KEVOS® MAKEOS · Maintenance
Critical Spares Plan (Poisson Failures over the Lead Time, Spares for a Service Level)
For a group of identical repairable or randomly failing parts, how many failures should I expect while a replacement is on order, and how many spares must I hold to be this sure of not running out?
Spares holding for parts that fail at a constant rate (random failures, such as electronic boards, drives, seals or repairable units): the expected failures across the installed parts during the resupply or repair lead time from the MTBF and running hours, the smallest number of spares whose Poisson probability of covering all failures in that time reaches your service level, and the cover the spares held give, against your service level.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Identical parts installed | parts | Number of identical parts in service that the spares cover. |
| Mean time between failures of one part | h | Mean running time between failures of one part, from your maintenance records or the maker’s data. |
| Running hours per day | h/day | Hours a day each part runs. |
| Resupply or repair lead time | days | Calendar days to get a replacement or repair back (order, transit and repair). |
| Chance of not running out | % | Probability that the spares cover every failure while waiting for resupply. |
| Spares held | parts | Good spares in stock now. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Identical parts installed
- What it is
- The number of identical parts in service that the spares on the shelf must cover, such as the same drive on several machines.
- Units and format
- Enter a number in parts: parts. The form accepts 1 parts to 1000000 parts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 parts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Expected failures, and the spares needed, rise with the number installed.
- Get it right
- Count only parts that can take the same spare; different revisions need separate plans.
What this means: Mean time between failures of one part
- What it is
- The average running time between failures of one part, the reciprocal of its constant failure rate.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer MTBF lowers the expected failures and the spares needed.
- Get it right
- Work it out from your own failure records where possible; maker MTBF figures are often optimistic.
What this means: Running hours per day
- What it is
- The number of hours each part runs per day, which turns the lead time into running hours.
- Units and format
- Enter a number in h/day: h/day. The form accepts 0.000001 h/day to 24 h/day. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 h/day as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More running hours raise the expected failures during the lead time.
- Get it right
- Use running hours, not the hours the plant is staffed.
What this means: Resupply or repair lead time
- What it is
- The calendar days from a failure until a replacement or repaired part is back on the shelf: ordering, transit and repair.
- Units and format
- Enter a number in days: days. The form accepts 0.000001 days to 3650 days. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 days as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Expected failures, and usually the spares needed, rise in proportion.
- Get it right
- Use the realistic worst lead time, including import delays and repair queues.
What this means: Chance of not running out
- What it is
- The probability that the spares on hand cover every failure while waiting for resupply, the service level the stock is sized to.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 50% to 99.99%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 95% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher service level raises the spares needed.
- Get it right
- Choose a high level for parts whose failure stops production; each extra few per cent costs more spares.
What this means: Spares held
- What it is
- The number of good spares in stock now, compared with the number needed.
- Units and format
- Enter a number in parts: parts. The form accepts 0 parts to 100000 parts. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 parts as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the cover reported.
- Get it right
- Count only tested, ready-to-fit spares; a unit waiting for repair is not a spare.
Method and formulas
- Failures in the lead time are taken as Poisson with mean λ = parts × running hours per day × lead time ÷ MTBF (constant failure rate).
- P(X ≤ s) = Σ e^(−λ) λ^k ÷ k! for k = 0 … s (NIST Poisson distribution).
- Spares needed = smallest s with P(X ≤ s) ≥ the service level; cover of the spares held = P(X ≤ held).
- Example: 1.08 failures expected in 45 days; 3 spares give 95 % cover.
Limitations
- Constant failure rate: parts that wear out (bearings, belts, tools) fail more as they age; use a Weibull model such as the bearing fleet spares plan for those.
- Each failure uses one spare and every spare is good; repair turnaround is treated as fixed.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set stock levels for critical drives, boards or valves
- Decide how many repairable units to keep in the loop
- Show the cost of long supplier lead times in spares
Who it is for
- Maintenance planners
- Reliability engineers
- Stores and purchasing staff
What you get
- Failure rate and expected failures in the lead time
- Spares needed for the service level
- Cover given by the spares held
Interpreting the result
- Halving the lead time halves the expected failures while waiting, which often cuts the spares needed more than any other change.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.6.19 Poisson Distribution — https://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Spares and the repair pipeline
In Breakdowns and Buffers by the Numbers
What it covers: Spares for random failures: Poisson demand over the lead time, Palm's theorem for units out for repair, service level against the cost of a stock-out, and the hours that set the failure rate.
Method explained here · KEVOS® original book
Inverter heat, reliability and spares
In Rooftop Solar for Factories by the Numbers
What it covers: How to ventilate an inverter room so the inverters do not derate, read inverter failure records with confidence bounds, and decide whether a spare inverter is worth holding.
Method explained here · KEVOS® original book
Specifying, commissioning and maintaining drives
In Variable-Speed Drives by the Numbers
What it covers: How to write a drive specification from the load and the site, commission a drive step by step, record its settings, plan spares across a fleet, and keep its set-up on replacement.
Useful alongside · Library collection
Maintenance that prevents breakdowns: choosing a strategy for each machine in a small factory
In Lean, Maintenance and Continuous Improvement
What it covers: Running equipment until it breaks feels cheap until the breakdown comes at the worst time. How to rank machines, match maintenance to each, involve operators and learn from repeat failures.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.