Chapter 6 Time dependent reliability of components and system

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

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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### Chapter 6 Time dependent reliability of components and system

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)

reliability at time t:

The distribution function:

The reliability of the component:

Differentiation, yield

6.4 Modeling of failure Rates

and

Assuming linear variation:

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

6.6 Mean time before failure (MTBF)

Since all system fail after a finite time, we have

(6.26)

Failure time of the series system is

The failure time distribution :

The probability function of the failure time:

6.7.1 Failure rate of the system

Where the failure rate of the system:

The reliability can be expressed as:

6.8 Parallel System

Reliability of parallel system, first seven events

6.8.1 Failure Rate of the system

The system failure rate is given by:

6-8-2 MTBF of the system

For special case for n=2

Where relation is used:

6-9 (k,n) systems

Probability distribution function of the system

Failure time of the system

6.9.1 MTBF of the system

C

A

D

A

B

AB

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.

6.12 Reliability Enhancement

6.12.1 Series system

Constant constrain:

That is

The cost involved in achieving the new system