https://raw.githubusercontent.com/MatthewReid854/reliability/master/docs/images/logo.png

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 Nelson-Aalen 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 Nelson-Aalen Estimate column from results dataframe. This column is the non-parametric estimate of the Survival Function (reliability function).

  • xvals (array) – the x-values 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 Nelson-Aalen 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. Nelson-Aalen does obtain the HF directly which is then used to obtain the CHF, but this function is not smooth and is of little use.