Probability Plotting Method for Univariate Lifetime Distributions

This function is used to apply the graphical technique of probability plotting. It is either applied to the output of estimate_cdf (plot_prob.wt_cdf_estimation) or to the output of a mixture model from mixmod_regression / mixmod_em (plot_prob.wt_model). Note that in the latter case no distribution has to be specified because it is inferred from the model.

plot_prob(x, ...)

# S3 method for wt_cdf_estimation
plot_prob(
  x,
  distribution = c("weibull", "lognormal", "loglogistic", "sev", "normal", "logistic",
    "exponential"),
  title_main = "Probability Plot",
  title_x = "Characteristic",
  title_y = "Unreliability",
  title_trace = "Sample",
  plot_method = c("plotly", "ggplot2"),
  ...
)

# S3 method for wt_model
plot_prob(
  x,
  title_main = "Probability Plot",
  title_x = "Characteristic",
  title_y = "Unreliability",
  title_trace = "Sample",
  plot_method = c("plotly", "ggplot2"),
  ...
)

Arguments

x

A tibble with class wt_cdf_estimation returned by estimate_cdf or a list with class wt_model returned by rank_regression, ml_estimation, mixmod_regression or mixmod_em.

...

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

distribution

Supposed distribution of the random variable.

title_main

A character string which is assigned to the main title.

title_x

A character string which is assigned to the title of the x axis.

title_y

A character string which is assigned to the title of the y axis.

title_trace

A character string which is assigned to the legend trace.

plot_method

Package, which is used for generating the plot output.

Value

A plot object containing the probability plot.

Details

If x was split by mixmod_em, estimate_cdf with method "johnson" is applied to subgroup-specific data. The calculated plotting positions are shaped according to the determined split in mixmod_em.

In mixmod_regression a maximum of three subgroups can be determined and thus being plotted. The intention of this function is to give the user a hint for the existence of a mixture model. An in-depth analysis should be done afterwards.

For plot_method == "plotly" the marker label for x and y are determined by the first word provided in the argument title_x and title_y respectively, i.e. if title_x = "Mileage in km" the x label of the marker is "Mileage". The name of the legend entry is a combination of the title_trace and the number of determined subgroups (if any). If title_trace = "Group" and the data has been split in two groups, the legend entries are "Group: 1" and "Group: 2".

References

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

Examples

# Reliability data:
data <- reliability_data(
  alloy,
  x = cycles,
  status = status
)

# Probability estimation:
prob_tbl <- estimate_cdf(
  data,
  methods = c("johnson", "kaplan")
)

# Example 1 - Probability Plot Weibull:
plot_weibull <- plot_prob(prob_tbl)

# Example 2 - Probability Plot Lognormal:
plot_lognormal <- plot_prob(
  x = prob_tbl,
  distribution = "lognormal"
)

## Mixture identification
# Reliability data:
data_mix <- reliability_data(
  voltage,
  x = hours,
  status = status
)

prob_mix <- estimate_cdf(
  data_mix,
  methods = c("johnson", "kaplan")
)

# Example 3 - Mixture identification using mixmod_regression:
mix_mod_rr <- mixmod_regression(prob_mix)

plot_mix_mod_rr <- plot_prob(x = mix_mod_rr)

# Example 4 - Mixture identification using mixmod_em:
mix_mod_em <- mixmod_em(data_mix)

plot_mix_mod_em <- plot_prob(x = mix_mod_em)