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.