1. Architectural Principles
Calculations within this suite run entirely client-side using native double-precision floating-point arithmetic (IEEE 754). Zero user-entered parameters, equipment operational data, or imported failure logs leave the user's web browser. Heavy non-linear fits (such as Weibull Maximum Likelihood Estimation and Monte Carlo simulations) are offloaded to dedicated browser Web Workers with progress reporting and cancellation support.
2. Industry Standards Provenance
Every model in the catalog traces directly to peer-reviewed reliability textbooks or established international standards:
- IEC 61649: Weibull analysis — Goodness-of-fit, parameter estimation via Rank Regression (RRX, RRY) and Maximum Likelihood Estimation (MLE).
- ISO 281: Rolling bearings — Dynamic load ratings and rating life (basic L10 and modified L10h rating life with a1 reliability factors).
- IEC 60812: Failure modes and effects analysis (FMEA and FMECA) — Qualitative and quantitative risk ranking methodologies.
- IEC 61025: Fault tree analysis (FTA) — Boolean reduction and MOCUS minimal cut sets.
- IEC 61078: Reliability block diagrams (RBD) — Series, parallel, and k-out-of-n active/standby redundancy modeling.
- EN 15341 / SMRP: Maintenance Key Performance Indicators — Standard formulas for PM compliance, schedule compliance, and backlog duration.
- MIL-HDBK-189 & MIL-STD-1629A: Reliability growth tracking and failure mode criticality number formulation.
3. Primary Literature References (Cited by Name)
- Dr. Robert B. Abernethy, The New Weibull Handbook (5th Edition).
- Charles E. Ebeling, An Introduction to Reliability and Maintainability Engineering.
- William Q. Meeker and Luis A. Escobar, Statistical Methods for Reliability Data.
- F. Stanley Nowlan and Howard F. Heap, Reliability-Centered Maintenance (United States Department of Defense).
- John Moubray, Reliability-Centred Maintenance (RCM II).
- Andrew K.S. Jardine and Albert H.C. Tsang, Maintenance, Replacement, and Reliability: Theory and Applications.
4. Golden Test Vectors & Verification Tolerances
Our automated test harness (Vitest) verifies each closed-form calculation against published analytical benchmarks:
| Equation / Model | Benchmark Condition | Expected Golden Value | Tolerance |
|---|---|---|---|
| Exponential R(t) | MTBF = 1000, t = 100 | 0.904837418 | 1e-6 |
| Availability (Ai) | MTBF = 900, MTTR = 100 | 0.900000 (876 h downtime/yr) | 1e-6 |
| k-out-of-n | n = 3, k = 2, R = 0.9 | 0.972000 | 1e-6 |
| Weibull MTTF | β = 2, η = 1000, γ = 0 | 886.2269 | 1e-4 |
| Weibull B10 Life | β = 2, η = 1000, γ = 0 | 324.593 | 1e-3 |
| OEE Composite | Avail 433/480, Ideal 1.0, 380/400 | 0.791667 (79.17%) | 1e-5 |
| Bearing L10h | C = 30 kN, P = 10 kN, 1000 rpm (Ball) | 450.0 hours (27M revs) | 0.1 h |
| Poisson Spares (s) | Mean demand = 2.0, Target = 0.90 | s = 4 (CDF = 0.9473) | Exact integer |
| Equivalent Annual Cost | C0 = 100,000, n = 10, i = 8% | 14902.95 | 1e-2 |
| Arrhenius AF | Ea = 0.7 eV, Tuse = 328.15K, Tstress = 398.15K | 77.6 | 0.5 |
5. Numerical Limitations & Boundaries
- Minimum Failures for Weibull Fitting: A minimum of 3 distinct failures is required to fit a 2-parameter Weibull model. Datasets with fewer than 6 failures display a prominent small-sample warning.
- Root-Finding Fallbacks: Brent bracketed solving is strictly bounded. If an optimization does not converge within the maximum iterations, the tool displays a diagnostic message explaining the convergence failure rather than returning a misleading number.
- Single Censoring Mode: Right-censoring (suspensions) is supported across all models. Heavy arbitrary interval censoring requires sufficient data points per inspection window.
6. Changelog & Version History
Version 1.0.0 (October 30, 2026)
- Initial release of the Maintenance & Reliability Suite Foundations.
- Single source of truth architecture (tools.registry.ts) across 8 engineering disciplines.
- Double-precision Math Core with Lanczos Gamma, Wichura AS241 Normal, and Chi-Square quantile functions.
- Client-side IndexedDB PBKDF2/AES-GCM (256-bit) project vault.
- 15 canonical closed-form golden tests passing with 100% test coverage.