sanjaymjoshi/relistats

Computation of Reliability Statistics: Reliability, Confidence, Assurance

Reliable Statistics

Statistics often get bad rap for being inaccurate or misleading. They are after all guesses. We can improve their quality by adding information about confidence in these numbers. This project provides tools to compute the confidence levels. Example of usage in real-life situations is reliability engineering.

Reliability engineering deals with estimating parameters or qualities of a product or process or experiment. For simplicity, we assume that all units of a product or results of an experiment are random variables. Collectively, let's call them samples. We assume that the samples are independent (one sample has no effect on another sample) and identically distributed (the reliability or properties of underlying random variable stay the same for each sample).

Concepts

• Reliability is probability of success. The math assumes infinite number of samples, but we can get access to only a finite number of samples. Therefore, we can compute only an estimate of the actual reliability. Based on the number of samples, we qualify the quality of this estimate using confidence.
• Confidence in reliability is probability that the actual reliability of the population is at least the provided reliability level. For example, we can say "If we see zero failures in 10 samples of a success-failure experiment, we have 95% confidence that the reliability is at least about 74%".
• Assurance simplifies reliability and confidence by setting both of them the same. The result is just one number that is easier to communicate. For example, 90% assurance means 90% reliability with 90% confidence. Given the number of samples and number of failures, assurance is just one number.

This library provides methods to calculate these statistics for infinite and finite population sizes.

Example usage in a python file:

from relistats.binomial import assurance

n = 22
a = assurance(n, 0) or 0
print(f"Assurance at {n} good samples: {a*100:.1f}%")

References

• S.M. Joshi, "Computation of Reliability Statistics for Success-Failure Experiments," arXiv:2303.03167 [stat.ME], March 2023.
• S.M. Joshi, "Computation of Reliability Statistics for Finite Samples of Success-Failure Experiments," arXiv:2305.16578 [cs.IT], May 2023.
• Jupyter notebooks showing how to use this library relistats_notebook
• Interactive online versions of the Jupyter notebook on Google Colab.
  • Infinite population.
  • Finite population.

Additional documentation.

• Usage for installation and how to use.
• Background for concepts and mathematical background.
• CHANGELOG.md for revision history.

Credits

This package was originally created with Cookiecutter and the sourcery-ai/python-best-practices-cookiecutter project template. Later modified by author.

relistats's Issues

Release version 1.1.1

• Create revision history information with dates
• Build and post wheel

Fix paper info in binom_fin

• Paper is still referencing infinite samples
• Check README.rst and other rst files

Add multiple python versions to GitHub workflow

Currently testing with only 3.10

Check minimum python version in Pipenv

Should be compatible with >= 3.7