relaiblty ppt by vaibhav kumar

7/28/2019 Relaiblty Ppt by Vaibhav Kumar

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Presentation on reliability ofsystems

Name- Vaibhav Kumar

Roll no-0703240053


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Introduction

Most engineering systems consist of many elements or

components

Need to consider multiple failure modes and/or multiple

component failures

Analysis is fairly complicated

Need to consider1. The contribution of the component failure events to the systems

failure

2. The redundancy of the system

3. The post-failure behaviour of a component and the rest of the

system4. The statistical correlation between failure events

5. The progressive failure of components


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Reliability Block Diagrams


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Reliability Block Diagrams

Most systems are defined through a combination of both

series and parallel connections of subsystems

Reliability block diagrams (RBD) represent a system using

interconnected blocks arranged in combinations of series

and/or parallel configurations

They can be used to analyze the reliability of a systemquantitatively

Reliability block diagrams can consider active and stand-by

states to get estimates of reliability, and availability (or

unavailability) of the system

Reliability block diagrams may be difficult to construct forvery complex systems


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Series Systems

Series systems are also referred to as weakest link or chain

systems

System failure is caused by the failure of any one component

Consider two components in series

Failure is defined as the union of the individual component

failures

For small failure probabilities

1 2

where Q denotes the

probability of failure


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Series Systems (contd)

Forn components in series, the probability of failure is then

Therefore, for a series system, the system probability of

failure is the sum of the individual component probabilities

In case the component probabilities are not small, the system

probability of failure can be expressed as

Forn components in series


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Series Systems (contd)

Reliability is the complement of the probability of failure

For the two components in series, the system reliability can

be expressed as

Assuming independence

Forn components in series

Therefore, for a series system, the reliability of the system is

the product of the individual component reliabilities


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Parallel Systems

Parallel systems are also referred to as redundant

The system fails only ifall of the components fail

Consider two components in parallel

Failure is defined by the intersection of the individual

(component) failure events

Assuming independence

1

2


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Parallel Systems

Forn components in parallel, the probability of failure is then

Therefore, for a parallel system, the system probability of

failure is the product of the individual component

probabilities

The reliability of the parallel system is

Forn components in parallel, the system reliability is


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Example Problem

Solution:

First combine the parallel components 2 and 3

The probability of failure is

The reliability is

Example: Compute the reliability and probability of failure for the

following system. Assume the failure probabilities for the

components are Q1 = 0.01, Q2 = 0.02 and Q3 = 0.03.

2

3

1


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Solution (contd)

Next, combine component 1 and the sub-system (2,3) in

series

The probability of failure for the system is then

The system reliability is


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Solution (contd)

The system probability of failure is equal to

The system reliability is

which is also equal toRSYS= 1QSYS

As shown in this example, the system probability of failure

and reliability are dominated by the series component 1 i.e. a series system is as good as its weakest link


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Thank u

relaiblty ppt by vaibhav kumar

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