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.
Parameters:  failures (array, list) – The failure data. Must have at least 2 elements.
 right_censored (array, list, optional) – The right censored data. Optional input. Default = None.
 show_plot (bool, optional) – True or False. Default = True
 print_results (bool, optional) – Prints a dataframe of the results. True or False. Default = True
 plot_type (str) – Must be either ‘SF’, ‘CDF’, or ‘CHF’. Default is SF.
 CI (float, optional) – confidence interval for estimating confidence limits on parameters. Must be between 0 and 1. Default is 0.95 for 95% CI.
 plot_CI (bool) – Shades the upper and lower confidence interval. True or False. Default = True
 kwargs – Plotting keywords that are passed directly to matplotlib for the plot (e.g. color, label, linestyle)
Returns:  results (dataframe) – A pandas dataframe of results for the SF
 NA (array) – The NelsonAalen Estimate column from results dataframe. This column is the nonparametric estimate of the Survival Function (reliability function).
 xvals (array) – the xvalues to plot the stepwise plot as seen when show_plot=True
 SF (array) – 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 (array) – cumulative distribution function stepwise values
 CHF (array) – cumulative hazard function stepwise values
 SF_lower (array) – survival function stepwise values for lower CI
 SF_upper (array) – survival function stepwise values for upper CI
 CDF_lower (array) – cumulative distribution function stepwise values for lower CI
 CDF_upper (array) – cumulative distribution function stepwise values for upper CI
 CHF_lower (array) – cumulative hazard function stepwise values for lower CI
 CHF_upper (array) – cumulative hazard function stepwise values for upper CI
 data (array) – the failures and right_censored values sorted. Same as ‘Failure times’ column from results dataframe
 censor_codes (array) – the censoring codes (0 or 1) from the sorted data. Same as ‘Censoring code (censored=0)’ column from results dataframe
Notes
The confidence bounds are calculated using the Greenwood formula with Normal approximation, which is the same as featured in Minitab.
The NelsonAalen method provides the SF. The CDF and CHF are obtained from transformations of the SF. It is not possible to obtain a useful version of the PDF or HF as the derivative of a stepwise function produces discontinuous (jagged) 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.