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Mathcad ABC: G is for Graphs - Pareto Plots


Mathcad ABC: G is for Graphs - Pareto Plots

We've added several new graph types to both Mathcad 15 and Mathcad Prime 1.0. An earlier article demonstrated the new Box Plot graph type. (See Analyze Data with New Box Plots in Mathcad 15 and Prime 1.0).

This blog demonstrates the new Pareto plots.

Pareto Plots

Pareto plots are composed of vertical bars displaying frequency for each category. The data is displayed in descending order to show which factors are the most significant. A line curve above the bars shows the cumulative values of the data.

Example: Quality Control in Drill Production

The quality control division of a drill manufacturer wants to identify which factors are causing drills to be rejected. They categorize the rejected drills by their primary defects and the frequency of occurrence.

drill data

To present the data to manufacturing, the group prepares a Pareto plot.

For how to make a Pareto Plot in Mathcad 15, see the attached worksheet. The Mathcad Prime 1.0 worksheet is also attached. The process in Mathcad Prime 1.0 is described below, but both are similar.

In Mathcad Prime 1.0 and Mathcad 15, use the pareto function to set up your data for a Pareto plot.

Pareto function results

Note that the function reordered the factors by frequency.

  • The first column of the resulting matrix contains the labels for each category.
  • The second column lists the data in descending order of frequency.
  • The third column lists the cumulative percentages of the sorted data.

Insert an x-y plot. Then plot the frequencies of occurence (column 1) on the y-axis and the text labels on the x-axis (column 0). Note that the default ORIGIN for matrices in Mathcad is 0.

Then change the trace type of the plot to Column Trace.

Pareto plot

To show the cumulative effect of the defects, add the third column of the matrix (column 2) to the y-axis.

pareto plot

The total defects add up to 100%.

The Pareto plot quickly demonstrates that problems with the power supply and plastic case cause 86% of the defects. Concentrating on eliminating those two problem areas will rapidly shrink the defect rate. The other factors are not as important to address.

Reference: Data based on Practical Business Statistics, Andrew F. Siegel, Irwin, 1994.