library(likelihood.model)
library(algebraic.mle)

# Component failure data (hours to failure)
# Some components are still running at study end (censored)
reliability_data <- data.frame(
  hours = c(120, 340, 560, 780, 1000, 1200, 1200, 1200),
  failed = c(1, 1, 1, 1, 1, 0, 0, 0)  # 0 = still running
)

# Fit Weibull model
model <- likelihood_contr_model(
  obs_type = "right_censored",
  distribution = weibull_distribution(),
  time_col = "hours",
  status_col = "failed"
)

fit <- mle(model, data = reliability_data,
           start = c(shape = 1, scale = 500))

# Reliability at 1000 hours
shape <- coef(fit)["shape"]
scale <- coef(fit)["scale"]
reliability_1000 <- exp(-(1000/scale)^shape)
cat("R(1000) =", round(reliability_1000, 3))
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# Simulated clinical trial data
trial_data <- data.frame(
  patient_id = 1:50,
  survival_months = c(
    2.3, 5.1, 8.4, 12.0, 15.2, 18.0, 18.0, 18.0,  # Treatment group
    1.1, 3.2, 4.8, 7.5, 9.0, 11.2, 18.0, 18.0     # Control group
    # ... more patients
  ),
  event = c(1, 1, 1, 1, 1, 0, 0, 0,
            1, 1, 1, 1, 1, 1, 0, 0),
  treatment = rep(c("treatment", "control"), each = 8)
)

# Fit separate models per group
fit_treatment <- mle(
  likelihood_contr_model("right_censored", weibull_distribution()),
  data = subset(trial_data, treatment == "treatment"),
  start = c(shape = 1, scale = 10)
)

fit_control <- mle(
  likelihood_contr_model("right_censored", weibull_distribution()),
  data = subset(trial_data, treatment == "control"),
  start = c(shape = 1, scale = 10)
)

# Compare median survival times
median_treatment <- coef(fit_treatment)["scale"] * log(2)^(1/coef(fit_treatment)["shape"])
median_control <- coef(fit_control)["scale"] * log(2)^(1/coef(fit_control)["shape"])
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library(wei.series.md.c1.c2.c3)

# System with 3 components, masked failure cause
system_data <- data.frame(
  system_id = 1:20,
  failure_time = c(100, 150, 200, 180, 220, ...),
  candidate_set = list(
    c(1, 2),     # Could be component 1 or 2
    c(2, 3),     # Could be component 2 or 3
    c(1),        # Known to be component 1
    c(1, 2, 3),  # Any component possible
    ...
  )
)

# Fit the masked data model
fit <- mle_wei_series_md_c1_c2_c3(system_data)
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library(likelihood.model)
library(algebraic.mle)

# Fit model
fit <- mle(model, data = data, start = c(shape = 1, scale = 5))

# Profile likelihood for shape parameter
profile_shape <- profile_likelihood(
  fit,
  parameter = "shape",
  range = c(0.5, 3.0),
  n_points = 50
)

# Plot profile
plot(profile_shape$values, profile_shape$loglik, type = "l",
     xlab = "Shape", ylab = "Profile Log-Likelihood")
abline(h = max(profile_shape$loglik) - qchisq(0.95, 1)/2,
       lty = 2, col = "red")  # 95% CI threshold
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