maintainability {drimmR}

Maintainability function

Description

Maintainability of a system at time k \in N is the probability that the system is repaired up to time k, given that is has failed at time k=0.

Usage

maintainability(
  x,
  k1 = 0L,
  k2,
  upstates,
  output_file = NULL,
  plot = FALSE,
  ncpu = 2
)

Arguments

x

An object of class dmm

k1

Start position (default value=0) : a positive integer giving the start position along the sequence from which the maintainabilities of the DMM should be computed, such that k1<k2

k2

End position : a positive integer giving the end position along the sequence until which the maintainabilities of the DMM should be computed, such that k2>k1

upstates

Character vector of the subspace working states among the state space vector such that upstates < s

output_file

(Optional) A file containing matrix of maintainability probabilities (e.g, "C:/.../MAIN.txt")

plot

FALSE (default); TRUE (display a figure plot of maintainability probabilities by position)

ncpu

Default=2. Represents the number of cores used to parallelized computation. If ncpu=-1, then it uses all available cores.

Details

Consider a system (or a component) System whose possible states during its evolution in time are E = \{1 \ldots s \}. Denote by U = \{1 \ldots s_1 \} the subset of operational states of the system (the upstates) and by D =\{s_{1}+1 \ldots s \} the subset of failure states (the down states), with 0 < s1 < s(obviously, E = U \cup D and U \cap D = \emptyset, U \neq \emptyset, D \neq \emptyset). One can think of the states of U as different operating modes or performance levels of the system, whereas the states of D can be seen as failures of the systems with different modes.

Value

A vector of length k + 1 giving the values of the maintainability for the period [0 \ldots k]

Author(s)

Alexandre Seiller

References

Barbu VS, Vergne N (2018). “Reliability and survival analysis for drifting Markov models: modelling and estimation.” Methodology and Computing in Applied Probability, 1–33. doi: 10.1007/s11009-018-9682-8, https://doi.org/10.1007/s11009-018-9682-8.

See Also

fitdmm, getTransitionMatrix

Examples

data(lambda, package = "drimmR")
dmm <- fitdmm(lambda, 1, 1, c('a','c','g','t'),
init.estim = "freq", fit.method="sum")
k1 <- 1
k2 <- 200
upstates <- c("c","t")  # vector of working states
maintainability(dmm,k1,k2,upstates,plot=TRUE)