weibulltools (version 1.0.1)

confint_betabinom: Beta Binomial Confidence Bounds for Quantiles and/or Probabilities

Description

This non-parametric approach calculates confidence bounds for quantiles and/or failure probabilities using a procedure that is similar to that used in calculating median ranks. The location-scale (and threshold) parameters estimated by rank regression are needed.

Usage

confint_betabinom(x, event, loc_sc_params, distribution = c("weibull",
  "lognormal", "loglogistic", "normal", "logistic", "sev", "weibull3",
  "lognormal3", "loglogistic3"), bounds = c("two_sided", "lower",
  "upper"), conf_level = 0.95, direction = c("y", "x"))

Arguments

x

a numeric vector which consists of lifetime data. x is used to specify the range of confidence region(s).

event

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

loc_sc_params

a (named) numeric vector of estimated location and scale parameters for a specified distribution. The order of elements is important. First entry needs to be the location parameter \(\mu\) and the second element needs to be the scale parameter \(\sigma\). If a three-parametric model is used the third element is the threshold parameter \(\gamma\).

distribution

supposed distribution of the random variable. The value can be "weibull", "lognormal", "loglogistic", "normal", "logistic", "sev" (smallest extreme value), "weibull3", "lognormal3" or "loglogistic3". Other distributions have not been implemented yet.

bounds

a character string specifying the interval(s) which has/have to be computed. Must be one of "two_sided" (default), "lower" or "upper".

conf_level

confidence level of the interval. The default value is conf_level = 0.95.

direction

a character string specifying the direction of the computed interval(s). Must be either "y" (failure probabilities) or "x" (quantiles).

Value

A data frame containing the lifetime characteristic, interpolated ranks as a function of probabilities, the probabilities which are used to compute the ranks and computed values for the specified confidence bound(s).

References

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

Examples

# NOT RUN {
# Example 1: Beta-Binomial Confidence Bounds for two-parameter Weibull:
obs   <- seq(10000, 100000, 10000)
state <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0)

df_john <- johnson_method(x = obs, event = state)

mrr <- rank_regression(x = df_john$characteristic,
                       y = df_john$prob,
                       event = df_john$status,
                       distribution = "weibull",
                       conf_level = .95)

conf_betabin <- confint_betabinom(x = df_john$characteristic,
                                  event = df_john$status,
                                  loc_sc_params = mrr$loc_sc_coefficients,
                                  distribution = "weibull",
                                  bounds = "two_sided",
                                  conf_level = 0.95,
                                  direction = "y")

# Example 2: Beta-Binomial Confidence Bounds for three-parameter Weibull:
# Alloy T7987 dataset taken from Meeker and Escobar(1998, p. 131)
cycles   <- c(300, 300, 300, 300, 300, 291, 274, 271, 269, 257, 256, 227, 226,
              224, 213, 211, 205, 203, 197, 196, 190, 189, 188, 187, 184, 180,
              180, 177, 176, 173, 172, 171, 170, 170, 169, 168, 168, 162, 159,
              159, 159, 159, 152, 152, 149, 149, 144, 143, 141, 141, 140, 139,
              139, 136, 135, 133, 131, 129, 123, 121, 121, 118, 117, 117, 114,
              112, 108, 104, 99, 99, 96, 94)
state <- c(rep(0, 5), rep(1, 67))

df_john2 <- johnson_method(x = cycles, event = state)
mrr_weib3 <- rank_regression(x = df_john2$characteristic,
                       y = df_john2$prob,
                       event = df_john2$status,
                       distribution = "weibull3",
                       conf_level = .95)

conf_betabin_weib3 <- confint_betabinom(x = df_john2$characteristic,
                                  event = df_john2$status,
                                  loc_sc_params = mrr_weib3$loc_sc_coefficients,
                                  distribution = "weibull3",
                                  bounds = "two_sided",
                                  conf_level = 0.95,
                                  direction = "y")
# }