Constructs a likelihood model for exp_series_md_c1_c2_c3. — exp_series_md_c1_c2

Likelihood model for exponential series systems with masked component cause of failure with candidate sets that satisfy conditions C1, C2, and C3, described below.

Usage

exp_series_md_c1_c2_c3(
  rates = NULL,
  lifetime = "t",
  lifetime_upper = "t_upper",
  omega = "omega",
  candset = "x"
)

Arguments

rates: rate parameters for exponential component lifetimes (optional, used as initial values for MLE if provided)
lifetime: column name for system lifetime, defaults to "t"
lifetime_upper: column name for interval upper bound, defaults to "t_upper". Only used for interval-censored observations.
omega: column name for observation type, defaults to "omega". Must contain character values: "exact" (failure at t), "right" (right-censored at t), "left" (left-censored: failed before t), or "interval" (failed in (t, t_upper)).
candset: column prefix for candidate set indicators, defaults to "x"

Value

likelihood model object with class c("exp_series_md_c1_c2_c3", "series_md", "likelihood_model")

Details

This model satisfies the concept of a likelihood_model in the likelihood.model package by providing the following methods:

(1) loglik.exp_series_md_c1_c2_c3 (2) score.exp_series_md_c1_c2_c3 (3) hess_loglik.exp_series_md_c1_c2_c3

These are useful for doing maximum likelihood estimation, hypothesis testing (e.g., likelihood ratio test), estimation of asymptotic sampling distribution given data from the DGP according to the specified model, etc.

It is designed to work well with the likelihood_model R package. In particular, it is intended to be used with the likelihood_contr_model object, which is a likelihood_model object that allows likelihood contributions to be added for whatever data model you have in mind.

In this likelihood model, masked component data approximately satisfies the following conditions:

C1: Pr{K[i] in C[i]) = 1 C2: Pr{C[i]=c[i] | K[i]=j, T[i]=t[i]) = Pr(C[i]=c[i] | K[i]=j', T[i]=t[i]) for any j, j' in c[i]. C3: masking probabilities are independent of theta

As a special case, this model also includes exact component cause of failure data where the candidate set is a singleton.

Examples

# Create model and fit to data using generic dispatch
model <- exp_series_md_c1_c2_c3()
# solver <- fit(model)
# mle <- solver(data, par = c(1, 1, 1))