Question

Failure analysis testing is a mechanisms to understand how mechanical stress develops under the complex loading of vehicle dynamics to identify the cause of mechanical failure. It is known that mechanical failures due to metal fatigue of a certain type of jet engines follow a Poisson process. On the average based on the past records, a jet engine will have a failure once every 5000 flight hours.

a. If such engines are scheduled for inspection and maintenance after every 2500 flight hours, what is the probability of mechanical failure of an jet engine between inspections?

b. In a fleet of ten engines of the same type, what is the probability that not more than two will have mechanical failures within the above scheduled inspection/maintenance interval . (Assume that the failures between engines are statistically independent).

Answer 1

Solution :

The mean waiting time for a failure here is given to be 5000 flight hours. Therefore the distribution of the waiting time to failure is modelled here as:

a)

The probability of mechanical failure of an jet engine between inspections that is the failure time is less than 2500 flight hours is computed here as:

Therefore 0.3935 is the required probability here.

b)

Given a fleet of ten engines of same type, probability that not more two will have mechanical failures within the maintenance interval is computed here as:

= Probability that 0, 1 or 2 will have mechanical failures within the maintenance interval

Therefore 0.1780 is the required probability here.

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