Rcalc.hmmR: Calculate the reliability of a system based on HMM.

In HMMRel: Hidden Markov Models for Reliability and Maintenance

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)

HMMRel documentation built on April 4, 2025, 2:04 a.m.