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Assumptions for series system distributions

Source: R/dfr_dist_series.R
assumptions.dfr_dist_series.Rd

Returns the statistical and structural assumptions underlying a series system model, which are important for the validity of MLE-based inference.

Usage

# S3 method for class 'dfr_dist_series'
assumptions(model, ...)

Arguments

model

A dfr_dist_series object.

...

Additional arguments (unused).

Value

Character vector of model assumptions.

Details

The assumptions returned are:

  • Series structure: The system fails when any component fails (weakest-link model)

  • Component independence: Component lifetimes are statistically independent

  • Non-negative hazard: Each component hazard satisfies \(h_j(t) \geq 0\) for all \(t > 0\)

  • Proper distribution: The cumulative hazard diverges, ensuring \(S_{sys}(t) \to 0\) as \(t \to \infty\)

  • Positive support: The time domain is \((0, \infty)\)

  • Independent observations: The observed lifetimes are independent

  • Censoring convention: delta = 1 for exact, 0 for right-censored, -1 for left-censored

  • Non-informative censoring: The censoring mechanism carries no information about the failure process

These assumptions are required for the MLE fitting procedure (fit) to produce valid estimates. Violation of component independence, in particular, invalidates the hazard-sum property that defines series systems.

See also

assumptions for the generic, dfr_dist_series for the constructor, vignette("series-fitting") for how assumptions affect inference

Other series system: dfr_dist_series(), is_dfr_dist_series(), print.dfr_dist_series()

Examples

# \donttest{
library(flexhaz)

sys <- dfr_dist_series(list(
    dfr_exponential(0.1),
    dfr_weibull(shape = 2, scale = 100)
))
assumptions(sys)
#> [1] "Series system: system fails when any component fails"            
#> [2] "Component independence: component lifetimes are independent"     
#> [3] "Non-negative hazard: h_j(t) >= 0 for all j, t > 0"               
#> [4] "Cumulative hazard diverges: lim(t->Inf) H_sys(t) = Inf"          
#> [5] "Support is positive reals: t in (0, Inf)"                        
#> [6] "Observations are independent"                                    
#> [7] "Censoring indicator: 1=exact, 0=right-censored, -1=left-censored"
#> [8] "Non-informative censoring"                                       
# }