Overview of the Pareto Plot Platform
The Pareto Plot platform produces charts to display the relative frequency or severity of problems in a quality-related process or operation. The Pareto plot is displayed initially as a bar chart that shows the classification of problems arranged in decreasing order. The column whose values are the cause of a problem is assigned the Y role and is called the process variable.
You can also generate a comparative Pareto plot, which combines two or more Pareto plots for the same process variable. The single display shows plots for each value in a column assigned the X role, or combination of levels from two X variables. Columns assigned the X role are called classification variables.
The Pareto plot can chart a single Y (process) variable with no X classification variables, with a single X, or with two X variables. The Pareto function does not distinguish between numeric and character variables or between modeling types. You can switch between a bar chart and a pie chart. All values are treated as discrete, and bars or wedges represent either counts or percentages.
Example of the Pareto Plot Platform
This example uses the Failure.jmp sample data table, which contains failure data and a frequency column. It lists causes of failure during the fabrication of integrated circuits and the number of times each type of defect occurred. From the analysis, you can determine which factors contribute most toward process failure.
1. Select Help > Sample Data Library and open Quality Control/Failure.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select failure and click Y, Cause.
This column lists the causes of failure and is the variable that you want to inspect.
4. Select N and click Freq.
This column list the number of times each type of defect occurred.
5. Click OK.
Figure 12.2 Pareto Plot Report Window
The left axis represents the count of failures, and the right axis represents the percent of failures in each category. The bars are in decreasing order with the most frequently occurring failure to the left. The curve indicates the cumulative failures from left to right.
6. Select Label Cum Percent Points from the red triangle menu next to Pareto Plot.
Note that Contamination accounts for approximately 45% of the failures. The point above the Oxide Defect bar shows that Contamination and Oxide Defect together account for approximately 71% of the failures.
7. From the red triangle menu, deselect Label Cum Percent Points and Show Cum Percent Curve.
8. Double-click the y-axis labeled N and rename it Count.
9. Double-click the y-axis to display the Y Axis Specification window.
‒ In the Maximum field, type 15.
‒ In the Increment field, type 2.
‒ In the Tick Marks and Grid Lines area, select Grid Lines for the Major grid line.
‒ Click OK.
10. From the red triangle menu, select Category Legend.
Figure 12.3 Pareto Plot with Display Options
Figure 12.3 shows counts now instead of percents, and has a category legend. The vertical count axis is rescaled and has grid lines at the major tick marks.
11. To view the data as a pie chart, select Pie Chart from the red triangle menu.
Figure 12.4 Pareto Plot as a Pie Chart
Contamination and Oxide Defect clearly represent the majority of the failures.
Launch the Pareto Plot Platform
Launch the Pareto Plot platform by selecting Analyze > Quality and Process > Pareto Plot.
Figure 12.5 The Pareto Plot Launch Window
The Pareto Plot launch window contains the following options:
Y, Cause
Identifies the column whose values are the cause of a problem. It is called the process variable and is the variable that you want to inspect.
X, Grouping
Identifies the grouping factor. The grouping variable produces one Pareto plot window with side-by-side plots for each value. You can have no grouping variable, one grouping variable (see “One-Way Comparative Pareto Plot Example”), or two grouping variables (see “Two-Way Comparative Pareto Plot Example”).
Weight
Assigns a variable to give the observations different weights.
Freq
Identifies the column whose values hold the frequencies.
By
Identifies a variable to produce a separate analysis for each value that appears in the column.
Threshold of Combined Causes
Enables you to specify a threshold for combining causes by specifying a minimum rate or count. Select the option and then select Tail % or Count and enter the threshold value. The Tail % option combines smaller count groups against the percentage specified of the total (combined small groups count/total group count). The Count option enables you to specify a specific count threshold. For an example, see “Threshold of Combined Causes Example”.
Per Unit Analysis
Enables you to compare defect rates across groups. JMP calculates the defect rate as well as 95% confidence intervals of the defect rate. Select the option and then select Constant or Value in Freq Column and enter the sample size value or cause code, respectively. The Constant option enables you to specify a constant sample size on the launch window. The Value In Freq Column option enables you to specify a unique sample size for a group through a special cause code to designate the rows as cause rows.
Although causes are allowed to be combined in Pareto plots, the calculations for these analyses do not change correspondingly.
For examples, see “Using a Constant Size across Groups Example” and “Using a Non-Constant Sample Size across Groups Example”.
The Pareto Plot Report
The Pareto plot combines a bar chart displaying percentages of variables in the data with a line graph showing cumulative percentages of the variables.
Figure 12.6 Pareto Plot Example
The Pareto plot can chart a single Y (process) variable with no X classification variables, with a single X, or with two X variables. The Pareto plot does not distinguish between numeric and character variables or between modeling types. All values are treated as discrete, and bars represent either counts or percentages. The following list describes the arrangement of the Pareto plot:
• A Y variable with no X classification variables produces a single chart with a bar for each value of the Y variable. For an example, see “Example of the Pareto Plot Platform”.
