRITICAL ≥ 7.0; HIGH 5.5–7.0; MEDIUM 3.5–5.5; LOW < 3.5.
DMSMS / EOL exposure	Qualitative DMSMS score	Low / Medium / High / Critical	Urgency of last-time-buy or requalification action.
LTB economic qty	⌈μ_A × years_remaining × 1.15⌉	units	Economic last-time-buy quantity with 15% consumption uncertainty buffer.
Sourcing quadrant	Kraljic 2×2	Strategic / Leverage / Bottleneck / Non-critical	Drives supplier relationship strategy and contracting approach.
Days of cover	(Q* / μ_A) × 365	days	How long Q* stock lasts at the mean annual demand rate.

06 Worked example — UPS 50 kW power module

A 4-unit installed fleet (N = 4), single-string N configuration, λ = 0.25 failures/unit/yr, severity 9/10 (site outage risk), detectability 7/10. Unit cost $40 000, understock cost Cu = $150 000/event, carrying rate 25%/yr, part life 8 yr, lead time 16 weeks ± 4 weeks. Target fill rate 99%. All numbers reproduced exactly by node -e calling RZEngine.models.spares.newsvendor() and poissonCdf().

Redundancy & effective severity (N config): redFactor = 1.00 → S_eff = 9.0/10
FMECA criticality: Cm = (9.0/10) × (7/10) × 0.25 × 4 = 0.630 → tier VITAL (Cm ≥ 0.50) → decision: STOCK + DUAL-SOURCE
RPN: occurrence_scaled = min(10, 0.25 × 10) = 2.5 → RPN = 9.0 × 7 × 2.5 = 158
Fleet failures/yr: 0.25 × 4 = 1.00 events/yr
Lead-time demand (μ_LT): μ_A = 1.0 /yr, L = 16/52 = 0.3077 yr → μ_LT = 1.0 × 0.3077 = 0.308 units → Poisson mode (μ_LT < 5)
σ_LT: √(0.3077 × 0.6² + 1.0² × (4/52)²) = 0.342
Costs: Co = 0.25 × $40 000 × 8 = $80 000 (overstock cost over part life)
Critical ratio: CR = $150 000 / ($150 000 + $80 000) = 0.6522
Q* via Poisson inversion: P(X≤0; 0.308) = e⁻⁰·³⁰⁸ = 0.7351 ≥ CR = 0.6522 → Q* = 0 units (current Q* = 0 is sufficient; add N+1 redundancy to push tier to ESSENTIAL)
Safety stock for 99% fill rate: Φ⁻¹(0.99) = 2.3263 → SS = ⌈2.3263 × 0.342⌉ = ⌈0.796⌉ = 1 unit
Reorder point: ROP = ⌈0.308 + 1⌉ = 2 units
Fill rate achieved at Q*=0: P(X≤0; 0.308) = 73.5% → below 99% target; hold SS=1 to achieve 96.1%
Annual cost at Q*: (Co/8) × max(0, 0−0.308) + $150 000 × 1.0 × (1−0.735) = $0 + $39 700/yr expected stockout exposure
N+1 scenario check: With N+1 redundancy, S_eff = 9 × 0.65 = 5.85, Cm = (5.85/10)×(7/10)×0.25×4 = 0.410 → tier ESSENTIAL, RPN drops to 102
LTB economics (EOL in 5 yr): LTB qty = ⌈1.0 × 5 × 1.15⌉ = 6 units, LTB cost = 6 × $40 000 = $240 000 vs stockout exposure $39 700 × 5 = $198 500 → LTB is marginal; compare against requalification cost to decide
Poisson CDF verification: poissonCdf(k=2, λ=1.3) = Σ_{i=0}^{2} e⁻¹·³ × 1.3^i/i! = 0.857112 (engine-verified)

Engineering reading: a single-string (N) UPS module fleet is VITAL by Cm even with one alternate supplier. Adding N+1 redundancy drops the tier to ESSENTIAL and reduces RPN from 158 to 102 — the redundancy investment also buys a materially lower spares program cost. The fill-rate target of 99% requires holding 1 unit of safety stock beyond Q* = 0, with ROP = 2 units as the replenishment trigger.

07 References & standards

MIL-STD-1629A — Failure Mode, Effects and Criticality Analysis (FMECA). US Department of Defense, 1980. Defines severity, occurrence, detection scales and criticality number Cm. Adapted here for M&E DC spares.
Sherbrooke (1968) — "METRIC: A Multi-Echelon Technique for Recoverable Item Control." Operations Research, 16(1). Originating paper for the two-echelon hub-site Poisson model used in M4 MEIO.
Axsäter (1990) — "Modelling Emergency Lateral Transshipments in Inventory Systems." Basis for VARI-METRIC and the backorder approximation B(s, λ) used for hub effective lead-time correction.
Clark & Scarf (1960) — "Optimal Policies for a Multi-Echelon Inventory Problem." Management Science, 6(4). Foundation of nested decomposition in multi-echelon inventory theory.
Whitin (1955) — "Inventory Control and Price Theory." Management Science. Original critical-fractile newsvendor formulation.
Porteus (1990) — "Stochastic Inventory Theory." In Handbooks in Operations Research and Management Science. Modern treatment of the newsvendor / critical-ratio model.
Kraljic (1983) — "Purchasing Must Become Supply Management." Harvard Business Review, September–October. Sourcing matrix 2×2 quadrant framework implemented in M7.
DMSMS SD-22 — Diminishing Manufacturing Sources and Material Shortages: A Guidebook of Best Practices. Office of the Under Secretary of Defense, 2019. Governs the last-time-buy and requalification decision framework in M6.
Acklam (2003) — "An Approximation to the Percentage Points of the Normal Distribution." Rational polynomial Φ⁻¹ approximation, |relative error| < 1.15×10⁻⁹. Implemented as RZEngine.models.spares.normInv(p).
Abramowitz & Stegun (1964) — Handbook of Mathematical Functions. §26.2.17 rational approximation for Normal CDF used in RZEngine.models.spares.normCdf(x).
Engine source — rz-engine.js (RZEngine v2.5+, models.spares.*) + spares-readiness-calculator.html module logic.

08 Assumptions & limitations

Failure rates are assumed constant (exponential distribution, constant hazard rate) — the model does not directly represent bathtub-curve infant-mortality or wear-out phases; apply a correction factor for end-of-useful-life assets. Poisson demand assumes failures arrive independently; demand aggregation at the fleet level is appropriate for homogeneous fleets but may over-smooth mixed-age cohorts. Lead time is modelled as Normal — the Normal approximation is adequate for σ_LT / μ_LT < 0.5; highly skewed lead times (e.g., long-tail supply disruptions) require scenario analysis via the Monte-Carlo module.

The METRIC two-echelon model assumes a single hub serves all sites with identical lead times; lateral transshipments between sites are not modelled. Spare parts pricing bands in DATA.sparesPricing are public SCREENING benchmarks only — they must be validated against your OEM or distributor contract schedule before use in capital-program budgets.

DMSMS last-time-buy economics are deterministic; they do not model inventory carrying costs after the facility's useful life, nor the probability of alternative requalification success. This tool and manual are an engineering education and pre-design planning aid; all material procurement decisions must be validated against your facilities management programme, OEM contractual terms, and applicable statutory requirements.

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