cost.cspc: Maintenance Policy based on Critical State Probability...

In HMMRel: Hidden Markov Models for Reliability and Maintenance

Maintenance Policy based on Critical State Probability Critera.

Description

Preventive maintenance based on Critical State Probability Criteria (CSPC).

Usage

cost.cspc(prob,hmmR,n.up1,cost.C,cost.P,t.max)

Arguments

prob	A real number in the interval (0,1).
hmmR	A hidden Markov Model.
n.up1	An integer value for indicating the total number of optimal performance states of the hidden MC.
cost.C	A positive real number denoting the cost value in monetary units incurred by a corrective maintenance action.
cost.P	A positive real number denoting the cost value in monetary units incurred by a preventive maintenance action.
t.max	A time value for the maximum time the system will be in use. After that time the system will not operate anymore.

Details

Preventive maintenance policies based on critical states probability critera (CSPC) are considered. Roughly speaking, a preventive maintenance action is carried out once the system enters a subset of operational states that are considered critical in some sense. The subset of operative states up is in turn split into two subsets: optimal states or up1 and operative but critical states or up2, where up=up1 \cup up2. For a given probability value (prob) this function first calculates the optimal inspection time

\code{t.insp}=\min \{t>0: \Pr( X(t) \in \text{up2}, X(u) \in \text{up1}, \forall u < t )\geq \code{prob}\}.

The system is inspected every t.insp time-units. At the time of inspection, any of three situations can be found:

1. the system is in failure, then the system is returned to operational conditions (up1), and a cost of cost.C monetary-units is implied;

2. the system is in a state of up2, then a preventive maintenance action is carried out, returning the system to a state in up1 and implying a cost of cost.P monetary-units; and

3. the system is found in a state of up1, then no maintenance action is carried out and there is no associated cost.

Value

time.insp	The time at which preventive maintenance is carried out.
t.max	The maximum time that the system is being used.
n.insp	The total number of inspections that are carried out during the system lifetime, i.e. in the interval (0, t.max).
total.cost	The total cost incurred by all maintenance actions (corrective and preventive) developed in the system.

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 cost.wspc for the implementation of the WSPC algorithm for maintenance policy.

Examples

model<-'other'
rate<-p<-NA
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=model,rate=NA,p=NA,alpha=alpha,P=P,M=M,Nx=Nx,Ny=Ny,n.up=n.up,n.green=n.green)
prob<-0.8;
n.up1<-n.green1<-1;cost.C<-10;cost.P<-1;t.max<-50
cost1<-cost.cspc(prob=prob,hmmR=hmm1,n.up1=n.up1,cost.C=cost.C,cost.P=cost.P,t.max=t.max)
cost1
#
v.prob<-seq(0.1,0.99,length=100)
v.cost1<-inspection.time<-double(100)
for(i in 1:100)
{cost<-cost.cspc(prob=v.prob[i],hmmR=hmm1,n.up1=n.up1,
   cost.C=cost.C,cost.P=cost.P,t.max=t.max)
v.cost1[i]<-cost$total.cost
inspection.time[i]<-cost$time.insp
}
oldpar <- par(mar = c(5, 5, 10, 10))
plot(v.prob,v.cost1,type='s',main='CSPC Algorithm for Maintenance Policy',
xlab='Probability of critical state',
ylab='Cost of maintenance')
grid()
par(oldpar)

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