maskedcauses
Likelihood Models for Systems with Masked Component Cause of Failure
Maximum likelihood estimation for series systems where the
component cause of failure is masked. Implements analytical log-likelihood,
score, and Hessian functions for exponential, homogeneous Weibull, and
heterogeneous Weibull component lifetimes under masked cause conditions
(C1, C2, C3). Supports exact, right-censored, left-censored, and
interval-censored observations via composable observation functors.
Provides random data generation, model fitting, and Fisher information
for asymptotic inference. See Lin, Loh, and Bai (1993)
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)