Masked-Cause Likelihood Model for DFR Series Systems

Constructs a likelihood model for series systems with masked component cause of failure, where components are arbitrary dfr_dist distributions. Supports exact, right-censored, left-censored, and interval-censored observations with candidate sets satisfying C1-C2-C3.

Usage

dfr_series_md(
  series = NULL,
  components = NULL,
  par = NULL,
  n_par = NULL,
  lifetime = "t",
  lifetime_upper = "t_upper",
  omega = "omega",
  candset = "x"
)

Arguments

series

A dfr_dist_series object. Ignored if components is provided.

components

A list of dfr_dist objects. If provided, a dfr_dist_series is built from these.

par

Optional concatenated parameter vector.

n_par

Optional integer vector of parameter counts per component.

lifetime

Column name for system lifetime (default "t").

lifetime_upper

Column name for interval upper bound (default "t_upper").

omega

Column name for observation type (default "omega").

candset

Column prefix for candidate set indicators (default "x").

Value

An object of class c("dfr_series_md", "series_md", "likelihood_model").

Details

The model computes the masked-cause log-likelihood for series systems where the system lifetime is the minimum of independent component lifetimes, and the causing component is partially observed through candidate sets.

Observation types (stored in the omega column):

"exact"

Failed at time t, cause masked among candidates

"right"

Right-censored: survived past time t

"left"

Left-censored: failed before time t

"interval"

Failed in interval (t, t_upper)

Masking conditions:

C1

Failed component is in candidate set with probability 1

C2

Uniform probability for candidate sets given component cause

C3

Masking probabilities independent of system parameters

See also

is_dfr_series_md for the type predicate, dfr_dist_series for the series distribution, loglik for the likelihood interface

Examples

# \donttest{
library(flexhaz)
library(serieshaz)

# From components
model <- dfr_series_md(components = list(
    dfr_exponential(0.1),
    dfr_exponential(0.2),
    dfr_exponential(0.3)
))

# From pre-built series
sys <- dfr_dist_series(list(
    dfr_weibull(shape = 2, scale = 100),
    dfr_exponential(0.05)
))
model2 <- dfr_series_md(series = sys)
# }