BUILT-IN MATHEMATICA SYMBOL
StandbyDistribution
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[..., ...] 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 {a1
A1, a2A2, ..., i2I2, i3I3, ..., sS, uUniformDistribution[{0, 1}]}.
-
- StandbyDistribution can be used with such functions as Mean, SurvivalFunction, HazardFunction, ReliabilityDistribution, and RandomVariate.
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]= |  |
New in 9
. When component 
fails, component 
will become active. 
component lifetime distribution follows 
in inactive mode and 
in active mode.
p>u]+a3Boole[i3>a1+ a2Boole[i2>a1]
