A QQ plot is a quantile-quantile plot which 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).
Inputs: X_dist - a probability distribution. The failure times at given quantiles from this distribution will be plotted along the X-axis. Y_dist - a probability distribution. The failure times at given quantiles from this distribution will be plotted along the Y-axis. show_fitted_lines - True/False. Default is True. These are the Y=mX and Y=mX+c lines of best fit. show_diagonal_line - True/False. Default is False. If True the diagonal line will be shown on the plot.
Outputs: The QQ_plot will always be output. Use plt.show() to show it. [m,m1,c1] - these are the values for the lines of best fit. m is used in Y=mX, and m1 and c1 are used in Y=m1X+c1