• A Y variable with one X classification variable produces a row of Pareto plots. There is a plot for each level of the X variable with bars for each Y level. These plots are referred to as the cells of a comparative Pareto plot. There is a cell for each level of the X (classification) variable. Because there is only one X variable, this is called a one-way comparative Pareto plot. For an example, see “One-Way Comparative Pareto Plot Example”.
• A Y variable with two X variables produces rows and columns of Pareto plots. There is a row for each level of the first X variable and a column for each level of the second X variable. Because there are two X variables, this is called a two-way comparative Pareto plot. The rows have a Pareto plot for each value of the first X variable, as described previously. The upper left cell is called the key cell. Its bars are arranged in descending order. The bars in the other cells are in the same order as the key cell. You can reorder the rows and columns of cells. The cell that moves to the upper left corner becomes the new key cell and the bars in all other cells rearrange accordingly. For an example, see “Two-Way Comparative Pareto Plot Example”.
• Each bar is the color for which the rows for that Y level are assigned in the associated data table. Otherwise, a single color is used for all of the bars whose Y levels do not have rows with an assigned color. If the rows for a Y level have different colors, the bar for that Y level is the color of the first row for that Y level in the data table.
You can change the type of scale and arrangement of bars and convert the bars into a pie chart using the options in the Pareto Plot red triangle menu. For more information, see “Pareto Plot Platform Options”.
Pareto Plot Platform Options
The red triangle menu next to Pareto Plot has commands that customize the appearance of the plots. It also has options in the Causes submenu that affect individual bars within a Pareto plot. The following commands affect the appearance of the Pareto plot as a whole:
Percent Scale
Shows or hides the count and percent left vertical axis display.
N Legend
Shows or hides the total sample size in the plot area.
Category Legend
Shows or hides labeled bars and a separate category legend.
Pie Chart
Shows or hides the bar chart and pie chart representation.
Reorder Horizontal, Reorder Vertical
Reorders grouped Pareto plots when there is one or more grouping variables.
Ungroup Plots
Splits up a group of Pareto charts into separate plots.
Count Analysis
Performs defect per unit analyses. Enables you to compare defect rates and perform ratio tests across and within groups:
‒ Per Unit Rates compares defect rates across groups. If a sample size is specified, Defects Per Unit (DPU) and Parts Per Million (PPM) columns are added to the report.
‒ Test Rate Within Groups tests (a likelihood ratio chi-square) whether the Defects Per Unit (DPU) across causes are the same within a group.
‒ Test Rates Across Groups tests (a likelihood ratio chi-square) whether the Defects Per Unit (DPU) for each cause is the same across groups.
Show Cum Percent Curve
Shows or hides the cumulative percent curve above the bars and the cumulative percent axis on the vertical right axis.
Show Cum Percent Axis
Shows or hides the cumulative percent axis on the vertical right axis.
Show Cum Percent Points
Shows or hides the points on the cumulative percent curve.
Label Cum Percent Points
Shows or hides the labels on the points on the cumulative curve.
Cum Percent Curve Color
Changes the color of the cumulative percent curve.
Causes
Has options that affect one or more individual chart bars. See “Causes Options”, for a description of these options.
See the JMP Reports chapter in the Using JMP book for more information about the following options:
Local Data Filter
Shows or hides the local data filter that enables you to filter the data used in a specific report.
Redo
Contains options that enable you to repeat or relaunch the analysis. In platforms that support the feature, the Automatic Recalc option immediately reflects the changes that you make to the data table in the corresponding report window.
Save Script
Contains options that enable you to save a script that reproduces the report to several destinations.
Save By-Group Script
Contains options that enable you to save a script that reproduces the platform report for all levels of a By variable to several destinations. Available only when a By variable is specified in the launch window.
Causes Options
You can highlight a bar by clicking on it. Use Control-click to select multiple bars that are not contiguous. When you select bars, you can access the commands on the red triangle menu that affect Pareto plot bars. They are found on the Causes submenu on the red triangle menu. These options are also available with a right-click anywhere in the plot area. The following options apply to highlighted bars instead of to the chart as a whole:
Combine Causes
Combines selected (highlighted) bars. You can select either Selected, Last Causes, First Causes or select from a list of variables as shown in Figure 12.7.
Figure 12.7 Combine Causes Window
Separate Causes
Separates selected bars into their original component bars.
Move to First
Moves one or more highlighted bars to the left (first) position.
Move to Last
Moves one or more highlighted bars to the right (last) position.
Colors
Shows the colors palette for coloring one or more highlighted bars.
Markers
Shows the markers palette for assigning a marker to the points on the cumulative percent curve, when the Show Cum Percent Points command is in effect.
Label
Displays the bar value at the top of all highlighted bars.
Additional Examples of the Pareto Plot Platform
This section contains additional examples using the Pareto Plot platform.
Threshold of Combined Causes Example
This example uses the Failure.jmp sample data table, which contains failure data and a frequency column. It lists causes of failure during the fabrication of integrated circuits and the number of times each type of defect occurred. A threshold value of 2 is specified for this example.
