INTRODUCTION TO RELIABILITY THEORY — DU B.Sc (hons) Statistics Previous Year Question Papers

3. Attempt six questions in all 1. Attempt the following: a) Define Hazard funetion and find out its relation with failure distribution function. b) Define Reliability of a system with a suitable example. c) Define mean inactive time (MIT) d) If hazard rate of a component is. 7 x 10-4, then find MTTF. e) Define Proportional reverse hazard rate model. (5 × 3 = 15) 2. The failure density function of the random variable T is given by f(t) = 0.5e-o.st,t≥0. Calculate i. Reliability of the component ii. Reliability of the component for a 100 hours mission time ili. Mean Time to Failure (MTTF) iv. Median time of the random variable T v. What is the life of the component, if the reliability of 0.96 is desired? (5×3=15) b) Describe the maximum likelihood estimation (MLE) method for estimating the parameter of the exponential distribution for complete samples. (7,8) a) How do you do estimation with Censored Samples? Differentiate between failure censored and time censor.ed sinplcs. Find out the mean and variance of the unknown parameter G. a) The lifetime of a component is assumed to follow an exponential distribution with a mean of 5 hours. Obtain the following probabilities: (i) The probability that the component survives beyond 10 hours. (ii) The probability that the component fails within the first 3 hours` b) A system consists of four independent components arranged in a.2-out-of-4 configuration in which probability of success of each component is 0.5. (i) Find the probability that the system functions successfully. (ii) Determine the probability that ex.actly two components fail. (7, 8) a) Explain the role of ageing in system reliability analysis and discuss different ageing properties of lifetime distributions. b) What is redundancy? Explain different types of redundancy in systems. (7, 8) a) For a weibull distribution with scale parameters `d' and shape parameter `S', write down the expression for probability density function, reliability function, and Hazard function. b) The failure time of a certain component has a Weibul] distribution with a = 2000 Find (i) Reliability function (ii) Hazard function (iii) Reliability and hazard at t = 1500 hours. (9, 6)