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JNTU B.Tech IV Year RELIABILITY ENGINEERING Previous Question Paper (July - 2021 - R16)
Answer any five questions
Main
Define Reliability and discuss about the discrete random variables and continuous random variables.
Answer
Reliability is defined as the probability that a system, component, or device will perform its intended function satisfactorily for a specified period of time under stated operating conditions. Mathematically, it is represented as:
where T is the random variable representing the time to failure.
Discrete Random Variables: A random variable is discrete if it can take on only a countable number of distinct values. These are typically associated with counting processes. The probability distribution is defined by the probability mass function (PMF), P(X = x), where the sum of all probabilities equals 1. Examples include the number of failures in a fixed number of trials (Binomial distribution) or the number of arrivals in a fixed time interval (Poisson distribution).
Continuous Random Variables: A random variable is continuous if it can take on any value within a given range or interval. These are typically associated with measurements such as time, weight, or temperature. The distribution is defined by a probability density function (PDF), f(x), where the probability of the variable falling within an interval [a, b] is the integral of the PDF over that range:
In a certain manufacturing process, one percent of the products are known to be defective. If 50 items are purchased by a customer, what is the probability of getting two or less number of defectives?
Answer
This problem follows a Binomial Distribution because there are a fixed number of trials (n = 50), two possible outcomes (defective or non-defective), and a constant probability of success (failure/defect) (p = 0.01).
The probability of getting exactly k defectives is given by:
We need to find the probability of two or less defectives, P(X ≤ 2) = P(0) + P(1) + P(2).
- For k = 0: 50C0 * (0.01)0 * (0.99)50 ≈ 0.6050
- For k = 1: 50C1 * (0.01)1 * (0.99)49 ≈ 50 * 0.01 * 0.6111 ≈ 0.3056
- For k = 2: 50C2 * (0.01)2 * (0.99)48 ≈ 1225 * 0.0001 * 0.6173 ≈ 0.0756
Summing these values:
The probability of getting two or less defectives is approximately 0.9862 or 98.62%.
Define cut-set. Evaluate a general expression for system shown in Fig 1. below success and the reliability of the system using cut-set method. If each component has a reliability of 0.99 using cut-set method.
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An electronic circuit consists of 5 silicon transistors, 3 silicon diodes, 10 composition resistors and 2 ceramic capacitors connected in series configuration. The hourly failure rate of each component is given below: Silicon transistor : λt = 4 × 10−5; Silicon diode : λd = 3 × 10−5; Composition resistor : λr = 2 × 10−4; Ceramic capacitor : λc = 2 × 10−4. Calculate the reliability of the circuit for 10 hours, when the components follow exponential distribution.
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Define Hazard function and derive the relation between R(t), h(t) and f(t).
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A mechanical pumping device has a constant failure rate of 0.023 failure per hour and an exponential repair time with a mean of 10 hours. If two pumps operate in an active redundant configuration, determine the system MTTF and the system reliability for 72 hours.
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How would you describe about stochastic state transitional probability matrix of three state system?
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How would you explain common mode failures modeling and evaluation techniques?
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A pumping station has two identical pumps connected in parallel, each capable of supplying 3000 gallons/hr. The failure rate and repair rate of each is 0.5f/hr and 4r/hr respectively. Evaluate the frequency of encountering and duration of residing in each possible throughput state.
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How would you explain with a neat sketch various regions of bath-tub-curve?
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How would you explain reliability evaluation of series system?
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For a two component standby system with repair permitted for either component with a single repair crew and no failures in standby, the failure and repair rates are given by λ1 = rate of failure of main unit = 0.002, λ2 = rate of failure of standby unit = 0.001, μ = repair rate for either unit = 0.01. Compute the steady-state availability of the system.
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Calculate the reliability of the bridge Network using Minimal Cut Set method as shown in fig 2. If each component reliability is 0.9.
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How would you explain the absorbing states with one example?
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