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QQ_plot_parametric

class reliability.Probability_plotting.QQ_plot_parametric(X_dist=None, Y_dist=None, show_fitted_lines=True, show_diagonal_line=False, downsample_scatterplot=False, **kwargs)

A QQ plot (quantile-quantile plot) consists of plotting failure units vs failure units for shared quantiles. A quantile is simply the fraction failing (ranging from 0 to 1). To generate this plot we calculate the failure units (these may be units of time, strength, cycles, landings, etc.) at which a certain fraction has failed (0.01,0.02,0.03…0.99) for each distribution and plot them together. The time (or any other failure unit) at which a given fraction has failed is found using the inverse survival function. If the distributions are similar in shape, then the QQ plot should be a reasonably straight line. By plotting the failure times at equal quantiles for each distribution we can obtain a conversion between the two distributions which is useful for Field-to-Test conversions that are necessary during accelerated life testing (ALT).

Parameters:

  • X_dist (object) – A probability distribution object created using the reliability.Distributions module. The failure times at given quantiles from this distribution will be plotted along the X-axis.

  • Y_dist (object) – A probability distribution object created using the reliability.Distributions module. The failure times at given quantiles from this distribution will be plotted along the Y-axis.

  • show_fitted_lines (bool) – Default = True. These are the Y=mX and Y=mX+c lines of best fit.

  • show_diagonal_line (bool) – Default = False. If True the diagonal line will be shown on the plot.

  • 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.

  • kwargs – Plotting keywords that are passed directly to matplotlib (e.g. color, label, linestyle).

Returns:

model_parameters (list) – [m,m1,c1] - these are the values for the lines of best fit. m is used in Y=m.X, and m1 and c1 are used in Y=m1.X+c1

Notes

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