Construct a Continuous-time Markov Chain Generator
This function enables easy construction of an absorbing continuous-time Markov chain generator matrix representation for a system when components are treated as having Exponential failure and repair times.
systemGraphToGenerator(g, failRate, repairRate)
the rate parameter of the Exponentially distributed lifetime distribution of the components.
the rate parameter of the Exponentially distributed repair time distribution of the components.
When the system or network is specified by means of an
igraph object, each end of the system must be denoted by nodes named "s" and "t" which are taken to be perfectly reliable. It is easy to construct the appropriate graph representation using the function
This function then creates the generator matrix for an absorbing continuous-time Markov chain representation of such a system where components are repairable. All system states which in which the system is inoperative are collapsed into the absorbing state.
The returned values are in the format required by the
Full details are in Aslett (2012).
A list is returned with both a numeric generator matrix (in
$G with the failure rate,
failRate, and repair rate,
repairRate) and a symbolic matrix (in
$structure$G), along with a matrix of the constant multiples of generator entries (in
Please feel free to email firstname.lastname@example.org with any queries or if you encounter errors when running this function.
Aslett, L. J. M. (2012), MCMC for Inference on Phase-type and Masked System Lifetime Models, PhD Thesis, Trinity College Dublin.
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