Probability Plot

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Probability Plot


Purpose

The probability plot is to display an estimate of the cumulative distribution function which best fits a given set of data. It is a graphical technique for assessing whether or not a data set follows a given distribution such as the normal or Weibull.

Data are plotted against a theoretical distribution in such a way that the points should form approximately a straight line. Departures from this straight line indicate departures from the specified distribution.


The correlation coefficient associated with the linear fit to the data in the probability plot is a measure of the goodness of the fit. Estimates of the location and scale parameters of the distribution are given by the intercept and slope.

Probability plots can be generated for several competing distributions to see which provides the best fit, and the probability plot generating the highest correlation coefficient is the best choice since it generates the straightest probability plot.

Anatomy

Probability Plot

Reference: Juran Quality Control Handbook

Terminology

A. Data scale.

B. Cumulative percentage, based upon an assumed probability distribution.

C. Best- fit line generated by Linear Regression.

D. Actual data points plotted against the probability.

E. Confidence intervals.


Major Considerations

Fits of data using Probability Plots can be done by assuming a variety of distributions. While the best distribution to start with is the Normal, the data can also be tested against the Lognormal, Weibull, Exponential, etc.
Probability plots are best done using Minitab’s Graph>Probability Plot function

Application Cookbook

1. Gather the data and tabulate it in column form.

2. Select the probability distribution to be used to test the data.

3. Given the observed data, calculate the cumulative relative frequency of the data, in percent.

4. Calculate the expected (i.e. theoretical) cumulative relative frequency in percent, based upon the chosen frequency distribution.

5. On a cumulative probability graph, plot the actual data points against a straight line plot of the theoretical distribution.

6. If required, decide the level of statistical confidence required, calculate the confidence limits for the distribution and plot them as curves on either side of the theoretical distribution.

From Probability Plot to Six Sigma Tools.

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