Series System Distributions from Dynamic Failure Rate Components.

serieshaz

Series System Distributions from Dynamic Failure Rate Components

serieshaz composes multiple dfr_dist objects into a series system distribution. A series system fails when any component fails, so the system hazard is the sum of component hazards:

$$h_{sys}(t) = \sum_{j=1}^{m} h_j(t, \theta_j)$$

The resulting object inherits from dfr_dist, so all existing methods — hazard, survival, CDF, density, sampling, log-likelihood, and MLE fitting — work automatically.

Installation

Install from r-universe:

install.packages("serieshaz", repos = "https://queelius.r-universe.dev")

Quick Start

library(serieshaz)

# Three-component server with different failure modes
server <- dfr_dist_series(list(
    dfr_weibull(shape = 2, scale = 500),     # disk wear-out
    dfr_exponential(0.001),            # random memory failure
    dfr_gompertz(a = 0.0001, b = 0.02)       # PSU degradation
))

# Evaluate system hazard and survival
h <- hazard(server)
S <- surv(server)

h(100)   # system hazard at t = 100
#> [1] 0.002538906
S(100)   # probability of surviving past t = 100
#> [1] 0.8420252

# Sample system lifetimes
set.seed(42)
samp <- sampler(server)
times <- samp(5)
times
#> [1] 294.9884 302.0998 150.3888 274.2224 236.8369

# Introspect: which component contributes most at t = 200?
for (j in 1:ncomponents(server)) {
    hj <- component_hazard(server, j)
    cat(sprintf("Component %d hazard at t=200: %.6f\n", j, hj(200)))
}
#> Component 1 hazard at t=200: 0.001600
#> Component 2 hazard at t=200: 0.001000
#> Component 3 hazard at t=200: 0.005460

Key Features

• Composition: Combine any dfr_dist objects (Weibull, exponential, Gompertz, log-logistic, custom) into series systems
• Full interface: All distribution methods (hazard, survival, CDF, density, quantile, sampling) work out of the box
• MLE fitting: Fit series system parameters to observed failure data with fit()
• Introspection: ncomponents(), component(), param_layout(), component_hazard(), sample_components()
• Nesting: Series systems can be nested as components of larger series systems
• Analytical cumulative hazard: When all components provide closed-form cumulative hazard, the series system does too

Ecosystem

serieshaz builds on:

• algebraic.dist — Base distribution generics
• likelihood.model — Statistical inference generics
• flexhaz — Dynamic failure rate distributions

Documentation

• vignette("series-overview") — Package overview and quick start
• vignette("series-math") — Mathematical foundations
• vignette("series-fitting") — MLE fitting and inference
• vignette("series-advanced") — Advanced composition patterns.