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Spare Parts Optimization Calculator

Spare holdings are a bet: too few and you extend downtime, too many and you tie up capital in parts that may never be used. When failures are random and independent, demand over a lead time follows a Poisson distribution, which turns the decision into an explicit trade between stock level and service level.

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Formula

Expected demand over lead timeλ = n × t / MTBF
n installed units, t lead time.
Probability of exactly k demandsP(k) = e^(−λ) · λ^k / k!
Service level with s sparesP(demand ≤ s) = Σ (k = 0 to s) e^(−λ) λ^k / k!
Expected shortage costCost = P(stockout) × downtime hours × cost per hour

Worked example

12 identical pumps, each with MTBF = 8760 hours. Spare lead time is 90 days (2160 hours).

  1. λ = 12 × 2160 / 8760 = 25920 / 8760 = 2.959
  2. P(0) = e^(−2.959) = 0.0519
  3. P(≤1) = 0.0519 × (1 + 2.959) = 0.2055
  4. P(≤2) = 0.2055 + e^(−2.959)·2.959²/2 = 0.2055 + 0.2273 = 0.4328
  5. P(≤5) = 0.9166; P(≤6) = 0.9666; P(≤7) = 0.9877

Six spares give a 96.7% service level; seven give 98.8%. The seventh spare buys 2.1 percentage points — whether that is worth its purchase and carrying cost depends entirely on the cost of an hour of downtime. This is the calculation that turns a stocking argument into an arithmetic one.

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Common mistakes

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Spare Parts Optimizer is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.

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