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Calculating Aircraft Spare Parts

Run out of spare parts and you're in for trouble. First there's the hassle. Late nights and pressure from managers and crew. Then there's the money. A short outage might be okay. A longer outage might need a replacement aircraft or even a night in a hotel for 300 passengers and crew. Finally there's the ill-will. Passengers don't like outages.
There's a fine line between holding too many spares and too few. Compare the cost of an outage of a typical commercial jet ($10,000-$50,000) with the cost of a typical component such as a cockpit display unit ($15,000).
But, how do you decide how many spares to keep? How do you make sure that there won’t be any outages? And how do you make sure that you aren’t buying parts that will sit on the shelf and never be used?
Let's look at an example and see.
An airline operator has ten Boeing 737s which are supported from a single airport. The equipment operates for 14 hours per day and there are 4 identical CDUs per aircraft. Assume a CDU has the following specification:
Units in Service = 10ac x 4CDUs/ac = 40 units
MTBF is 16,800 hours
A repair takes 30 days
Therefore, the equipment operates for 560 hours per day and if a unit failed and was repaired in 30 days the fleet of equipment would operate for a further 16,800 hours. The same as the unit MTBF.
It would be natural to assume that 1 spare would be enough. However, MTBF is not a measure of the exact time to failure. It is a measure of the mean time between failures. Say 10 units failed in 168,000 of operation. The MTBF would be 16,800 hours. However, all of the failures could have occurred in the first few hours of service. The MTBF would still be the same. In fact, by using a compound logarithmic Poisson distribution (see results) we can show that there is a 0.01% probability that up to 6 failures could occur in the first 16,800 hours of operation. Don’t be too disheartened though. This should happen only once every 986 years.
The calculations show that 3 spare units might be a sensible choice in this situation. The mean-time-between-stock-out would be every 4 years if the store was left unattended. However, it can be shown that the average period between stock-out would increase to 92 years if:
Stock levels were monitored
An alarm trigger set at 1 unit
A 5 day emergency resupply period was agreed with the supplier
On the other hand the supplier might impose a charge for a faster repair turn-around. Say for example the supplier charged $1,000 per emergency repair. The results show that 2 spare parts will be demanded on average once every 1.02 years. If the life of the equipment was 20 years you would spend around $20,000 in emergency repairs. An additional spare only costs $15,000 and the results show that the mean time between stock-out would be 22 years. Therefore, 4 spare parts would be a better alternative and would be more cost effective.
Stock-out-risk can be forecast with a number of readily available off-the-shelf software packages. Prices range between $1500 and $70,000. Compare this with the cost of a single outage or MEL spare part .