Overview of the Control Chart Builder
A control chart is a graphical way to filter out routine variation in a process. Filtering out routine variation helps manufacturers and other businesses determine whether a process is stable and predictable. If the variation is more than routine, the process can be adjusted to create higher quality output at a lower cost.
This version of JMP continues a shift in the approach to control charts. We are moving toward an all-in-one, interactive workspace called the Control Chart Builder. The Control Chart Builder enables you to create several types of control charts (Shewhart Variables, Shewhart Attribute, and Rare Event) and is intended to be an interactive tool for problem solving and process analysis. Shewhart control charts are broadly classified into control charts for variables and control charts for attributes. Rare event charts are useful for events that occur so infrequently that a traditional chart is inappropriate.
To use Control Chart Builder, you do not need to know the name of a particular chart beforehand. When you drag a data column to the workspace, Control Chart Builder creates an appropriate chart based on the data type and sample size. Once the basic chart is created, use the menus and other options to:
• Change the type of chart. You can switch between Attribute, Variables, and Rare Event charts without relaunching the platform.
• Change the statistic on the chart. You can add, remove, and switch variables without relaunching the platform.
• Format the chart and create subgroups that are defined by multiple X variables.
• Add additional charts, including three-in-one charts: subgroup means, within-subgroup variation, and between-subgroup variation.
Example of the Control Chart Builder
This example uses the Socket Thickness.jmp sample data table, which includes measurements for the thickness of sockets. There has been an increase in the number of defects during production and you want to investigate why this is occurring. Use Control Chart Builder to investigate the variability in the data and the control of the process.
1. Select Help > Sample Data Library and open Quality Control/Socket Thickness.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Thickness to the Y zone.
4. Drag Hour to the Subgroup zone (at bottom).
Figure 3.2 Control Charts for Socket Thickness
Looking at the Average chart, you can see that there are several points below the lower control limit of 7.788772. You want to see whether another variable might be contributing to the problem.
5. Drag Cavity into the Phase zone.
Figure 3.3 Control Charts for Each Cavity
From the Average chart, you can conclude the following:
• There are differences between the cavities, each deserving separate control limits.
• Cavity 1 is producing sockets with a higher average thickness, indicating that further investigation of the differences between cavities is warranted.
• All of the cavities have points that are outside the control limits. Therefore, you should investigate the lack of control in the data for each cavity.
The Range chart for each cavity shows that the within-subgroup measurements are in control.
Control Chart Types
The Control Chart Builder (CCB) enables you to create several types of control charts (Shewhart Variables, Shewhart Attribute, and Rare Event). To create a chart, you do not need to know the name or structure of a particular chart beforehand. Select the variables (or columns) that you want to chart, and then drag and drop them into zones. When you drag a data column to the workspace, Control Chart Builder creates an appropriate chart based on the data type and sample size. Once the basic chart is created, you can use the menus and other options to change the type, the statistic, and the format of the chart.
Shewhart Control Charts for Variables
Control charts for variables are classified according to the subgroup summary statistic plotted on the chart.
• X-charts display subgroup means (averages)
• R-charts display subgroup ranges (maximum – minimum)
• S-charts display subgroup standard deviations
• Presummarize charts display subgroup means and standard deviations
• Individual Measurement charts display individual measurements
• Moving Range charts display moving ranges of two successive measurements
XBar-, R-, and S- Charts
For quality characteristics measured on a continuous scale, a typical analysis shows both the process mean and its variability with a mean chart aligned above its corresponding R- or S-chart.
Individual Measurement Charts
Individual Measurement charts displays individual measurements. Individual Measurement charts are appropriate when only one measurement is available for each subgroup sample. If you are charting individual measurements, the individual measurement chart shows above its corresponding moving range chart. Moving Range charts displays moving ranges of two successive measurements.
Presummarize Charts
If your data consist of repeated measurements of the same process unit, you can combine these into one measurement for the unit. Pre-summarizing is not recommended unless the data have repeated measurements on each process or measurement unit.
Presummarize summarizes the process column into sample means and/or standard deviations, based either on the sample size or sample label chosen. Then it charts the summarized data based on the options chosen in the window.
Levey-Jennings Charts
Levey-Jennings charts show a process mean with control limits based on a long-term sigma. The control limits are placed at 3s distance from the center line. The standard deviation, s, for the Levey-Jennings chart is calculated the same way standard deviation is in the Distribution platform.
