Critical Spare Stockout Risk Calculator (Poisson)
Critical spares move so slowly that average-based reorder points do not work. With demand of a few units a year, stockout risk follows the Poisson distribution, and this calculator uses it to compare the cost of holding zero to five units.
Your numbers
Average units consumed per year, counting failures and planned use.
Capital, storage, insurance and obsolescence as a share of unit value.
Downtime and expedite cost when a failure occurs and no spare is on hand.
Your results
Assumes a one-for-one replenishment policy with random, independent demand. Compare the total cost at each stock level by changing the select input; the lowest total is the economic choice before considering safety rules.
Total annual cost vs lead time
Sweeps Replenishment lead time from 5 to 365, holding your other inputs fixed.
Review slow-moving critical spares in your ERP
An optional review of min and max settings for critical spares against demand history.
Optional. The tool and every export work without this. No spam.
How to use it
Enter annual demand, replenishment lead time and the cost of one unit. Add an annual holding cost percentage and the cost of a demand that finds the shelf empty, such as downtime plus expedited freight. Change the stock level from zero to five and compare the fill probability and total expected annual cost. The chart shows how total cost grows with lead time at the stock level you chose.
- Count only demand that actually consumes the part, not transfers or returns.
- Use the supplier's realistic lead time, not the catalog promise.
- Test several stock levels; the cost curve is often U-shaped.
The math
Demand during lead time follows a Poisson distribution with mean lambda = annual demand x lead time / 365. With one-for-one replenishment and S units on the shelf, a new demand is served from stock when fewer than S orders are outstanding, so the fill probability is P(X <= S - 1), the sum of e^(-lambda) x lambda^k / k! for k up to S - 1. Expected shortage events are demand x (1 - fill). Total cost adds holding to expected stockout cost.
Reading the result
At low lambda, the first unit usually buys the largest drop in risk, and the second or third unit buys much less. If a unit costs more than the expected stockout loss it prevents, do not stock it and use a contract, a pooled spare across sites or a repair-and-return pool instead. Also check whether the part can be repaired or refurbished, which shortens the effective lead time.
Common mistakes
Applying a normal-distribution safety stock formula to parts that move a few times a year gives nonsense. Understating the stockout cost, particularly for single points of failure, pushes the answer toward no stock. Finally, set the ERP min and max to match: for a one-for-one policy that means a reorder point of S - 1 and a max of S, or a manual review rule, in SAP, Infor, Epicor or your system of record.
Frequently Asked Questions
Why Poisson instead of a normal distribution?
With only a few events per year, demand is discrete and skewed. The normal distribution can give negative or fractional demand and misstate tail risk, while Poisson handles rare random events correctly.
What if demand is not random?
If usage follows a schedule, such as planned overhauls, order for the schedule and use this tool only for the unplanned portion. Mixing scheduled and random demand overstates the stock you need.
How do I set the stockout cost?
Include lost production per hour times expected downtime, expedite freight, overtime and any penalty. If a failure idles a bottleneck machine, the figure often dwarfs the part price.
Can I use it for several identical machines?
Yes, add demand across all machines using the same part. Pooling demand across assets is a cheap way to improve fill rate without buying more units per machine.
Netray can help rank slow-moving spares in your ERP by criticality and demand so stocking decisions follow the numbers. The calculator itself needs no contact.
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