ReliabilityDistribution

ReliabilityDistribution[bexpr,{{x1,dist1},{x2,dist2},}]
represents the reliability distribution for a system with components having reliability distribution , where the whole system is working when the Boolean expression bexpr is True, and component is working when is True.

DetailsDetails

  • ReliabilityDistribution[bexpr,] corresponds to a reliability block diagram specification.
  • The Boolean expression bexpr is also known as the structure function for the system.
  • Typical structure functions include:
  • series system
    parallel system
    TemplateBox[{BooleanCountingFunction, paclet:ref/BooleanCountingFunction}, RefLink, BaseStyle -> InlineFormula][{k,n},n]k-out-of-n system
    BooleanConsecutiveFunction[k,n]consecutive-k-out-of-n system
  • The structure function bexpr can be any positive unate Boolean function.
  • UnateQ[bexpr] can be used to test whether a Boolean expression is positive unate.
  • The component reliability distributions need to be univariate with PDF[disti,t] and zero for t0.
  • For ReliabilityDistribution[bexpr,] with component indicator variables :
  • xiTrueindicates component working
    xiFalseindicates component failed
  • The survival function at time t for ReliabilityDistribution[bexpr,{{x1,dist1},}] is given by Probability[bexpr/.{x1->t1>t,},{t1disti,}].
  • ReliabilityDistribution can be used with such functions as Mean, SurvivalFunction, HazardFunction, and RandomVariate.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

A series-connected system:

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Mean time to failure:

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A parallel-connected system:

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Mean time to failure:

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One component in series with two parallel components:

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Distribution functions:

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Mean and median time to failure:

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The probability that the system fails before time :

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Introduced in 2012
(9.0)