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Maximum likelihood estimator for exponential series system (C1,C2,C3)

Source: R/md_candidate_set_models.R
md_mle_exp_series_C1_C2_C3.Rd

Computes the MLE of component failure rates for an exponential series system with masked data under C1, C2, C3 candidate set conditions.

Usage

md_mle_exp_series_C1_C2_C3(
  md,
  theta0 = NULL,
  sysvar = "t",
  setvar = "x",
  deltavar = "delta",
  use_annealing = FALSE,
  control = list(),
  lower = 1e-10,
  upper = Inf,
  hessian = TRUE
)

Arguments

md

Masked data frame containing:

  • System lifetime column (default: "t")

  • Candidate set columns (default: "x1", "x2", ..., "xm")

  • Optional right-censoring indicator (default: "delta")

theta0

Initial parameter values for optimization. If NULL, uses the method of moments estimator based on total system hazard.

sysvar

Column name for system lifetime. Default is "t".

setvar

Column prefix for candidate set (Boolean matrix). Default is "x".

deltavar

Column name for right-censoring indicator. Default is "delta". If NULL or column doesn't exist, assumes no censoring.

use_annealing

Logical. If TRUE, uses simulated annealing to find a good starting point before local optimization. Default is FALSE.

control

List of control parameters passed to optim(). Default uses L-BFGS-B with reasonable settings.

lower

Lower bounds for parameters. Default is 1e-10.

upper

Upper bounds for parameters. Default is Inf.

hessian

Logical. If TRUE, compute Hessian at the MLE. Default is TRUE.

Value

An object of class mle (from algebraic.mle package) containing:

  • theta.hat: The MLE of rate parameters

  • sigma: Estimated variance-covariance matrix

  • loglike: Log-likelihood at the MLE

  • info: Observed Fisher information matrix

  • nobs: Number of observations

  • converged: Whether optimization converged

Details

Uses L-BFGS-B optimization with optional simulated annealing for finding a good starting point.

The MLE for exponential series systems with masked data has a closed-form solution only in special cases. In general, numerical optimization is required. This function uses the L-BFGS-B algorithm with analytically computed gradients for efficiency.

Examples

if (FALSE) { # \dontrun{
# Generate masked data
library(tibble)
set.seed(42)
n <- 100
theta_true <- c(1, 1.5, 2)
# ... (data generation code)

mle <- md_mle_exp_series_C1_C2_C3(md, theta0 = theta_true)
print(mle)
confint(mle)
} # }