Probability plots
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Use a probability plot to assess whether a particular distribution fits your data. The plot consists of:

·    Plot points, which represent the proportion of failures up to a certain time. Minitab calculates the plot points using a nonparametric method. The observed failure times are plotted on the x-axis vs. the estimated cumulative probabilities (p) on the y-axis. Transformations of both the x and y data are needed to ensure that the plotted y values are a linear function of the plotted x values if the data are sampled from the particular distribution.

·    Fitted line, which is a graphical representation of the percentiles. To make the fitted line, Minitab first calculates the percentiles for the various percents, based on the chosen distribution. The associated probabilities are then transformed and used as the y-variables. The percentiles may be transformed, depending on the distribution, and are used as the x-variables. The transformed scales, chosen to linearize the fitted line, differ depending on the distribution used.

·    Confidence intervals, set of approximate 95.0% confidence intervals for the fitted line.

For more information on probability plot calculations, see Methods and formulas - parametric distribution analysis.

Because the plot points do not depend on any distribution, they would be the same (before being transformed) for any probability plot made. The fitted line, however, differs depending on the parametric distribution chosen. So you can use the probability plot to assess whether a particular distribution fits your data. In general, the closer the points fall to the fitted line, the better the fit. Minitab provides two goodness of fit measures to help assess how the distribution fits your data.

To choose from various methods to estimate the plot points, see Tools > Options > Individual Graphs > Probability Plots. To choose from various methods to obtain the fitted line, see Parametric Distribution Analysis - Estimate.

Tip

To quickly compare the fit of up to eleven different distributions at once, see Distribution ID Plot (Right Censoring) or Distribution ID Plot (Arbitrary Censoring).

The Weibull probability plot below shows failure times associated with running engine windings at a temperature of 80° C: