Frequency distributions

July 1, 2022

The amount of time each Stage requires at run time should be treated as a frequency distribution to be designed by the Process, ultimately by the Cyclo. When implemented by the Facility, the Times of Gain from the running Cyclo should be captured and analyzed, in order to check how close they are from the expected timing.

The timing analysis should detect variations due to existing common and special causes in the Process, according to SPC (Statistical Process Control) and TPM (Total Productive Maintenance) directives.

Summary of a frequency distribution

Inspired on Tukey’s idea, referenced in Martin Bland’s An Introduction to Medical Statistics, a measure based on Quartiles & Box/Whisker Plots would summarize frequency distributions in a few numbers. The image below shows that median, quartiles, maximum and minimum may be used as a convenient five figure summary of a distribution.

The box shows the distance between the quartiles, with the median marked as a line in between, and the whiskers at extremes. Plots are also useful for comparison, the example shows results from patients with AIDS, AIDS Related complex, HIV positive but asymptomatic, and normal.

Distribution

• name: Distribution name.
• sample: [data] array.
• size: Sample size.
• is_normal: True if sample fits a normal distribution.
• is_uniform: True if sample fits an uniform distribution.
• value: {max, qt3, med, qt1, min} as distribution summary.

TODO: Confidence interval narrows estimated percentiles?

• 95% confidence interval
• Normal range or reference interval

Published in Business Amplifier, also e-book and Amplificador de Negócios.