Shewhart Control Charts for Attributes
In the previous types of charts, measurement data was the process variable. This data is often continuous, and the charts are based on theory for continuous data. Another type of data is count data or level counts of character data, where the variable of interest is a discrete count of the number of defects or blemishes per subgroup. For discrete count data, attribute charts are applicable, as they are based on binomial and Poisson models. Because the counts are measured per subgroup, it is important when comparing charts to determine whether you have a similar number of items in the subgroups between the charts. Attribute charts, like variables charts, are classified according to the subgroup sample statistic plotted on the chart.
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Statistic
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Sigma
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Proportion
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Count
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Binomial
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p-chart
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np-chart
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Poisson
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u-chart
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c-chart
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The CCB makes a few decisions for you based on the variable selected. For example, if there is no X variable, a c-chart is originally created because there is no way to estimate the binomial distributions. Upon adding an X variable (or lot size), the platform switches to a np-chart if the count per subgroup is less than the subgroup sample size. Once the basic chart is created, you can use the menus and other options to change the type, the statistic, and the format of the chart.
• p-charts display the proportion of nonconforming (defective) items in subgroup samples, which can vary in size. Because each subgroup for a p-chart consists of Ni items, and an item is judged as either conforming or nonconforming, the maximum number of nonconforming items in a subgroup is Ni.
• np-charts display the number of nonconforming (defective) items in subgroup samples. Because each subgroup for a np-chart consists of Ni items, and an item is judged as either conforming or nonconforming, the maximum number of nonconforming items in subgroup i is Ni.
• c-charts display the number of nonconformities (defects) in a subgroup sample that usually, but does not necessarily, consists of one inspection unit.
• u-charts display the number of nonconformities (defects) per unit in subgroup samples that can have a varying number of inspection units.
Rare Event Control Charts
A Rare Event chart is a control chart that provides information about a process where the data comes from rarely occurring events. Tracking processes that occur infrequently on a traditional control chart tend to be ineffective. Rare event charts were developed in response to the limitations of control charts in rare event scenarios. The Control Chart Builder provides two types of rare event charts (g- and t-charts).
A g-chart is used to count the number of events between rarely occurring errors or nonconforming incidents, and creates a chart of a process over time. Each point represents the number of units between occurrences of a relatively rare event. For example, in a production setting, where an item is produced daily, an unexpected line shutdown can occur. You can use a g-chart to look at the number of units produced between line shutdowns. A traditional plot of data such as this is not conducive to control chart interpretation. The g-chart helps visualize such data in traditional control chart form.
A t-chart measures the time elapsed since the last event and creates a picture of a process over time. Each point on the chart represents an amount of time that has passed since a prior occurrence of a rare event. A traditional plot of this data might contain many points at zero and an occasional point at one. A t-chart avoids flagging numerous points as out of control. The t-chart helps identify special and common cause variation, so that appropriate improvements can be made.
A t-chart can be used for numeric, nonnegative data, date/time data, and time-between data:
• Numeric, nonnegative data is the number of intervals between events. It can be continuous or integer.
• Date/time data records the date and time of each event. Each data value must be greater than or equal to the preceding value.
• Time-between data (also known as elapsed-time data) represent the elapsed time between event i and event i-1.
Like the g-chart, the t-chart is used to detect changes in the rate at which the adverse event occurs. When reading the t-chart, the points above the upper control limit indicate that the amount of time between events has increased. Thus, the rate of the events has decreased. Points below the lower control limit indicate that the rate of adverse events has increased.
Because of how time is measured for these charts, one fundamental difference is that a point flagged as out of control above the limits is generally considered a desirable effect because it represents a significant increase in the time between events. The difference between a g- and t-chart is the scale used to measure distance between events. The g-chart uses a discrete scale, whereas the t-chart uses a continuous scale.
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Statistic
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Sigma
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Count
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Negative Binomial
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g-chart
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Weibull
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t-chart
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Control Chart Types
The most common control charts are available in the Control Chart Builder and in the Control Chart platform. Use the Control Chart Builder as your first choice to easily and quickly generate charts. JMP automatically chooses the appropriate chart type based on the data. Table 3.3 through Table 3.8 summarize the different control chart types.
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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Individual
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Individual
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Moving Range
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Moving Range on Individual
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Moving Range
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Moving Range
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Levey Jennings
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Individual
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Levey Jennings
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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XBar (limits computed on range)
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Average
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Range
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XBar (limits computed on standard deviation)
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Average
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Standard Deviation
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R
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Range
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Range
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S
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Standard Deviation
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Standard Deviation
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Levey Jennings
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Individual measurements. Control limits are based on an estimate of long-term sigma.
