# Weibull Distribution|Logonormally distributed random variable| Exponentially Distributed|Pobability Distribution

Budget $30-35 USD

RISK AND RELIABILITY ASSIGNMENT-

Q.1 (Using MS Office Excel)

The demand placed on a system is described by a lognormally distributed random variable with mean 50 and standard deviation of 10. The capacity of the system is modeled by a Weibull random variable with mean 62 and standard deviation of 14.

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

Q.2 (Using MS Office Excel)

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, compute the sample mean, i.e., mean of 20 simulated values. Repeat this process for all N = 50 samples.

The end result will 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 the probability paper method to determine a suitable probability distribution for the sample mean.

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

Q.3 (Using MS Office Excel)

A component has the 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 determine the age at which the component should be replaced.