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

1. Which of the following gives the arithmetic mean time required to perform maintenance action?

a) MTBF

b) MTTF

c) MTTR

d) MDT

View Answer

Explanation: Mean time to repair (MTTR) is the arithmetic mean of time required to perform maintenance action. It is the ratio of total maintenance time to the number of maintenance actions.

2. Which of the following expression is correct?

a) MTTR = \(\frac {Total \, working \, time}{Number \, of \, failures}\)

b) MTTF = \(\frac {No \, of \, failures}{No \, of \, survivors}\)

c) MTBF = \(\frac {1}{Failure \, rate}\)

d) MTBF = \(\frac {Total \, maintenance \, time}{No \, of \, maintenance \, actions \, taken}\)

View Answer

Explanation: We know that the correct equations for MTTR, MTBF and MTTF are as below.

MTTR = \(\frac {Total \, maintenance \, time}{No \, of \, maintenance , actions \, taken}\)

MTBF = \(\frac {1}{Failure \, rate} = \frac {Total \, working \, time}{Number \, of \, failures}\)

MTTF = \(\frac {Total \, operating \, time \, of \, all \, components }{Total \, no \, of \, components}\)

3. Express the MTTF in terms of failure density.

a) MTTF = \(\frac {Total \, working \, time}{Number \, of \, failures}\)

b) MTTF = \(\frac {\sum_{t=1}^{N}ti}{N}\)

c) MTTF = \(\frac {1}{N} \sum_{k=1}^t\)kn_{k}Δt

d) MTTF = \(\sum_{k=1}^t\)fd_{k}(kΔt)Δt

View Answer

Explanation: All the equations are correct to find the MTTF. But, the equation MTTF = \(\sum_{k=1}^t\)fd

_{k}(kΔt)Δt expresses the MTTF in terms of failure density (fd

_{k}) for each k

^{th}interval.

4. What is the mean waiting time?

a) The average length of time a customer waits before being served

b) The arithmetic mean of time required to perform maintenance action

c) The average time between successive failures

d) The average time an item will function before failure

View Answer

Explanation: Mean waiting time is the average length of time a customer waits before being served. The arithmetic mean of time required to perform maintenance action is MTTR. The average time between successive failures is MTBF. The average time an item will function before failure is called MTTF.

5. What is the maintenance action rate?

a) It is the number of maintenance actions taken on equipment in an hour

b) The arithmetic mean of time required to perform maintenance action

c) The average time between successive failures

d) The average time an item will function before failure

View Answer

Explanation: Maintenance action rate is the number of maintenance actions taken on equipment in an hour. It is denoted by the symbol ‘μ’. It is reciprocal of MTTR. Mathematically, μ = \(\frac {1}{MTTR}\).

6. Which of the following equation is/are not correct?

Consider MWT – Mean Waiting time; ADT – Administrative delay time; LDT – Logistic delay time; MDT – Mean down time; MTTR – Mean time to repair; MTTF – Mean time to failure.

a) MWT = ADT + LDT

b) MDT = MTTR + ADT + LDT

c) MDT = MTTR + MWT

d) MDT = MTTF + MWT

View Answer

Explanation: The equation MDT = MTTF + MWT is wrong because MTTR and MTTF are different. MDT is the total time required to restore a system to a given level performance. Hence, MDT consists of MTTR, ADT and LDT.

7. Match the following.

p) Maintenance i) Repairable system q) Maintainability ii) Act of repairing r) MTBF iii) Making repair in less time with limited resources s) MTTF iv) Non-Repairable system

a) p – ii, q – iii, r – i, s – iv

b) p – iii, q – ii, r – i, s – iv

c) p – iii, q – i, r – ii, s – iv

d) p – iii, q – ii, r – iv, s – i

View Answer

Explanation: Maintenance is the act of repairing whereas Maintainability is making the repair in less time with limited resources. MTBF is applicable for repairable systems only whereas MTTF is applicable for non-repairable systems.

8. What is the inherent availability of the system if MTBF is 200 hours and MTTR is 10 hours?

a) 99.5

b) 93.5

c) 95.2

d) 98.5

View Answer

Explanation Given,

MTBF = 200 hours

MTTR = 10 hours

Inherent Availability = A

_{i}= \(\frac {MTBF}{MTTR+MTBF} = \frac {200}{10+200}\) = 0.9523 = 95.20%

9. Which of the following equations is/are correct to calculate inherent availability?

a) A_{i} = \(\frac {MTBF}{MTTR+MTBF}\)

b) A_{i} = \(\frac {MTBF}{MTTR+MDT}\)

c) A_{i} = \(\frac {MTBF}{MTTR+MTTF}\)

d) A_{i} = \(\frac {MTBF}{MTTR+MMT}\)

View Answer

Explanation: Inherent availability is the ideal availability. This is also known as steady-state availability. The following equation shows the formula to calculate inherent availability.

Inherent Availability = A

_{i}= \(\frac {MTBF}{MTTR+MTBF}\)

10. What is the achieved availability of the system if MTBMA is 100 hours and MMT is 1.33?

a) 98.68%

b) 96.68%

c) 96.86%

d) 96.66%

View Answer

Explanation: Given,

MTBMA = Mean time between maintenance actions = 100 hours

MMT = Mean maintenance action time = 1.33

Achieved availability = \(\frac {MTBMA}{MTBMA + MMT} = \frac {100}{100+1.33}\) = 0.9868 = 98.68%

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