NelsonAalen¶

class
reliability.Nonparametric.
NelsonAalen
(failures=None, right_censored=None, show_plot=True, print_results=True, plot_CI=True, CI=0.95, plot_type='SF', **kwargs)¶ Uses the NelsonAalen 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. The NelsonAalen method provides the CHF. With a little algebra, the CDF and SF are also obtained from the CHF. 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. NelsonAalen does obtain the HF directly which is then used to obtain the CHF, but this function is not smooth and is of little use
Inputs: failure  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 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. plot_type  SF, CDF, or CHF. Default is SF.
Outputs: results  dataframe of results NA  list of NelsonAalen 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 NA 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] NelsonAalen(failures = f, right_censored = rc)