# Exponential_probability_plot_Weibull_Scale¶

class reliability.Probability_plotting.Exponential_probability_plot_Weibull_Scale

Generates a probability plot on Weibull scaled probability paper so that the CDF of the distribution appears linear. This differs from the Exponential probability plot on Exponential scaled probability paper as the Weibull paper will make multiple distributions with different Lambda parameters appear as parallel lines rather than as lines radiating from the origin. This change in scale has applications in ALT probability plotting. This function can be used to show Exponential_1P or Exponential_2P distributions.

Parameters: failures (array, list) – The failure data. Must have at least 1 element. right_censored (array, list, optional) – The right censored data. Optional input. Default = None. fit_gamma (bool, optional) – Specify this as True in order to fit the Exponential_2P distribution and scale the x-axis to time - gamma. Default = False. show_fitted_distribution (bool, optional) – If True, the fitted distribution will be plotted on the probability plot. Defaults = True. show_scatter_points (bool, optional) – If True, the plot will include the scatter points from the failure times. Defaults = True. downsample_scatterplot (bool, int, optional) – If True or None, and there are over 1000 points, then the scatterplot will be downsampled by a factor. The default downsample factor will seek to produce between 500 and 1000 points. If a number is specified, it will be used as the downsample factor. Default is False which will result in no downsampling. This functionality makes plotting faster when there are very large numbers of points. It only affects the scatterplot not the calculations. a (float, int, optional) – The heuristic constant for plotting positions of the form (k-a)/(n+1-2a). Default = 0.3 which is the median rank method (same as the default in Minitab). For more heuristics, see: https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot#Heuristics CI (float, optional) – The confidence interval for the bounds. Must be between 0 and 1. Optional input. Default = 0.95 for 95% CI. kwargs – Plotting keywords that are passed directly to matplotlib (e.g. color, label, linestyle). figure (object) – The figure handle of the probability plot is returned as an object

Notes

This function works because a Weibull Distribution with alpha = x and beta = 1 is identical to an Exponential Distribution with Lambda = 1/x.

There is a hidden parameter called __fitted_dist_params which is used to specify the parameters of the distribution that has already been fitted. Passing a distribution object to this parameter will bypass the fitting process and use the parameters of the distribution provided. When this is done the minimum length of failures can be 1. The distribution object must contain the SE and Cov of the parameters so it needs to be generated by the Fitters module.

CI_type is not required as the Exponential distribution has the same confidence interval bounds on both time and reliability.

If your plot does not appear automatically, use plt.show() to show it.