1. Select Help > Sample Data Library and open Quality Control/Failure.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select failure and click Y, Cause.
4. Select N and click Freq.
5. Select Threshold of Combined Causes and then select Count.
6. Enter 2 as the threshold value.
7. Click OK.
Figure 12.8 Pareto Plot with a Threshold Count of 2
Figure 12.8 displays the plot after specifying a count of 2. All causes with counts 2 or fewer are combined into the final bar labeled 4 Others.
8. To separate the combined bars into original categories as shown in Figure 12.9, select Causes > Separate Causes.
Figure 12.9 Pareto Plot with Separated Causes
Using a Constant Size across Groups Example
This example uses the Failures.jmp sample data table, which contains failure data and a frequency column. It lists causes of failure during the fabrication of integrated circuits and the number of times each type of defect occurred for two processes. A constant sample size of 1000 is specified for this example.
1. Select Help > Sample Data Library and open Quality Control/Failures.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select Causes and click Y, Cause.
4. Select Process and click X, Grouping.
5. Select Count and click Freq.
6. Select Per Unit Analysis and then select Constant.
7. Enter 1000 in Sample Size.
8. Click OK.
Figure 12.10 Pareto Plot Report Window
Process A indicates Contamination as the top failure while Process B indicates Oxide Defect as the leading failure.
9. Select Count Analysis > Test Rates Across Groups from the red triangle menu.
Figure 12.11 Test Rates across Groups Results
Note that the DPU for Contamination across groups (Process A and B) is around 0.06.
Using a Non-Constant Sample Size across Groups Example
This example uses the Failuressize.jmp sample data table, which contains failure data and a frequency column. It lists causes of failure during the fabrication of integrated circuits and the number of times each type of defect occurred for two processes. Among the other causes (Oxide Defect, Silicon Defect, and so on) is a cause labeled size. Specifying size as the cause code designates the rows as size rows.
1. Select Help > Sample Data Library and open Quality Control/Failuressize.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select Causes and click Y, Cause.
4. Select Process and click X, Grouping.
5. Select Count and click Freq.
6. Select Per Unit Analysis and then select Value in Freq Column.
7. Enter size in Cause Code.
8. Click OK.
Figure 12.12 Pareto Plot Report Window
9. Select Count Analysis > Per Unit Rates and Count Analysis > Test Rates Across Groups from the red triangle menu.
Figure 12.13 Per Unit Rates and Test Rates across Groups Results
Note that the sample size of 101 is used to calculate the DPU for the causes in group A. However, the sample size of 145 is used to calculate the DPU for the causes in group B.
If there are two group variables (say, Day and Process), Per Unit Rates lists DPU or rates for every combination of Day and Process for each cause. However, Test Rate Across Groups only tests overall differences between groups.
One-Way Comparative Pareto Plot Example
This example uses the Failure2.jmp sample data table. This table records failures in a sample of capacitors manufactured before cleaning a tube in the diffusion furnace and in a sample manufactured after cleaning the furnace. For each type of failure, the variable clean identifies the samples with the values “before” or “after.”
1. Select Help > Sample Data Library and open Quality Control/Failure2.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select failure and click Y, Cause.
4. Select clean and click X, Grouping.
5. Select N and click Freq.
6. Click OK.
Figure 12.14 displays the side-by-side plots for each value of the variable, clean.
Figure 12.14 One-way Comparative Pareto Plot
The horizontal and vertical axes are scaled identically for both plots. The bars in the first plot are in descending order of the y-axis values and determine the order for all cells.
7. Rearrange the order of the plots by clicking the title (after) in the first tile and dragging it to the title of the next tile (before).
A comparison of these two plots shows a reduction in oxide defects after cleaning. However, the plots are easier to interpret when presented as the before-and-after plot shown in Figure 12.15. Note that the order of the causes changes to reflect the order based on the first cell.
Figure 12.15 One-way Comparative Pareto Plot with Reordered Cells
Two-Way Comparative Pareto Plot Example
This example uses the Failure3.jmp sample data table. The data monitors production samples before and after a furnace cleaning for three days for a capacitor manufacturing process. The data table has a column called date with values OCT 1, OCT 2, and OCT 3.
1. Select Help > Sample Data Library and open Quality Control/Failure3.jmp.
2. Select Analyze > Quality and Process > Pareto Plot.
3. Select failure and click Y, Cause.
4. Select clean and date and click X, Grouping.
5. Select N and click Freq.
6. Click OK.
Figure 12.16 displays the Pareto plot with a two-way layout of plots that show each level of both X variables. The upper left cell is called the key cell. Its bars are arranged in descending order. The bars in the other cells are in the same order as the key cell.
7. Click Contamination and Metallization in the key cell and the bars for the corresponding categories highlight in all other cells.
Figure 12.16 Two-way Comparative Pareto Plot
The Pareto plot shown in Figure 12.16 illustrates highlighting the vital few. In each cell of the two-way comparative plot, the bars representing the two most frequently occurring problems are selected. Contamination and Metallization are the two vital categories in all cells. After furnace cleaning, Contamination is less of a problem.
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