# Industrial Engineering Questions and Answers – Reliability Maintainability and Availability – Set 2

This set of Industrial Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Reliability Maintainability and Availability – Set 2”.

1. What is availability?
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) It is the ratio of equipment uptime to the sum of equipment uptime and downtime over a given time

Explanation: Availability is the ratio of equipment uptime to sum of equipment uptime and downtime over a given time. It is the ratio of equipment operating time to sum of total operating time and maintenance time.

2. What is maintainability?
a) Probability a system or unit will restore to specified conditions
b) It is the number of maintenance actions taken on equipment in an hour
c) The arithmetic mean of time required to perform maintenance action
d) It is the ratio of equipment uptime to the sum of equipment uptime and downtime over a given time

Explanation: Maintainability is the probability that a system or unit will restore to its previous specified operating conditions subjected to a maintenance action and defined procedure within a given time.

3. Match the following.

p) Inherent reliability                                       i) Inherent availability
q) Achievable reliability                                   ii) Quality of material and design of machine parts
r) Steady-state availability                              iii) Maintenance and operation of equipment


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

Explanation: Reliability is of two types. They are as follows:
i. Inherent reliability – Quality of material and design of machine parts
ii. Achievable reliability – Depends on other factors such as maintenance and operation of equipment
Note: Please note that Availability and Reliability are two different terms and does not mean the same.
Inherent availability is also known as Steady-state availability.

4. Match the following.

p) Inherent Availability                                       i) Actual availability
q) Achievable Availability                                   ii) Potential and steady-state availability
r) Operational availability                                  iii) Final availability


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

Explanation: Availability is of three types. They are as follows:
i. Inherent Availability – Inherent availability is also known as Steady-state availability
ii. Achievable Availability – Final availability
iii. Operational availability – Actual availability

5. Which of the following gives the repair rate?
a) Ai = $$\frac {MTBF}{MTTR+MTBF}$$
b) λ = $$\frac {1}{MTBF}$$
c) μ = $$\frac {1}{MTTR}$$
d) Ai = $$\frac {MTBF}{MTTR+MTBF}$$

Explanation: Maintenance action rate which is also known as repair 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. Find the mean maintenance action time when Fc is 0.5, FP = 1, Mct = 2, Mpt = 1.
a) 1.33
b) 3.33
c) 3.13
d) 1.13

Explanation: We know that,
Mean maintenance action time MMT = $$\frac {Fc \times \overline{Mct} + Fp \times \overline{Mpt}}{Fp + Fc}$$
Given,
Fc is 0.5; FP = 1; Mct = 2; Mpt = 1
∴ MMT = $$\frac {Fc \times \overline{Mct} + Fp \times \overline{Mpt}}{Fp + Fc} = \frac {0.5 \times 2+1 \times 1}{0.5+1}$$ = 1.33

7. Find the operational availability when a system has MTBMA of 168 hours and MDT of 4 hours.
a) 91.7%
b) 93.7%
c) 97.7%
d) 99.7%

Explanation: Given,
MTBMA = 168 hours
MDT = 4 hours
We know that,
Operational availability = A0 = $$\frac {MTBMA}{MTBMA+MDT} = \frac {168}{168+ 4}$$ = 0.977 = 97.7%

8. What is the instantaneous availability at 0.2 hours if failure rate and steady rate are 5 and 3 respectively?
a) 0.051
b) 0.501
c) 0.015
d) 0.105

Explanation: Given,
λ = 5; μ = 3
We know that,
The instantaneous availability at a given instance if time is A = $$\frac {\mu }{\lambda+ \mu } + \frac {\mu}{\lambda+ \mu }$$ × e[-(λ + μ)t]
∴ A = $$\frac {\mu }{\lambda+ \mu } + \frac {\mu}{\lambda+ \mu }$$ × e[-(λ + μ)t] = $$\frac {3}{5+ 3} + \frac {3}{5+ 3}$$ × e[-(5 + 3) × 0.2] = 0.501

9. What is the instantaneous unavailability at 0.2 hours if failure rate and steady rate are 5 and 3 respectively?
a) 0.051
b) 0.501
c) 0.499
d) 0.944

Explanation: We know that,
The instantaneous availability at a given instance if time is A = $$\frac {\mu }{\lambda+ \mu } + \frac {\mu}{\lambda+ \mu }$$ × e[-(λ + μ)t]
∴ A = $$\frac {\mu }{\lambda+ \mu } + \frac {\mu}{\lambda+ \mu }$$ × e[-(λ + μ)t] = $$\frac {3}{5+ 3} + \frac {3}{5+ 3}$$ × e[-(5 + 3) × 0.2] = 0.501
∴ Unavailability = 1 – Availability = 1 – 0.501 = 0.499

Sanfoundry Global Education & Learning Series – Industrial Engineering.

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