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## Engineering

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Q.1

The demand placed on the system is described by a log normally distributed random variable with mean 50 and standard deviation of 10. Capacity of a system is modelled by a Weibull random variable with mean 62 and standard deviation of 14.

find out the probability of failure of this system using Monte Carlo simulation technique.

Q.2

A random variable (X) is modelled as an exponentially distributed with mean 30 units. Simulate N = 50 samples from this distribution, and each sample must contain m = 20 simulated values. From one simulated sample, find out the sample mean, i.e., mean of 20 simulated values. Repeat this process for all N = 50 samples.

The end result would be a sample of 50 values of the sample mean. Using this data, answer the following:

(1) Plot its histogram of these mean values.

(2) Use probability paper method to find out a suitable probability distribution for the sample mean.

(3) find out the bias and standard error associated with sample mean estimates.

Q.3

A component has a time to failure distribution that is modelled as the Weibull distribution with shape parameter 3 and scale parameter of 36 months. This component is planned to be deployed for a mission of 6 months at a time. If the required mission reliability is 0.85, will a new component fulfil this requirement?

Plot the mission reliability versus of the age of the system and find out the age at which the component must be replaced.

Other Engineering, Engineering

• Category:- Other Engineering
• Reference No.:- M91897

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