weibulltools (version 1.0.1)

plot_prob_mix: Probability Plot for Separated Mixture Models

Description

This function is used to apply the graphical technique of probability plotting to univariate mixture models that where separated with functions mixmod_regression or mixmod_em.

Usage

plot_prob_mix(x, event, id = rep("XXXXXX", length(x)),
  distribution = c("weibull", "lognormal", "loglogistic"),
  mix_output = NULL, title_main = "Probability Plot",
  title_x = "Characteristic", title_y = "Unreliability",
  title_trace = "Sample")

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.

event

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

id

a character vector for the identification of every unit.

distribution

supposed distribution of the random variable. For output provided by mixmod_em distribution must be "weibull". Can be "weibull", "lognormal" or "loglogistic" for output provided mixmod_regression. Other distributions have not been implemented yet.

mix_output

a list provided by mixmod_regression or mixmod_em, which consists of values necessary to visualize the subgroups.The default value of mix_output is NULL.

title_main

a character string which is assigned to the main title of the plot.

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 whis is assigned to the trace shown in the legend.

Value

Returns a plotly object containing the layout of the probability plot provided by plot_layout and the plotting positions.

Details

Depending on the separation method the function johnson_method is called in various ways. If mixmod_regression is used, johnson_method is applied to all data. If data was splitted by mixmod_em the function johnson_method is applied to subgroup-specific data. The calculated plotting positions are colored regarding the obtained split of the used splitting function. If mix_output = NULL johnson_method is applied to all data, too. The obtained plot is then equal to plot_prob. See Examples for all three cases.

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.

The marker label for x is determined by the first word provided in the argument title_x, i.e. if title_x = "Mileage in km" the x label of the marker is "Mileage".

The marker label for y is determined by the string provided in the argument title_y, i.e. if title_y = "Probability in percent" the y label of the marker is "Probability".

The name of the legend entry is a combination of the title_trace and the number of determined subgroups. If title_trace = "Group" and the data could be splitted in two groups, the legend entries would be "Group 1" and "Group 2".

References

Doganaksoy, N.; Hahn, G.; Meeker, W. Q., Reliability Analysis by Failure Mode, Quality Progress, 35(6), 47-52, 2002

Examples

# NOT RUN {
# Data is taken from given reference:
hours <- c(2, 28, 67, 119, 179, 236, 282, 317, 348, 387, 3, 31, 69, 135,
          191, 241, 284, 318, 348, 392, 5, 31, 76, 144, 203, 257, 286,
          320, 350, 412, 8, 52, 78, 157, 211, 261, 298, 327, 360, 446,
          13, 53, 104, 160, 221, 264, 303, 328, 369, 21, 64, 113, 168,
          226, 278, 314, 328, 377)
state <- c(1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1,
          1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0,
          1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
          0, 1, 1, 1, 1, 1, 1)
id <- 1:length(hours)

# Example 1 - mix_output = NULL:
plot_weibull <- plot_prob_mix(x = hours,
                              event = state,
                              id = id,
                              distribution = "weibull",
                              mix_output = NULL,
                              title_main = "Weibull Probability Plot",
                              title_x = "Time in Hours",
                              title_y = "Probability of Failure",
                              title_trace = "Failed Items")

# Example 2 - Using result of mixmod_em in mix_output:
mix_mod_em <- mixmod_em(x = hours, event = state, distribution = "weibull",
                        conf_level = 0.95, k = 2, method = "EM", n_iter = 150)

plot_weibull_em <- plot_prob_mix(x = hours,
                                 event = state,
                                 id = id,
                                 distribution = "weibull",
                                 mix_output = mix_mod_em,
                                 title_main = "Weibull Mixture EM",
                                 title_x = "Time in Hours",
                                 title_y = "Probability of Failure",
                                 title_trace = "Subgroup")

# Example 3 - Using result of mixmod_regression in mix_output:
john <- johnson_method(x = hours, event = state)
mix_mod_reg <- mixmod_regression(x = john$characteristic,
                                 y = john$prob,
                                 event = john$status,
                                 distribution = "weibull")

plot_weibull_reg <- plot_prob_mix(x = hours,
                                  event = state,
                                  id = id,
                                  distribution = "weibull",
                                  mix_output = mix_mod_reg,
                                  title_main = "Weibull Mixture Regression",
                                  title_x = "Time in Hours",
                                  title_y = "Probability of Failure",
                                  title_trace = "Subgroup")
# }