def.hmmR: Define a HMM object for Reliability Analysis.

In HMMRel: Hidden Markov Models for Reliability and Maintenance

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 Nx with the initial law of the hidden Markov chain.
P	A square matrix of dimension Nx with the transition probabilities between the hidden states.
M	A matrix of dimension Nx \times Ny with the emission probabilities.
Nx	An integer indicating the total number of states in the system. By default the states are labelled: 1,...,Nx.
Ny	An integer indicating the total number of signals received. By default the signals are labelled: 1,...,Ny.
n.up	An integer lower than Nx indicating the number of (hidden) operative states in the system. The first n.up values in the state set denote operative states.
n.green	An integer lower then Ny indicating the number of signals of good performance. The first n.green signals are read as good performance of the system.

Details

• When model="KooN" the argument Nx is the maximum number of units in the system. There must be K=n.up operative units for the system to function. If K=1 a parallel system is built. If K=Nx a series system is built.

• When model="shock" the argument Nx 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 Nx characters or integers decribing the hidden states of the system.
signals	A set of Ny characters or integers decribing the possible signals observed.
P	A square matrix with Nx rows with the transition probabilities between the hidden states.
M	A matrix of dimension Nx \times Ny with the emission probabilities.

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

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