mdrelax extends my work on series system reliability by handling cases where traditional masking assumptions break down.
Background: The C1-C2-C3 Framework
My master’s thesis developed maximum likelihood techniques for series systems with masked failure data. The standard framework assumes three conditions:
- C1: The failed component is always in the candidate set
- C2: Non-informative masking (uniform probability within candidate set)
- C3: Masking mechanism is independent of system parameters
Under these conditions, the masking probabilities factor out and can be ignored for parameter estimation. The expo-masked-fim paper derives closed-form Fisher Information for the exponential case, and likelihood.model.series.md implements the general framework.
The Problem: Real-World Violations
In practice, C2 and C3 are often violated:
Informative masking (C2 violation): Diagnostic tests may be more likely to correctly identify certain failure modes. A component that fails catastrophically might be easier to identify than one that fails subtly.
Parameter-dependent masking (C3 violation): The masking mechanism might depend on component reliabilities. Components with shorter lifetimes might be easier to diagnose because they fail more frequently and technicians gain experience.
What mdrelax Provides
The package implements likelihood-based inference when conditions are relaxed:
library(mdrelax)
# Generate masked data with Bernoulli candidate sets
md <- md_bernoulli_cand_C1_C2_C3(data, p = 0.3)
# Sample candidate sets
md <- md_cand_sampler(md)
# MLE for exponential series system
fit <- md_mle_exp_series_C1_C2_C3(md)
# Fisher information matrix
fim <- md_fim_exp_series_C1_C2_C3(md, params(fit))
Key Features
- Flexible masking models: Bernoulli, rank-based, KL-divergence constrained
- Identifiability analysis: Tools to check when parameters can be estimated
- Fisher information: Efficiency analysis under relaxed conditions
- Simulation utilities: Monte Carlo studies for method validation
Relationship to Other Work
This package builds on a family of related projects:
| Project | Focus |
|---|---|
| expo-masked-fim | Closed-form FIM for exponential case |
| likelihood.model.series.md | General R framework for masked data likelihood |
| reliability-estimation-in-series-systems | Master’s thesis implementation |
| wei.series.md.c1.c2.c3 | Weibull series systems under C1-C2-C3 |
| mdrelax | Relaxed conditions (C2, C3 violations) |
The progression represents increasing generality:
- Exponential + C1-C2-C3 → Closed-form solutions
- Weibull + C1-C2-C3 → Numerical MLE
- Weibull + relaxed conditions → mdrelax
When to Use mdrelax
Use this package when you suspect:
- Diagnostic accuracy varies by component type
- Masking patterns correlate with component reliabilities
- Standard C1-C2-C3 assumptions are too restrictive
The trade-off: relaxed models have more parameters and may require larger samples for reliable estimation.
Resources
- GitHub: github.com/queelius/mdrelax
- Documentation: queelius.github.io/mdrelax
- Master’s Thesis: Reliability Estimation in Series Systems
- Theoretical Foundation: Closed-Form Fisher Information
Discussion