This function computes normal-approximation confidence intervals for quantiles and failure probabilities.

confint_fisher(x, ...)

# S3 method for wt_model
confint_fisher(
  x,
  b_lives = c(0.01, 0.1, 0.5),
  bounds = c("two_sided", "lower", "upper"),
  conf_level = 0.95,
  direction = c("y", "x"),
  ...
)

Arguments

x

A list with classes wt_model and wt_ml_estimation returned by ml_estimation.

...

Further arguments passed to or from other methods. Currently not used.

b_lives

A numeric vector indicating the probabilities \(p\) of the \(B_p\)-lives (quantiles) to be considered.

bounds

A character string specifying the bound(s) to be computed.

conf_level

Confidence level of the interval.

direction

A character string specifying the direction of the confidence interval. "y" for failure probabilities or "x" for quantiles.

Value

A tibble with class wt_confint containing the following columns:

  • x : An ordered sequence of the lifetime characteristic regarding the failed units, starting at min(x) and ending up at max(x). With b_lives = c(0.01, 0.1, 0.5) the 1%, 10% and 50% quantiles are additionally included in x, but only if the specified probabilities are in the range of the estimated probabilities.

  • prob : An ordered sequence of probabilities with specified b_lives included.

  • std_err : Estimated standard errors with respect to direction.

  • lower_bound : Provided, if bounds is one of "two_sided" or "lower". Lower confidence limits with respect to direction, i.e. limits for quantiles or probabilities.

  • upper_bound : Provided, if bounds is one of "two_sided" or "upper". Upper confidence limits with respect to direction, i.e. limits for quantiles or probabilities.

  • cdf_estimation_method : A character that is always NA_character. Only needed for internal use.

Further information is stored in the attributes of this tibble:

  • distribution : Distribution which was specified in ml_estimation.

  • bounds : Specified bound(s).

  • direction : Specified direction.

  • model_estimation : Input list with classes wt_model and wt_ml_estimation.

Details

The basis for the calculation of these confidence bounds are the standard errors obtained by the delta method.

The bounds on the probability are determined by the z-procedure. See 'References' for more information on this approach.

References

Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998

Examples

# Reliability data preparation: ## Data for two-parametric model: data_2p <- reliability_data( shock, x = distance, status = status ) ## Data for three-parametric model: data_3p <- reliability_data( alloy, x = cycles, status = status ) # Model estimation with ml_estimation(): ml_2p <- ml_estimation( data_2p, distribution = "weibull" ) ml_3p <- ml_estimation( data_3p, distribution = "lognormal3", conf_level = 0.90 ) # Example 1 - Two-sided 95% confidence interval for probabilities ('y'): conf_fisher_1 <- confint_fisher( x = ml_2p, bounds = "two_sided", conf_level = 0.95, direction = "y" ) # Example 2 - One-sided lower/upper 90% confidence interval for quantiles ('x'): conf_fisher_2_1 <- confint_fisher( x = ml_2p, bounds = "lower", conf_level = 0.90, direction = "x" ) conf_fisher_2_2 <- confint_fisher( x = ml_2p, bounds = "upper", conf_level = 0.90, direction = "x" ) # Example 3 - Two-sided 90% confidence intervals for both directions using # a three-parametric model: conf_fisher_3_1 <- confint_fisher( x = ml_3p, bounds = "two_sided", conf_level = 0.90, direction = "y" ) conf_fisher_3_2 <- confint_fisher( x = ml_3p, bounds = "two_sided", conf_level = 0.90, direction = "x" )