confint_betabinom.default {weibulltools}R Documentation

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

## Default S3 method:
confint_betabinom(
  x,
  status,
  dist_params,
  distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic",
    "weibull3", "lognormal3", "loglogistic3", "exponential", "exponential2"),
  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 numeric vector which consists of lifetime data. Lifetime data could be every characteristic influencing the reliability of a product, e.g. operating time (days/months in service), mileage (km, miles), load cycles.

status

A vector of binary data (0 or 1) indicating whether a unit is a right censored observation (= 0) or a failure (= 1).

dist_params

The parameters (coefficients) returned by rank_regression.

distribution

Supposed distribution of the random variable. Has to be in line with the specification made in rank_regression.

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.

...

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

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.

Value

A tibble with class wt_confint containing the following columns:

Further information is stored in the attributes of this tibble:

See Also

confint_betabinom

Examples

# Vectors:
obs <- seq(10000, 100000, 10000)
status_1 <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0)

cycles <- alloy$cycles
status_2 <- alloy$status

# Probability estimation:
prob_tbl <- estimate_cdf(
  x = obs,
  status = status_1,
  method = "johnson"
)

prob_tbl_2 <- estimate_cdf(
  x = cycles,
  status = status_2,
  method = "johnson"
)

# Model estimation with rank_regression():
rr <- rank_regression(
  x = prob_tbl$x,
  y = prob_tbl$prob,
  status = prob_tbl$status,
  distribution = "weibull",
  conf_level = 0.9
)

rr_2 <- rank_regression(
  x = prob_tbl_2$x,
  y = prob_tbl_2$prob,
  status = prob_tbl_2$status,
  distribution = "lognormal3"
)

# Example 1 - Two-sided 95% confidence interval for probabilities ('y'):
conf_betabin_1 <- confint_betabinom(
  x = prob_tbl$x,
  status = prob_tbl$status,
  dist_params = rr$coefficients,
  distribution = "weibull",
  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 = prob_tbl$x,
  status = prob_tbl$status,
  dist_params = rr$coefficients,
  distribution = "weibull",
  bounds = "lower",
  conf_level = 0.9,
  direction = "x"
)

conf_betabin_2_2 <- confint_betabinom(
  x = prob_tbl$x,
  status = prob_tbl$status,
  dist_params = rr$coefficients,
  distribution = "weibull",
  bounds = "upper",
  conf_level = 0.9,
  direction = "x"
)

# Example 3 - Two-sided 90% confidence intervals for both directions using
# a three-parametric model:

conf_betabin_3_1 <- confint_betabinom(
  x = prob_tbl_2$x,
  status = prob_tbl_2$status,
  dist_params = rr_2$coefficients,
  distribution = "lognormal3",
  bounds = "two_sided",
  conf_level = 0.9,
  direction = "y"
)

conf_betabin_3_2 <- confint_betabinom(
  x = prob_tbl_2$x,
  status = prob_tbl_2$status,
  dist_params = rr_2$coefficients,
  distribution = "lognormal3",
  bounds = "two_sided",
  conf_level = 0.9,
  direction = "x"
)


[Package weibulltools version 2.1.0 Index]