Advanced Analysis
Spare Parts Calculator
How many spares to stock, using Poisson demand modelling and MTBF-based failure forecasting at the confidence level you choose.
λ = (T ÷ MTBF) × NPoisson demand model
When failure events are rare and independent (constant failure rate), spare parts demand follows a Poisson distribution. The key input is the expected number of failures over the planning period.
Expected failures over the period
λ = (T ÷ MTBF) × N_systemsProbability of exactly k failures
P(X = k) = e^(−λ) × λ^k ÷ k!The recommended stock is the smallest k whose cumulative probability reaches your chosen confidence level.
Choosing a confidence level
| Confidence | When to use it |
|---|---|
| 80% | Budget-conscious; acceptable for non-critical parts with short lead times |
| 90% | Standard stocking level for general industrial parts |
| 95% | Critical equipment with significant downtime costs |
| 99% | Safety-critical applications or very long lead-time parts |
Frequently asked questions
When is the Poisson model appropriate?
The Poisson model works well when failures are independent, occur at a constant rate (exponential time between failures), and the expected number per period is relatively small. For wear-out parts with increasing failure rates (Weibull β > 1), consider adjusting your MTBF to reflect the planning horizon.
How do I balance stocking cost vs. stockout risk?
Compare the cost of carrying an extra spare (unit cost × carrying rate × time) against the expected cost of a stockout (downtime cost per event × probability of need). Stock more when downtime costs are high relative to part cost.