Rcalc.hmmR {HMMRel} | R Documentation |
Calculate the reliability of a system based on HMM.
Description
For a given time t
this function returns the value of the probability that the system does not fail in the interval (0,t]
.
It gives the probability that the system survives and is still working beyond time t
.
Usage
Rcalc.hmmR(hmmR,t)
Arguments
hmmR |
A Hidden Markov Model. |
t |
A value of time, it must be an integer equal or greater than 0. |
Details
The state space is split into two subsets, i.e. states
=up
\cup
down
. The subset up
contains the states of good functioning, while the subset down
contains the failure states.
The signals aphabet is split into two subsets, i.e. signals
= green
\cup
red
.
A green
-signal indicates good performance of the system, while a red
-signal alerts of something wrong in the system.
This function returns the probability that the system has not entered the set of down
states or any signal from the red
subset of signals has been emitted at any time before t
.
Value
This function returns the probability that the system is working through a state in the up
subset, and a green
signal is being received.
If t
=0, then the returned value is 1.
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 def.hmmR
to define a HMM object.
Examples
model<-'other'
rate<-NA
p<-NA
P<-matrix(c(0.7,0.3,1,0),2,2,byrow=TRUE)
M<-matrix(c(0.6,0.4,0,0,0,1),2,3,byrow=TRUE)
alpha<-c(1,0)
Nx<-2
Ny<-3
n.up<-1
n.green<-2
hmm0<-def.hmmR(model=model,rate=NA,p=NA,alpha=alpha,P=P,M=M,Nx=Nx,Ny=Ny,n.up=n.up,n.green=n.green)
times<-0:30
Rt<-Rcalc.hmmR(hmmR=hmm0,t=times)
oldpar <- par(mar = c(5, 5, 10, 10))
plot(times,Rt,type='s',ylim=c(0,1),ylab='',xlab='time',main='Reliability based on HMM')
grid()
par(oldpar)