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Chapter 6 Time dependent reliability of components and system - PowerPoint PPT Presentation


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Chapter 6 Time dependent reliability of components and system. 6.2 Failure rate time curve. 6.3 Reliability and Hazard functions Reliability: (6.1) (6.2)

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slide3
6.3 Reliability and Hazard functions

Reliability:

(6.1)

(6.2)

(6.3)

Failure rate (instantaneous rate of failure, hazard function or hazard rate):

(6.4,6.5)

slide4
reliability at time t:

The distribution function:

The reliability of the component:

slide5
Differentiation, yield

6.4 Modeling of failure Rates

slide6
and

Assuming linear variation:

slide9
6.5 Estimation of failure rate from emperical data

The estimate reliability function at time t:

(6.23)

The failure rate can be computed as

(6.24)

example:6.1

slide12
6.6 Mean time before failure (MTBF)

Since all system fail after a finite time, we have

(6.26)

slide18

Failure time of the series system is

The failure time distribution :

The probability function of the failure time:

slide19

6.7.1 Failure rate of the system

Where the failure rate of the system:

The reliability can be expressed as:

slide21
6.8 Parallel System

Reliability of parallel system, first seven events

slide22
6.8.1 Failure Rate of the system

The system failure rate is given by:

6-8-2 MTBF of the system

slide23
For special case for n=2

Where relation is used:

6-9 (k,n) systems

slide24
Probability distribution function of the system

Failure time of the system

6.9.1 MTBF of the system

slide33

C

A

D

A

B

AB

slide34

6.11.3 Cut set method

  • Identify the minimal cut sets of the system
  • Model the components of each minimal cut set to be in parallel .
  • Assume that the various cut sets are in series
  • Find the reliabilityof the system using the parallel-series model.
slide37

6.12 Reliability Enhancement

6.12.1 Series system

slide39
Constant constrain:

That is

The cost involved in achieving the new system