Package: maskedcauses 0.10.0

Introduction | Series System Model | Definition | System reliability | Additive hazards | R code: Exponential example | Component Cause of Failure | Conditional cause probability | R code: Exponential vs Weibull cause probabilities | The Observational Model | Four observation types | Masking | Observe functors | The C1--C2--C3 Likelihood | The three conditions | Deriving the likelihood | Censored observations | Combined log-likelihood | R code: Log-likelihood evaluation | Distribution Families | Worked Example: Exponential Components | Setup | Specializing the likelihood | Data generation and fitting | Score and Hessian verification | Fisher information and confidence intervals | Homogeneous Weibull | Key properties | R code: Setup and hazard visualization | Cause probabilities | Data generation and MLE | Heterogeneous Weibull | Differences from the homogeneous model | R code: Mixed failure regimes | Time-varying cause probabilities | Model comparison: heterogeneous vs homogeneous | Monte Carlo Assessment | Practical Considerations

Overview of Observation Types | Data Generation with Observe Functors | Exponential Model: Closed-Form Verification | Simulation: Information Content by Censoring Mix | Results Table | Visualization | Per-Component Detail | Key Findings | Cross-Model Comparison Under Mixed Censoring | Computational Considerations | Practical Recommendations

Motivation | Component hazard and cause probability profiles | Hazard functions | Conditional cause probability | Numerical integration for left and interval censoring | Why numerical integration is necessary | Timing comparison | MLE with mixed censoring | Model comparison: heterogeneous vs homogeneous | Monte Carlo study | Bias, variance, and MSE | Confidence interval coverage | Sampling distribution | Summary

Theory | Component lifetime model | System lifetime | Conditional cause probability | Marginal cause probability | Connection to the exponential model | Worked Example | Component hazards | Cause probabilities | Data generation with periodic inspection | Likelihood Contributions | Exact observation ($\omega_i = \text{exact}$) | Right-censored ($\omega_i = \text{right}$) | Left-censored ($\omega_i = \text{left}$) | Interval-censored ($\omega_i = \text{interval}$) | Why homogeneous shapes enable closed forms | MLE Fitting | Score and Hessian computation | Monte Carlo Simulation Study | Bias and MSE by shape regime | Confidence interval coverage | Censoring rates | Sampling distribution visualization | Interpretation | Weibull($k=1$) = Exponential Identity

Exponentially Distributed Component Lifetimes | Likelihood Model | Candidate set models | Reduced likelihood model | Bernoulli candidate set model #1 | Bernoulli candidate set model #2 | Simulation | Masked component cause of failure | Constructing the Likelihood Model | Maximum likelihood estimation | Log-likelihood of $\theta$ given masked data | Observation Types and Censoring | Observe functors | Generating mixed-censoring data | Likelihood evaluation on mixed-censoring data | Monte Carlo simulation study | Bias, Variance, and MSE | Confidence Interval Coverage | Sampling Distribution Visualization | Summary | Sensitivity Analysis | Effect of Masking Probability | Effect of Right-Censoring Rate | Practical Recommendations

Introduction | The Weibull Nesting Chain | Three levels of complexity | The two LRT steps | Physical interpretation | Top-down testing cascade | Worked Example: Homogeneous True Model | Setup and data generation | Fitting all three models | Likelihood ratio tests | Worked Example: Heterogeneous True Model | Monte Carlo Study: Power of the Heterogeneity Test | Design | Rejection rates | Power curve | AIC/BIC model selection accuracy | Practical Guidelines

The Problem | Package Ecosystem | Foundation: Distribution and MLE Infrastructure | Hazard-Based Components: flexhaz | Series System Topology: serieshaz | This Package: maskedcauses | General Masked Inference: maskedhaz | Choosing the Right Package