RankAdjustment¶

class
reliability.Nonparametric.
RankAdjustment
(failures=None, right_censored=None, print_results=True, a=None, show_plot=True, plot_CI=True, CI=0.95, plot_type='SF', **kwargs)¶ Uses the rankadjustment estimation method to calculate the reliability from failure data. Right censoring is supported and confidence bounds are provided. The confidence bounds are calculated using the Greenwood formula with Normal approximation, which is the same as featured in Minitab. The rankadjustment method provides the SF. With a little algebra, the CDF and CHF are also obtained from the SF. It is not possible to obtain a useful version of the PDF or HF as the derivative of a stepwise function produces very spikey functions. The Rankadjustment algorithm is the same as is used in Probability_plotting.plotting_positions to obtain yvalues for the scatter plot. As with plotting_positions, the heuristic constant “a” is accepted, with the default being 0.3 for median ranks.
Inputs: failures  an array or list of failure times. Sorting is automatic so times do not need to be provided in any order. right_censored  an array or list of right censored failure times. Defaults to None. show_plot  True/False. Default is True. Plots the CDF, SF, or CHF as specified by plot_type. plot_type  SF, CDF, or CHF. Default is SF. print_results  True/False. Default is True. Will display a pandas dataframe in the console. plot_CI  shades the upper and lower confidence interval CI  confidence interval between 0 and 1. Default is 0.95 for 95% CI. a  the heuristic constant for plotting positions of the form (ka)/(n+12a). Default is a=0.3 which is the median rank method (same as the default in Minitab).
Must be in the range 0 to 1. For more heuristics, see: https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot#HeuristicsOutputs: results  dataframe of results for the SF RA  list of rankadjustment column from results dataframe. This column is the non parametric estimate of the Survival Function (reliability function). xvals  the xvalues to plot the stepwise plot as seen when show_plot=True SF  survival function stepwise values (these differ from the RA values as there are extra values added in to make the plot into a step plot) CDF  cumulative distribution function stepwise values CHF  cumulative hazard function stepwise values SF_lower  survival function stepwise values for lower CI SF_upper  survival function stepwise values for upper CI CDF_lower  cumulative distribution function stepwise values for lower CI CDF_upper  cumulative distribution function stepwise values for upper CI CHF_lower  cumulative hazard function stepwise values for lower CI CHF_upper  cumulative hazard function stepwise values for upper CI
Example Usage: f = [5248,7454,16890,17200,38700,45000,49390,69040,72280,131900] rc = [3961,4007,4734,6054,7298,10190,23060,27160,28690,37100,40060,45670,53000,67000,69630,77350,78470,91680,105700,106300,150400] RankAdjustment(failures = f, right_censored = rc)