Chapter 6 Time dependent reliability of components and system

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Chapter 6 Time dependent reliability of
components and system
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• 6.2 Failure rate time curve

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• 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)

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• reliability at time t
• The distribution function
• The reliability of the component
• 
  

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• Differentiation, yield
• 6.4 Modeling of failure Rates

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• and
• Assuming linear variation

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• 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)
• example6.1

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• 6.6 Mean time before failure (MTBF)
• Since all system fail after a finite time, we
  have
• 
  (6.26)

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• 6.7 Series system

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Failure time of the series system is The
failure time distribution The probability
function of the failure time
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6.7.1 Failure rate of the system
Where the failure rate of the system
The reliability can be expressed as
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6.7.2 MTBF of the system
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• 6.8 Parallel System
• Reliability of parallel system, first seven
  events

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• 6.8.1 Failure Rate of the system
• The system failure rate is given by

6-8-2 MTBF of the system
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• For special case for n2

Where relation is used
6-9 (k,n) systems
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• Probability distribution function of the system

Failure time of the system
6.9.1 MTBF of the system
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• 6.10 Mixed series and parallel system

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• The system failure rate is given by

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• The reliability R0 shown in fig. 6-8

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• 6.11 complex systems

A
C
D
B
E
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• 6.11.1 Enumeration method

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No component fail 1. ABCDE
0
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6.11.2 Conditional Probability method
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C
A
D
A
B
AB
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6.11.3 Cut set method

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

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6.12 Reliability Enhancement 6.12.1 Series system
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• Constant constrain

That is
The cost involved in achieving the new system
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• 6.12.2 parallel system

(6.73)
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• For minimum cost

6.13 reliability allocation- agree method
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6.87