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## Probability Plots

### What are probability plots?

Probability plots make sense of the chaos of failure data on an X-Y plot. Each type of plot is divided differently on the X and Y axis based on the fundamental mathematics for a given distribution. The decision which type of graph paper to use is based on: 1) a simple pragmatic approach (use the one that gives the best curve fit to the data), and 2) the physics of failure or the mechanism driving the data for non-failures. For reliability data, 85% to 95% of the data will adequately fit a Weibull distribution. For repair data, 85% to 95% of the data will adequately fit a lognormal distribution. Often Weibull plots or lognormal plots compete to which distribution best fits the failure data.

### Why use are probability plots?

The acquired data is plotted in the units acquired on the X-axis of a probability plot and the data is plotted in rank order. The Y-axis in most cases is determined using Benards median rank approximation to provided the probability percentage. The result is often a straight line on the properly divided X-Y graph paper. Please note, over the years many different plotting positions have been tried with Benard's plot position being the strongest survivor for tailed data.

### When to use are probability plots?

Use when you have failure data or repair data. They work best when age-failure plots are made by individual failure modes or individual repair modes. They also will handle high level failure data and repair times where the data represent how the system is behaving.

### Where to use are probability plots?

Use probability plots to get complicated data summarized onto one side of one sheet of paper. When the plots have the cumulative distribution plotted on the Y-axis, it tells what percent of the population will have a life (or repair time) less than the corresponding X-value.

These definitions are written by H. Paul Barringer