failureRate {drimmR}

Failure rates function

Description

Computation of two different definition of the failure rate : the BMP-failure rate and RG-failure rate.

As for BMP-failure rate, consider a system S starting to work at time k = 0. The BMP-failure rate at time k \in N is the conditional probability that the failure of the system occurs at time k, given that the system has worked until time k - 1. The BMP-failure rate denoted by \lambda(k), k \in N is usually considered for continuous time systems.

The RG-failure rate is a discrete-time adapted failure-rate proposed by D. Roy and R. Gupta. Classification of discrete lives. Microelectronics Reliability, 32(10):1459–1473, 1992. The RG-failure rate is denoted by r(k), k \in N.

Usage

failureRate(
  x,
  k1 = 0L,
  k2,
  upstates,
  failure.rate = c("BMP", "RG"),
  output_file = NULL,
  plot = FALSE
)

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 failure rates 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 failure rates 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

failure.rate

Default="BMP", then BMP-failure-rate is the method used to compute the failure rate. If failure.rate= "RG", then RG-failure rate is the method used to compute the failure rate.

output_file

(Optional) A file containing matrix of failure rates at each position (e.g, "C:/.../ER.txt")

plot

FALSE (default); TRUE (display a figure plot of failure rates by position)

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 BMP (or RG) -failure rate 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. Roy D, Gupta R (1992). “Classification of discrete lives. Microelectronics Reliability.” Microelectronics Reliability, 1459–1473. doi: 10.1016/0026-2714(92)90015-D, https://doi.org/10.1016/0026-2714(92)90015-D.

See Also

fitdmm, getTransitionMatrix, reliability

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
failureRate(dmm,k1,k2,upstates,failure.rate="BMP",plot=TRUE)