weibulltools (version 2.1.0)

confint_betabinom: Beta Binomial Confidence Bounds for Quantiles and Probabilities

Description

This function computes the non-parametric beta binomial confidence bounds (BB) for quantiles and failure probabilities.

Usage

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

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.

• rank : Interpolated ranks as a function of probabilities, computed with the converted approximation formula of Benard.

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

• 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 : Method for the estimation of failure probabilities which was specified in estimate_cdf.

Further information is stored in the attributes of this tibble:

• distribution : Distribution which was specified in rank_regression.

• bounds : Specified bound(s).

• direction : Specified direction.

• model_estimation : Input list with class wt_model.

Arguments

x

A list with class wt_model (and further classes) returned by rank_regression.

...

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.

Details

The procedure is similar to the Median Ranks method but with the difference that instead of finding the probability for the j-th rank at the 50% level the probability (probabilities) has (have) to be found at the given confidence level.

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
)

# Probability estimation:
prob_tbl_2p <- estimate_cdf(
  data_2p,
  methods = "johnson"
)

prob_tbl_3p <- estimate_cdf(
  data_3p,
  methods = "johnson"
)

prob_tbl_mult <- estimate_cdf(
  data_3p,
  methods = c("johnson", "mr")
)

# Model estimation with rank_regression():
rr_2p <- rank_regression(
  prob_tbl_2p,
  distribution = "weibull"
)

rr_3p <- rank_regression(
  prob_tbl_3p,
  distribution = "lognormal3",
  conf_level = 0.90
)

rr_lists <- rank_regression(
  prob_tbl_mult,
  distribution = "loglogistic3",
  conf_level = 0.90
)

# Example 1 - Two-sided 95% confidence interval for probabilities ('y'):
conf_betabin_1 <- confint_betabinom(
  x = rr_2p,
  bounds = "two_sided",
  conf_level = 0.95,
  direction = "y"
)

# Example 2 - One-sided lower/upper 90% confidence interval for quantiles ('x'):
conf_betabin_2_1 <- confint_betabinom(
  x = rr_2p,
  bounds = "lower",
  conf_level = 0.90,
  direction = "x"
)

conf_betabin_2_2 <- confint_betabinom(
  x = rr_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_betabin_3_1 <- confint_betabinom(
  x = rr_3p,
  bounds = "two_sided",
  conf_level = 0.90,
  direction = "y"
)

conf_betabin_3_2 <- confint_betabinom(
  x = rr_3p,
  bounds = "two_sided",
  conf_level = 0.90,
  direction = "x"
)

# Example 4 - Confidence intervals if multiple methods in estimate_cdf, i.e.
# "johnson" and "mr", were specified:

conf_betabin_4 <- confint_betabinom(
  x = rr_lists,
  bounds = "two_sided",
  conf_level = 0.99,
  direction = "y"
)