JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year RELIABILITY ENGINEERING Previous Question Paper (October - 2020 - R16)

The Normal Distribution, also known as the Gaussian distribution, is a continuous probability distribution defined by the mean (μ) and standard deviation (σ). Its probability density function (PDF) is given by:

Key characteristics include:

• It is symmetric about the mean.
• The mean, median, and mode are equal.
• It is widely used in reliability engineering to model variations in component dimensions or material strengths.

The Exponential Distribution is a continuous distribution used to model the time between independent events occurring at a constant average rate (λ). Its PDF is defined as:

Key characteristics include:

• It exhibits the memoryless property, meaning the probability of failure in the next interval is independent of the age of the component.
• It is the standard model for the useful life phase of the bathtub curve, assuming a constant failure rate.
• The reliability function is given by R(t) = exp(-λt).

This is a binomial distribution problem where n = 6 trials and the probability of success (getting a 2) is p = 1/6. The probability of failure is q = 5/6. The probability of k successes is given by:

Calculating for k = 0 to 6:

The Probability Mass Function (PMF) is a bar chart where the x-axis represents k (0-6) and the y-axis represents P(X=k). The Cumulative Distribution Function (CDF) is a step function where F(x) = Σ P(X=k) for all k ≤ x, starting at 0 and rising to 1 at x=6.