def.hmmR {HMMRel} | R Documentation |
Define a HMM object for Reliability Analysis.
Description
This function creates a list with all the elements that describe a HMM in the context of Reliability and Maintenance.
Usage
def.hmmR(model,rate,p,alpha,P,M,Nx,Ny,n.up,n.green)
Arguments
model |
A character string to choose which HMM model is considered. Possible values are "KooN", "shock", "other" |
rate |
A positive real number indicating the failure rate of one unit of the system. |
p |
A real number in the interval (0,1) indicating the probability that the system receives one shock during a unit of time. |
alpha |
A vector of size |
P |
A square matrix of dimension |
M |
A matrix of dimension |
Nx |
An integer indicating the total number of states in the system. By default the states are labelled: 1,..., |
Ny |
An integer indicating the total number of signals received. By default the signals are labelled: 1,..., |
n.up |
An integer lower than |
n.green |
An integer lower then |
Details
When
model
="KooN"
the argumentNx
is the maximum number of units in the system. There must beK
=n.up
operative units for the system to function. IfK
=1 a parallel system is built. IfK
=Nx
a series system is built.When
model
="shock"
the argumentNx
minus 1 is the maximum number of shocks that the system can accumulate before breakdown.
Value
A list with the elements of the HMM.
states |
A set of |
signals |
A set of |
P |
A square matrix with |
M |
A matrix of dimension |
Author(s)
M.L. Gamiz, N. Limnios, and M.C. Segovia-Garcia (2024)
References
Gamiz, M.L., Limnios, N., and Segovia-Garcia, M.C. (2023). Hidden Markov models in reliability and maintenance. European Journal of Operational Research, 304(3), 1242-1255.
See Also
See also sim.hmmR
to simulate data from a given HMM.
Examples
## Define a HMM object describing a repairable system
## The system can be in one of 3 states: 2 up states and 1 down state.
## 3 different signals can be received: 2 good performance signals (green)
## and 1 signal of failure (red)
P<-matrix(c(8,2,1,0,6,4,6,2,2)/10,3,3,byrow=TRUE)
M<-matrix(c(7,3,0,4,3,3,0,4,6)/10,3,3,byrow=TRUE)
Nx<-3; Ny<-3
n.up<-2; n.green<-2
alpha<-c(1,0,0)
hmm1<-def.hmmR(model='other',rate=NA,p=NA,alpha=alpha,P=P,M=M,Nx=Nx,Ny=Ny,
n.up=n.up,n.green=n.green)
hmm1