🛡️ Definsjelogistyk en ynsetberens Live model

Basis — it model efter de sifers

Elke relaasje dy't de simulator brûkt, mei de boarne. Konstanten dy't as oanname markearre binne, binne yllustrative kalibraasjes.

Operasjonele beskikberens: it diel fan de tiid dat in systeem klear is, ynklusyf logistike fertraging.

Ao = uptime / (uptime + downtime) ≈ MTBF / (MTBF + MTTR + MLDT)[1][2]

Platfoarms falle willekeurich út mei in eksponinsjele tiid oant útfal wylst se yn wurking binne.

P(fail during h operating hours) = 1 − e^(−h/MTBF), MTBF = 40 h[2]Oanname: MTBF, ûnderdielkâns, ferbrûkssifers en ferkear binne generike plansifers, gjin gegevens oer in echt systeem.

Palm's stelling: by ien-foar-ien oanfolling folgje ûnderdielen yn de pipeline in Poisson-ferdieling.

pipeline ~ Poisson(mean = demand rate × lead time); backorders = (pipeline − S)⁺[4][3]

Reparaasjes wachtsje yn in rige dy't troch in fêst oantal teams bedjinne wurdt.

c teams serve the maintenance queue (M/M/c); site teams + fleet teams = 8[9]Oanname: MTBF, ûnderdielkâns, ferbrûkssifers en ferkear binne generike plansifers, gjin gegevens oer in echt systeem.

Dagen foarrie (days of supply): hoe lang it depot meigiet by it hjoeddeistich ferbrûk.

DOS = stock / daily consumption[10]Dagen foarrie is in planmaat dy't brûkt wurdt yn sustainment-doktrine; de ferhâlding sels is gewoane rekkenkunde.

Erlang B-blokkearring, en de krekte útwreiding dêrfan as kanalen reservearre binne foar prioriteitsferkear.

B(0)=1, B(k) = A·B(k−1) / (k + A·B(k−1)); with reservation r: exact birth–death chain[5][6]

Radarfergeliking: it deteksjeberik groeit mei de fjirde woartel fan it útstjoerde fermogen.

R ∝ P^(1/4) ⇒ πR² ∝ √P[7]

Oare plankonstanten dy't it model brûkt.

MTBF 40 operating h · part needed 40 % · repair Exp(6 h) · sites MTBF 300 h, repair Exp(8 h) · convoy 200 u · burn 1 u per operating h + 0.5 u/h per site at full power · relay +4 channels after 3 h · priority shipment: ≤ 4 open orders, lands within 24 h, one in flight at a time · ≥2 channels always open to routine trafficOanname: MTBF, ûnderdielkâns, ferbrûkssifers en ferkear binne generike plansifers, gjin gegevens oer in echt systeem.

Boolean dekkingsmodel: de kâns dat in punt sjoen wurdt troch teminsten ien fan ferskate sensorskiven.

coverage = 1 − exp(−Σ πR_i² / A)[8]Oanname: MTBF, ûnderdielkâns, ferbrûkssifers en ferkear binne generike plansifers, gjin gegevens oer in echt systeem.

Willekeur: in seeded mulberry32-generator; brûkte ferdielingen — unifoarm, eksponinsjeel (omkearde CDF), normaal (Box–Muller), Poisson (Knuth). It seed wurdt toand en is te dielen.

Boarnen

1. DoD Reliability, Availability, Maintainability, and Cost Rationale Report Manual (operational availability Ao) — U.S. Office of the Secretary of Defense, 2009
2. MIL-HDBK-338B Electronic Reliability Design Handbook (exponential failure model, availability) — U.S. DoD, 1998
3. C. C. Sherbrooke — METRIC: A Multi-Echelon Technique for Recoverable Item Control (Palm’s theorem, expected backorders) — Operations Research 16(1), 1968
4. C. Palm — Analysis of the Erlang traffic formulae for busy-signal arrangements (Palm’s theorem on (S−1,S) pipelines) — Ericsson Technics No. 4, pp. 39–58, 1938
5. ITU-D Study Group 2 — Teletraffic Engineering Handbook: Erlang B recursion E_x = A·E_(x−1)/(x + A·E_(x−1)); Erlang C — ITU, 2002
6. F. P. Kelly — Loss Networks (trunk reservation) — Annals of Applied Probability 1(3), 1991
7. MIT Lincoln Laboratory — Introduction to Radar Systems, Lecture 2: radar range equation S/N = P_t G² λ² σ / ((4π)³ R⁴ k T_s B_n L) — MIT Lincoln Laboratory
8. P. Hall — Introduction to the Theory of Coverage Processes (Boolean model: vacancy = e^(−λ·E|disc|)) — Wiley, 1988
9. D. Gross, C. M. Harris — Fundamentals of Queueing Theory (M/M/c, machine-repair models) — Wiley, 2008
10. U.S. Army FM 4-0 Sustainment Operations — sustainment planning concepts (days of supply as a planning measure) — Headquarters, Department of the Army, 2026