BUILT-IN MATHEMATICA SYMBOL

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 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 need to be univariate with PDF[disti, t] and zero for t≤0.
• For ReliabilityDistribution[bexpr, ...] with component indicator variables :
•  xi=True indicates component working xi=False indicates 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:

Mean time to failure:

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One component in series with two parallel components:

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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