Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech IV RELIABILITY ENGINEERING Previous Question Paper (September - 2022 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Draw and explain Bath tub Curve.
Answer
The Bath Tub Curve represents the failure rate of a component or system over its entire lifecycle. It is divided into three distinct phases:
- Infant Mortality Phase (Decreasing Failure Rate): Characterized by a high initial failure rate caused by manufacturing defects, poor quality control, or installation errors. These failures are often referred to as 'burn-in' failures.
- Useful Life Phase (Constant Failure Rate): The failure rate is low and relatively constant. Failures during this period are random and occur due to unpredictable stresses or external shocks. This is the period where the component is considered reliable.
- Wear-out Phase (Increasing Failure Rate): The failure rate increases rapidly as components age, degrade, or suffer from fatigue. This is due to physical wear, corrosion, or chemical changes over time.
A controlled manufacturing process is 0.3% defective. What is the probability of taking two or more defectives from a lot of 100 pieces?
i) By using Poisson approximation.
ii) By using Binomial distribution.
Answer
Given: Total pieces n = 100, Probability of defect p = 0.003. We need to find P(X ≥ 2) = 1 - [P(X=0) + P(X=1)].
i) Poisson Approximation: Here, λ = np = 100 × 0.003 = 0.3. Using P(X=k) = (e^-λ × λ^k) / k!:
P(X=0) = e^-0.3 = 0.7408
P(X=1) = (e^-0.3 × 0.3^1) / 1! = 0.2222
P(X ≥ 2) = 1 - (0.7408 + 0.2222) = 0.0370.
ii) Binomial Distribution: Using P(X=k) = nCk × p^k × (1-p)^(n-k):
P(X=0) = (100C0) × (0.003)^0 × (0.997)^100 = 0.74077
P(X=1) = (100C1) × (0.003)^1 × (0.997)^99 = 0.22289
P(X ≥ 2) = 1 - (0.74077 + 0.22289) = 0.03634.
Define Random variable, MTTF, MTBF and availability and compare it with reliability.
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Derive expression for expected value of Binomial distribution.
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Find out the system reliability for a serial configuration with two components.
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How would you explain the event tree method with one example?
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Explain cutest approach for reliability analysis of complex systems.
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How to obtain reliability of parallel system using exponential distribution? Explain with example.
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A pump operates continuously with a mean time to fail of 200 hours that follows the exponential distribution. A second, identical pump is placed in standby redundancy, and the mean time to fail while the pump is inactive is 1,000 hours. The standby time to fail is also exponentially distributed. What is the mean time to fail for the system, and what is the system reliability at time = 300 hours?
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How would you define Hazard function and derive the relation between R(t), h(t) and f(t)?
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How would you describe the Markov process one component repairable system?
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How would you explain about stochastic state transitional probability matrix of three state system?
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How would you explain the frequency and duration concept?
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A system consists of two components, one of which must operate for system success. If the failure rates are 0.05 f/yr and 0.02 f/yr respectively and the average repair times are 20hr and 25hr respectively, evaluate the system failure rate, average repair time and unavailability.
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