# Industrial Engineering Questions and Answers – Reliability Engineering

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

1. Which of the following sum is one according to the theory of probability?
a) Reliability and availability
b) Availability and maintainability
c) Reliability and probability of failure
d) Availability and probability of failure

Explanation: As the probability of failure is inverse to the reliability, it can be said the sum of reliability and probability of failure is one. If R and F are reliability of a product and the probability of failure respectively, then mathematically,
R + F = 1

2. Calculate the reliability of the product when its probability of failure is 0.097.
a) 0.903
b) 0.993
c) 0.093
d) 0.939

Explanation: Given,
Probability of failure = P = 0.097
Let R be reliability of the product
We know that,
R + P = 1
R = 1 – P = 1 – 0.097 = 0.903

3. What it implies if a part/component is said to have a reliability of 0.997?
a) 3 out of 1000 components may fail
b) 10 out of 1000 components may fail
c) 997 out of 1000 components may fail
d) 100 out of 1000 components may fail

Explanation: We know that the probability of failure (F) and reliability (R) are inverse to each other.
Let us consider that 1000 components are being manufactured on the floor per day. Then, as the reliability of the component is 0.997, 997 components will function and perform their tasks under the standard operating conditions for a given period (say runs) and every 3 out of 1000 will fail to perform its functions within its stipulated life.

4. Which of the following does not need immediate attention?
i. Tolerable risk
ii. Acceptable risk
iii. Unacceptable risk
a) i and ii
b) iii and iv
c) iv only
d) ii and iv

Explanation: Tolerable risk is one that the level of risk is usually acceptable and a constant review of its causes and possible measures to reduce them are must. Similarly, the acceptable risk is also a level of risk that is acceptable and does not require immediate attention. But, unacceptable risk cannot be accepted and require immediate attention.

5. Reliability is defined as the system/component/product that will tend to perform its function without failure under for a given period under the stipulated operating conditions.
a) True
b) False

Explanation: The above statement is true. Within a given period, which is derived from a series of experiments the product/system/component will perform its functions successfully without failure under the stated operating environment.

6. Find the probability of failure when every 5 out of 20 components may fail.
a) 0.25
b) 0.5
c) 1.0
d) 0.109

Explanation: Given that,
No of components to fail = 5
Total no of components = 20
From the definition of probability,
The probability for the components to fail = $$\frac {No \, of \, components \, to \, fail}{Total \, no \, of \, components} = \frac {5}{20}$$ = 0.25.
Therefore, 25% of components may fail.

7. Which of the following specifies the number of failures per unit per for the parts exposed during a given time(t)?
a) Failure rate
b) Hazard rate
c) MTBF
d) MTTF

Explanation: We know that,
R + F = 1
R = 1 – F = 1 – $$\frac {NF}{N}$$
h = $$\frac {dNF}{dt} * \frac {1}{N}$$
where, NF = No of failures, N = total no of parts exposed, h = instantaneous failure rate
Hence, from the above mathematical proof, it can be said that the rate of change of failure is envisaged as the failure rate.

8. Which of the following is the abbreviation of MTBF?
a) Meridian time to failure
b) Mean time to failure
c) Medium time to failure
d) Most likely time to failure

Explanation: MTBF is the abbreviation of Mean time between failure. It refers to the time between successive failures.

9. Calculate the mean time between failure (MTBF) when there are 23 failures out of 40 operating pumps within a month.
a) 1.74 months
b) 1.4 months
c) 0.74 month
d) 1.47 months

Explanation: Given that,
No of failures over a month = 23
Total no of operating pumps = 40
MTBF = $$\frac {No \, of \, failures \, over \, a \, month}{Total \, no \, of \, operating \, pumps}= \frac {40}{23}$$ = 1.74 months

10. Calculate mean time to failure in hours when a sample of 3 components under testing each of which failed at 22, 27 and 20 hours respectively.
a) 23.23
b) 0.23
c) 2.3
d) 23

Explanation: We know that.
MTTF is the average time taken for each component to fail.
MTTF = $$\frac {22+27+20}{3} = \frac {69}{3}$$ = 23 hours.

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