BUILT-IN MATHEMATICA SYMBOL

# StandbyDistribution

StandbyDistribution[dist1, {dist2, ..., distn}]
represents a standby distribution with component lifetime distributions . When component fails, component will become active.

StandbyDistribution[dist1, {dist2, ..., distn}, p]
represents a standby distribution where switching from component to component succeeds with probability p.

StandbyDistribution[dist1, {dist2, ..., distn}, sdist]
represents a standby distribution where the switch component has lifetime distribution sdist.

StandbyDistribution[dist1, {..., {disti, inactive, disti, active}, ...}, ...]
represents a standby distribution where the component lifetime distribution follows in inactive mode and in active mode.

## DetailsDetails

• StandbyDistribution[..., ...] represents a system with perfect switching where transitioning between components always succeeds.
• StandbyDistribution[..., ..., s] represents a system with imperfect switching. If s is a distribution, it represents that lifetime of the switch; otherwise it represents the probability of a successful transition between components.
• StandbyDistribution[..., {..., Ai, ...}, ...] represents a standby distribution where the component follows a cold standby distribution when it is active, and does not deteriorate when it is inactive.
• StandbyDistribution[..., {..., {Ii, Ai}, ...}, ...] represents a standby distribution where the component follows a warm standby distribution. The component deteriorates following distribution when it is inactive and distribution when it is active.
• Any mix of cold and warm standby component distributions can be used.
• The survival function and other properties for StandbyDistribution can be derived from the equivalent TransformedDistribution[expr, dists] with the distribution assumptions dists given by {a1A1, a2A2, ..., i2I2, i3I3, ..., sS, uUniformDistribution[{0, 1}]}.
•  TransformedDistribution[..., dists] a1+ a2Boole[p>u]+a3Boole[p2>u]+ a1+a2Boole[s>a1]+a3Boole[s>a1+a2]+ a1+a2Boole[i2>a1]+a3Boole[i3>a1+a2Boole[i2>a1]]+ a1+a2 Boole[i2>a1p>u]+a3Boole[i3>a1+ a2Boole[i2>a1]p2>u]+ a1+a2 Boole[i2>a1s>a1]+a3Boole[i3>a1+a2Boole[i2>a1]s>a1+a2Boole[i2>a1]]+
• StandbyDistribution can be used with such functions as Mean, SurvivalFunction, HazardFunction, ReliabilityDistribution, and RandomVariate.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Define a cold standby system with perfect switching:

Compute its PDF:

 Out[2]=

Mean time to failure:

 Out[3]=

Compare to a non-standby system:

 Out[4]=

Define a cold standby system with imperfect switching:

Compute its PDF:

 Out[2]=

Mean time to failure:

 Out[3]=

Compare to a non-standby system:

 Out[4]=

Define cold and warm standby systems, with inactive failure rate half the active failure rate:

Compute the mean time to failure:

 Out[4]=

Compare the survival functions:

 Out[5]=

## See AlsoSee Also

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