# ReliabilityDistribution

ReliabilityDistribution[bexpr,{{x1,dist1},{x2,dist2},}]

represents the reliability distribution for a system with components xi having reliability distribution disti, where the whole system is working when the Boolean expression bexpr is True, and component xi is working when xi is True.

# Details

• 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 k-out-of-n system 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 disti need to be univariate with PDF[disti,t] zero for t0.
• For ReliabilityDistribution[bexpr,] with component indicator variables xi:
•  xiTrue indicates component xi working xiFalse indicates component xi 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.

# Examples

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## 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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