plot_conf: Add Confidence Region(s) for Quantiles or Probabilities

In weibulltools: Statistical Methods for Life Data Analysis

Description

This function is used to add estimated confidence region(s) to an existing probability plot which also includes the estimated regression line.

Usage

plot_conf(p_obj, x, y, direction = c("y", "x"),
  distribution = c("weibull", "lognormal", "loglogistic", "normal",
  "logistic", "sev", "weibull3", "lognormal3", "loglogistic3"),
  title_trace = "Confidence Limit")

Arguments

p_obj	a plotly object provided by function plot_mod.
x	a list containing the x-coordinates of the confidence region(s). The list can be of length 1 or 2. For more information see Details.
y	a list containing the y-coordinates of the Confidence Region(s). The list can be of length 1 or 2. For more information see Details.
direction	a character string specifying the direction of the plotted interval(s). Must be either "y" (failure probabilities) or "x" (quantiles).
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.
title_trace	a character string which is assigned to the trace shown in the legend.

Details

It is important that the length of the vectors provided as lists in x and y match with the length of the vectors x and y in the function plot_mod. For this reason the following procedure is recommended:

• Calculate confidence intervals with the function confint_betabinom or confint_fisher and store it in a data.frame. For instance call it df.

• Inside plot_mod use the output df$characteristic for x and df$prob for y of the function(s) named before.

• In Examples the described approach is shown with code.

Value

Returns a plotly object containing the probability plot with plotting positions, the estimated regression line and the estimated confidence region(s).

References

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

Examples

# 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))
id <- 1:length(cycles)

df_john <- johnson_method(x = cycles, event = state, id = id)
# Example 1: Probability Plot, Regression Line and Confidence Bounds for Three-Parameter-Weibull:
mrr <- rank_regression(x = df_john$characteristic,
                       y = df_john$prob,
                       event = df_john$status,
                       distribution = "weibull3",
                       conf_level = .90)

conf_betabin <- confint_betabinom(x = df_john$characteristic,
                                  event = df_john$status,
                                  loc_sc_params = mrr$loc_sc_coefficients,
                                  distribution = "weibull3",
                                  bounds = "two_sided",
                                  conf_level = 0.95,
                                  direction = "y")

plot_weibull <- plot_prob(x = df_john$characteristic,
                          y = df_john$prob,
                          event = df_john$status,
                          id = df_john$id,
                          distribution = "weibull",
                          title_main = "Three-Parametric Weibull",
                          title_x = "Cycles",
                          title_y = "Probability of Failure in %",
                          title_trace = "Failed Items")

plot_reg_weibull <- plot_mod(p_obj = plot_weibull,
                             x = conf_betabin$characteristic,
                             y = conf_betabin$prob,
                             loc_sc_params = mrr$loc_sc_coefficients,
                             distribution = "weibull3",
                             title_trace = "Estimated Weibull CDF")

plot_conf_beta <- plot_conf(p_obj = plot_reg_weibull,
                            x = list(conf_betabin$characteristic),
                            y = list(conf_betabin$lower_bound,
                                     conf_betabin$upper_bound),
                            direction = "y",
                            distribution = "weibull3",
                            title_trace = "Confidence Region")

# Example 2: Probability Plot, Regression Line and Confidence Bounds for Three-Parameter-Lognormal:
mrr_ln <- rank_regression(x = df_john$characteristic,
                       y = df_john$prob,
                       event = df_john$status,
                       distribution = "lognormal3",
                       conf_level = .90)

conf_betabin_ln <- confint_betabinom(x = df_john$characteristic,
                                  event = df_john$status,
                                  loc_sc_params = mrr_ln$loc_sc_coefficients,
                                  distribution = "lognormal3",
                                  bounds = "two_sided",
                                  conf_level = 0.95,
                                  direction = "y")

plot_lognormal <- plot_prob(x = df_john$characteristic,
                          y = df_john$prob,
                          event = df_john$status,
                          id = df_john$id,
                          distribution = "lognormal",
                          title_main = "Three-Parametric Lognormal",
                          title_x = "Cycles",
                          title_y = "Probability of Failure in %",
                          title_trace = "Failed Items")

plot_reg_lognormal <- plot_mod(p_obj = plot_lognormal,
                             x = conf_betabin_ln$characteristic,
                             y = conf_betabin_ln$prob,
                             loc_sc_params = mrr_ln$loc_sc_coefficients,
                             distribution = "lognormal3",
                             title_trace = "Estimated Lognormal CDF")

plot_conf_beta_ln <- plot_conf(p_obj = plot_reg_lognormal,
                            x = list(conf_betabin_ln$characteristic),
                            y = list(conf_betabin_ln$lower_bound,
                                     conf_betabin_ln$upper_bound),
                            direction = "y",
                            distribution = "lognormal3",
                            title_trace = "Confidence Region")

weibulltools documentation built on May 2, 2019, 11:01 a.m.