Likelihood Models for Systems with Masked Component Cause of Failure.
maskedcauses
Maximum likelihood estimation for series system parameters from masked component failure data. Supports exact, right-censored, left-censored, and interval-censored observations with composable observation schemes.
Installation
From r-universe:
install.packages("maskedcauses",
repos = "https://queelius.r-universe.dev")
Or from GitHub:
# install.packages("devtools")
devtools::install_github("queelius/maskedcauses")
Models
Three likelihood models, all using S3 generic dispatch:
| Model | Parameters | Description |
|---|---|---|
exp_series_md_c1_c2_c3 | m rates: (λ₁, ..., λₘ) | Exponential components. Closed-form loglik, score, and Hessian for all four observation types. |
wei_series_homogeneous_md_c1_c2_c3 | m+1: (k, β₁, ..., βₘ) | Weibull with shared shape. Closed-form loglik; hybrid analytical/numerical score. |
wei_series_md_c1_c2_c3 | 2m: (k₁, β₁, ..., kₘ, βₘ) | Weibull with per-component shapes. Numerical integration for left/interval types. |
Each model implements S3 methods for: loglik(), score(), hess_loglik(), rdata(), assumptions(), component_hazard(), cause_probability(), conditional_cause_probability(), ncomponents()
Quick Start
library(maskedcauses)
# Create model and generate data
model <- exp_series_md_c1_c2_c3()
gen <- rdata(model)
df <- gen(theta = c(1.0, 1.1, 0.95), n = 500, tau = 3, p = 0.3)
# Fit via MLE
solver <- fit(model)
mle <- solver(df, par = c(1, 1, 1))
mle$theta.hat # estimated rates
mle$sigma # asymptotic standard errors
# Evaluate likelihood functions at the MLE
loglik(model)(df, par = mle$theta.hat)
score(model)(df, par = mle$theta.hat)
hess_loglik(model)(df, par = mle$theta.hat)
Observation Types
The package supports four observation types via composable observation functors that separate the observation mechanism from the data-generating process:
| Type | Column omega | Description |
|---|---|---|
| Exact | "exact" | Failure time observed precisely |
| Right-censored | "right" | System survived past observation time |
| Left-censored | "left" | System failed before inspection time |
| Interval-censored | "interval" | Failure occurred in window [t, t_upper] |
# Right-censoring at tau (default, backwards-compatible)
df <- gen(theta, n = 500, tau = 5, p = 0.3)
# Periodic inspection every 0.5 time units
df <- gen(theta, n = 500, p = 0.3,
observe = observe_periodic(delta = 0.5, tau = 5))
# Mixed monitoring: 60% continuous, 20% single inspection, 20% periodic
df <- gen(theta, n = 500, p = 0.3,
observe = observe_mixture(
observe_right_censor(tau = 5),
observe_left_censor(tau = 3),
observe_periodic(delta = 0.5, tau = 5),
weights = c(0.6, 0.2, 0.2)
))
Masking Conditions
The candidate set models satisfy three conditions (C1, C2, C3) that yield a reduced likelihood depending only on observed data:
- C1: The failed component is always in the candidate set
- C2: Candidate set probabilities are symmetric across components in the set
- C3: Masking probabilities are independent of system parameters
Data Format
| Column | Description |
|---|---|
t | System lifetime (observed) |
omega | Observation type: "exact", "right", "left", or "interval" |
t_upper | Upper bound for interval-censored observations (NA otherwise) |
x1, x2, ..., xm | Boolean candidate set indicators |
For backwards compatibility, a delta column (TRUE/FALSE) is also accepted in place of omega for exact/right-censored data.
Vignettes
Four tutorial vignettes with worked examples and Monte Carlo studies:
vignette("exponential_series", package = "maskedcauses")
vignette("weibull_homogeneous_series", package = "maskedcauses")
vignette("weibull_series", package = "maskedcauses")
vignette("censoring_comparison", package = "maskedcauses")
Browse online at https://queelius.github.io/maskedcauses/articles/.
Related Packages
- likelihood.model -- generics for likelihood models (
loglik,score,fit, etc.) - algebraic.mle -- MLE objects with inference methods
- algebraic.dist -- distribution utilities
- md.tools -- masked data encoding/decoding
License
GPL (>= 3)