To: Stagger
First of all reliability and safety calculations are based on 10-6 so all failure rates must be converted to that value. Your calculations are correct. The probability of losing both engines using your failure rate of 30,000 hours is 1.1109 10-9. However your statement “No” is incorrect because the failure of one engine is independent from the failure of the other. The failure of both engines at the same time can be attributed to an external source (fuel starvation/contamination or, flying through an ash cloud or heavy rain/hail and there fore cannot be quantified in the calculation. It can be considered but the frequency of occurrence is unknown.
In the performance of a Safety Analysis (Fault Tree Analysis) the probability of failure of the two individual engines are joined at an And Gate. That means that to have a total loss of power both engines must fail. The way they arrive at the total figure is to multiply the individual failure rates against each other. Based on your failure rate of 30,000 hours the rate of failure on one engine would be 33.33 10-6 or, 33.33 times in a million hours of operation for that type of engine being used on what ever type of aircraft. By multiplying one failure rate against the other you get 1.1109 10-9.
That is the number that is in the final safety document that is turned over to the certification authorities. However the FAA/CAA may have indicated that the failure of both engines due to independent failure modes might be higher that 1 10-9. If that’s the case the reliability analyst may have to plug in some different numbers when they perform their reliability analysis. The whole thing is based on numbers that may not even have related to the parts being analyzed. Every thing is based on statistical analysis and the numbers in most cases do not reflect the true reliability and safety of the aircraft or its components and appliances. That is why aircraft crash at a frequency higher than that required to gain certification.
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The Cat