Failure Rate and the Reliability Function

1
Failure Rate and the Reliability Function

• The reliability of a system is a function of
  time, R(t), defined as the conditional
  probability that a system performs correctly
  throughout the interval of time, t0, t, given
  that the system was performing correctly at time
  t0.
• The probability that a component has survived
  the interval to, t

2
Failure Rate and the Reliability Function

• The probability that a component has not survived
  the time interval is called the unreliability
• At any time t, R(t) 1.0 Q(t)
• Instantaneous rate at which components are
  failing

3
Failure Rate and the Reliability Function

• At time t, there are still No(t) components
  operating
• Z(t) hazard function, hazard rate, or failure
  rate function failures per unit of time

4
Failure Rate and the Reliability Function

• In terms of unreliability Q(t)
• dQ(t)/dt is called the failure density function
• The failure rate function depends on time -
  and the value of change as
  functions of time
• Experience has shown that the failure rate
  function for electronic components does have a
  period where the value of z(t) is approximately
  constant

5
Failure Rate and the Reliability Function
6
Failure Rate and the Reliability Function

• Assuming that the system is in the useful-life
  stage where the failure rate function has a
  constant value of
• Exponential failure law

7
Failure Rate and the Reliability Function

• Weibull distribution for time-varying failure
  rate functions

8
Failure Rate and the Reliability Function

• The reliability function based on the Weibull
  distribution is the solution of
• i.e.,