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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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%

View Answer

Explanation: Given,

MTBMA = 168 hours

MDT = 4 hours

We know that,

Operational availability = A

_{0}= \(\frac {MTBMA}{MTBMA+MDT} = \frac {168}{168+ 4}\) = 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

View Answer

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

View Answer

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

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