# Industrial Engineering Questions and Answers – Reliability

This set of Industrial Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Reliability”.

1. Which of the following stage of the bath-tub curve has an increasing failure rate?
a) Early failure
b) Random failure zone
c) Wear out failure
d) High failure

Explanation: The last stage i.e. the third stage of the failure curve observes an increasing failure rate. In this stage, failures are prone to happen due to wear and tear of the mechanical components.

2. Which of the following stage of the bath-tub curve has the highest wear out failures?
a) Early failure
b) Random failure zone
c) Wear out failure
d) High failure

Explanation: The last stage i.e. the third stage of the failure curve observes an increasing failure rate. In this stage, failures are prone to happen due to wear and tear of the mechanical components. This stage has the highest wear-out failures.

3. Which of the following stage of the bath-tub curve has the highest early “infant mortality” rate?
a) Early failure
b) Random failure zone
c) Wear out failure
d) High failure

Explanation: It is the first stage in the failure curve. Failures are prone to happen due to manufacturing defects, design errors or installations errors. This stage has the highest early “infant mortality” rate.

4. Calculate the mean time between failures (in hours) for a system with a failure rate of 20%.
a) 5
b) 6
c) 7
d) 3

Explanation: Given,
Failure rate, λ = 20% = 0.2 per hour
Mean time between failure (MTBF) = $$\frac {1}{λ} = \frac {1}{0.2}$$ = 5 hours

5. What is the failure rate of a component when its mean time between failures (MTBF) is 25 hours?
a) 0.04
b) 4.40
c) 4.44
d) 4.04

Explanation: Given,
MTBF = 25 hours
According to the exponential distribution,
MTBF = $$\frac {1}{Failure \, rate} = \frac {1}{\lambda }$$
∴ λ = $$\frac {1}{MTBF} = \frac {1}{25}$$ = 0.04

6. Find the mean time to failure when a sample of 5 items are tested for reliability, each item being failed at 20 hours, 25 hours, 21 hours, 22 hours and 23 hours.
a) 2.22
b) 22.2
c) 222.0
d) 0.22

Explanation: Mean time to failure is the mean or average time an item may be expected to function before failure.
Given,
The time to failure for each item is 20hours, 25 hours, 21 hours, 22 hours and 23 hours.
∴ MTTF = $$\frac {20+25+21+22+23}{5}$$ = 22.2

7. Match the following.

p) MTTF                                             i) Repairable items
q) MBTF                                            ii) Non-repairable items
r) Reliability function                      iii) R(t) = e-λt


a) p – ii, q – iii, r – i
b) p – ii, q – i, r – iii
c) p – iii, q – ii, r – i
d) p – i, q – iii, r – ii

Explanation: MTTF is applicable for non-repairable items and MTBF is applicable for repairable items. Reliability function for an exponential distribution is R(t) = e-λt.

8. Find the reliability function for a component having constant failure rate and MTBF is 25 hours.
a) R(t) = e-1.04t
b) R(t) = e-0.04t
c) R(t) = e-4.4t
d) R(t) = e-0.4t

Explanation: Given,
MTBF = 25 hours
According to the exponential distribution,
MTBF = $$\frac {1}{Failure \, rate} = \frac {1}{\lambda }$$
∴ λ = $$\frac {1}{MTBF} = \frac {1}{25}$$ = 0.04
∴ Reliability function = R(t) = e-0.04t.

9. Find the reliability of the item at 30 hours if it is having a constant failure rate and MTBF is 25 hours.
a) 0.031
b) 1.031
c) 0.011
d) 0.301

Explanation: Given,
MTBF = 25 hours
According to the exponential distribution,
MTBF = $$\frac {1}{Failure \, rate} = \frac {1}{\lambda }$$
∴ λ = $$\frac {1}{MTBF} = \frac {1}{25}$$ = 0.04
∴ Reliability function = R(t) = e-0.04t.
∴ The reliability of the item at 30 hours = R(30) = e-0.04 × 30 = 0.3011

10. Which of the following stage of the bath-tub curve has a decreasing failure rate?
a) Early failure
b) Random failure zone
c) Wear out failure
d) High failure

Explanation: Early failure or Infant mortality stage has a decreasing failure rate. It is the first stage in the failure curve. Failures are prone to happen due to manufacturing defects, design errors or installations errors.

Sanfoundry Global Education & Learning Series – Industrial Engineering.

To practice all areas of Industrial Engineering, here is complete set of 1000+ Multiple Choice Questions and Answers.

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