# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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 t0.
• 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:

 Out[1]=

Mean time to failure:

 Out[2]=

A parallel-connected system:

Mean time to failure:

 Out[2]=

One component in series with two parallel components:

Distribution functions:

 Out[2]=

Mean and median time to failure:

 Out[3]=
 Out[4]=

The probability that the system fails before time :

 Out[5]=