Reliability and Maintenance - Quality and Reliability - Production & Industrial Engineering Previous Year Questions

1

2007 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2007

The reliability of an equipment for a time to failure exceeding t is given by \(R(t) = \exp(-\lambda t)\). The mean time to failure (MTTF) for this equipment (in hours) is

A

\(\lambda\)

B

\(1/\lambda\)

C

\((1/\lambda^2)\)

D

\(\lambda^2\)

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2

2008 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2008

An assembly has 10 components in series. Each component has an exponential time-to-failure distribution with a constant failure rate of 0.02 per 3000 hours of operation. Assuming that the failed component of the assembly is replaced immediately with another component that has the same failure rate, the reliability of the assembly for 2000 hours of operation and the mean time-to-failure (MTTF) is

A

0.875, 10,000 hours

B

0.875, 15,000 hours

C

0.975, 10,000 hours

D

0.975, 15,000 hours

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3

2009 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2009

A company makes a product using three independent components I, II and III, with reliabilities of 0.80, 0.85 and 0.90 respectively. If the company decides to add one redundant unit of component I to improve reliability, then the reliability of the product is

A

0.612

B

0.734

C

0.837

D

0.969

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4

2010 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2010

The length of time, during which a particular piece of equipment operates before failure, is a random variable with the distribution function given as: \( F(t) = 1 - e^{-0.5t} \). Assume 100 pieces of the equipment are placed into service in year 0. Out of the units, which survive the first 4 years, the units (in percentage) that will fail during year 5 is

A

37

B

39

C

41

D

43

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5

2010 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2010

The length of time, during which a particular piece of equipment operates before failure, is a random variable with the distribution function given as: F(t) = 1 - e^{-0.5t}. Assume 100 pieces of the equipment are placed into service in year 0. Out of the units, which survive the first 4 years, the units (in percentage) that will fail during year 5 is

A

37

B

39

C

41

D

43

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6

2011 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2011

The reliabilities R_A, R_B, R_C and R_D for these four components after 1000 hours of operation will be

A

R_A = 0.855, R_B = 0.8, R_C = 0.8 and R_D = 0.855

B

R_A = 0.753, R_B = 0.9, R_C = 0.9 and R_D = 0.753

C

R_A = 0.951, R_B = 0.852, R_C = 0.852 and R_D = 0.951

D

R_A = 0.819, R_B = 0.779, R_C = 0.779 and R_D = 0.819

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7

2011 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2011

If the four components in the previous question are connected in a series-parallel structure as shown in the figure, the system reliability at the end of 1000 hours of operation will be

A

0.853

B

0.638

C

0.733

D

0.925

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8

2011 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2011

The reliabilities R_A, R_B, R_C and R_D for these four components after 1000 hours of operation will be

A

R_A = 0.855, R_B = 0.8, R_C = 0.8 and R_D = 0.855

B

R_A = 0.753, R_B = 0.9, R_C = 0.9 and R_D = 0.753

C

R_A = 0.951, R_B = 0.852, R_C = 0.852 and R_D = 0.951

D

R_A = 0.819, R_B = 0.779, R_C = 0.779 and R_D = 0.819

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9

2013 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2013 [Session 1]

A company plans to purchase a machine whose uptime needs to be atleast 95%. They have shortlisted two models of the machine with the following operational characteristics:

Machine	MTBF (hr)	MTTR (hr)
Model M	60	4
Model N	48	2

The company should buy

A

only Model M

B

only Model N

C

either Model M or N

D

neither Model M nor N

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10

2013 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2013 [Session 2]

A company plans to purchase a machine whose uptime needs to be atleast 95%. They have shortlisted two models of the machine with the following operational characteristics:

Machine	MTBF (hr)	MTTR (hr)
Model M	60	4
Model N	48	2

The company should buy

A

only Model M

B

only Model N

C

either Model M or N

D

neither Model M nor N

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11

2014 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2014

Two systems, P and Q, contain 3 components each. Reliability of the components is measured for 1000 hours operations and time-to-failure distributions for all the components are found to be exponential. System P components are connected in a series parallel structure with each component having a reliability of 0.8. System Q components, on the other hand, are connected in series with each component having a reliability of 0.9. See the configuration of the systems below.

The reliabilities of System P and System Q will be respectively

A

0.768, 0.729

B

0.512, 0.729

C

0.5, 0.271

D

0.232, 0.271

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12

2016 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2016

Consider a system with 10 identical components connected in series. The time to failure of each component is exponentially distributed with a failure rate of 0.10 per 500 days. The reliability of the system after 400 days of operation is ____.

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13

2017 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2017

An air conditioner unit is expected to run continuously. The mean time between failures (MTBF) for this unit is 2,000 hours and the mean time to repair (MTTR) is 48 hours. The availability of the air conditioning unit is ______________(up to three decimal places).

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14

2018 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2018

A machine consists of three components P, Q and R connected serially. The reliabilities of P, Q and R are 0.97, 0.86 and 0.93, respectively. To increase the reliability of the machine, two additional stand-by units of Q are attached. The overall reliability (up to two decimal places) of the machine is ______

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15

2018 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2018

The mean time between failures of a machine is 400 hour. If the availability of the machine is 80%, the mean time to repair (in hour) is ______

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16

2020 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2020

Suppose the control system of a fighter jet consists of three unrelated components in series, and it is desired to have 98% reliability of the system. If the reliability level of all the components is the same, then the reliability of each component (rounded off to three decimal places) is __________.

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17

2020 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2020

The availability of an old photocopier was 90% and the Mean Time Between Failure (MTBF) was 200 days. It has been replaced with a new photocopier having an availability of 95%. Now, the Mean Time to Repair (the time during which the photocopier is unavailable for service) has increased by 5 days. The MTBF of the new photocopier (rounded off to the nearest integer) in days is ______.

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18

2021 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2021

A product has an exponential time-to-failure distribution with a constant failure rate of 0.00006 per hour. The reliability of the product after 4000 hours of operation is

A

0.5866

B

0.6866

C

0.7866

D

0.8866

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19

2021 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2021

There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).

A

2

B

4

C

6

D

8

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20

2022 · Production & Industrial Engineering · Quality and Reliability · Reliability and Maintenance

Production & Industrial Engineering (PI) 2022

In a machine there are two motors, but only one motor is needed for the functioning of the machine. The reliabilities of the motors are 0.90 and 0.70. The overall reliability of the machine is__________. [round off to two decimal places]

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