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Levey Jennings or overall Standard Deviation
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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Individual on Group Means
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Average
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Moving Range
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Individual on Group Std Devs
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Standard Deviation
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Moving Range
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Moving Range on Group Means
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Moving Range on Means
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Moving Range
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Moving Range on Group Std Devs
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Moving Range on Std Dev
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Moving Range
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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p-chart
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Proportion
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Binomial
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np-chart
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Count
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Binomial
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c-chart
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Count
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Poisson
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u-chart
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Proportion
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Poisson
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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p-chart
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Proportion
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Binomial
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np-chart
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Count
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Binomial
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c-chart
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Count
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Poisson
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u-chart
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Proportion
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Poisson
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Chart Types
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Control Chart Builder Options
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Points > Statistic
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Limits > Sigma
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g-chart
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Count
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Negative Binomial
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t-chart
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Count
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Weibull
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Launch the Control Chart Builder
Launch the Control Chart Builder by selecting Analyze > Quality and Process > Control Chart Builder.
Figure 3.4 Initial Control Chart Builder Window
To begin creating a control chart, drag variables from the Select Columns box into the zones. If you drop variables in the center, JMP guesses where to put them based on whether the variables are continuous or categorical. The Control Chart Builder contains the following zones:
Y
Assigns the process variable.
Subgroup
Assigns subgroup variables. To define subgroup levels as a combination of multiple columns, add multiple variables to the Subgroup zone. When a subgroup variable is assigned, each point on the control chart corresponds to a summary statistic for all of the points in the subgroup.
Phase
Assigns phase variables. When a Phase variable is assigned, separate control limits are computed for each phase. See also “Add Color to Delineate Phases”
The initial Control Chart Builder window contains the following buttons:
Recall
Populates the window with the last analysis that you performed. The Recall button becomes the Undo button once you perform an action.
Undo
Reverses the last change made to the window.
Start Over
Returns the window to the default condition, removing all data, and clearing all zones.
Done
Hides the buttons and the Select Columns box and removes all drop zone outlines. In this presentation-friendly format, you can copy the graph to other programs. To restore the window to the interactive mode, click Show Control Panel on the Control Chart Builder red triangle menu.
By
Identifies the variable and produces a separate analysis for each value that appears in the column.
Shewhart Variables/Shewhart Attribute/Rare Event
Allows you to select Shewhart Variables, Shewhart Attribute, or Rare Event control chart types. If you select an Attribute chart type, an n Trials box and zone appear on the chart.
n Trials
Assigns a lot size when an attribute control chart is selected. Appears if you select an Attribute chart type.
New Y Chart
Produces a copy of the current chart for every column selected in the Select Columns box. The new charts use the selected columns in the Y role.
Once you drag variables to the chart, other buttons and options appear at the left bottom of the screen that enable you to show, hide or switch items on the chart (See Figure 3.5). Many of these functions (Points, Limits, Warnings) are the same as the functions available when you right-click the chart. For more information, refer to “Options Panel and Right-Click Chart Options”. For information about warnings and rules, see “Tests” and “Westgard Rules”.
3-way Chart
Enables you to produce a three-way chart for variable chart types. The subgroup size must be greater than one. The plotting statistic is based on subgroup averages, within-subgroup variation, or between-subgroup variation. The default set of three includes a presummarized chart of the averages using Moving Range limits, a Moving Range chart and a Range chart.
Event Chooser
Allows the chart to respond in real time to selection changes. There are several standard groups of responses that are recognized and pre-scored (for example, pass/fail, yes/no, Likert Scales, conforming/non-conforming, and defective/non-defective). If you are analyzing results from a survey and want to focus solely on a specific sector of the results for one or more questions, you can make the selection on the screen and the chart rescores and replots the chart immediately. The Event Chooser is available for attribute charts with response columns that have a modeling type of nominal or ordinal. The Event Chooser does not appear for response columns with a modeling type of continuous.
The Control Chart Builder Window
The analysis produces a chart that can be used to determine whether a process is in a state of statistical control. The report varies depending on which type of chart you select. Control charts update dynamically as data is added or changed in the data table. Figure 3.5 displays the Control Chart Builder window for the Bottle Tops.jmp sample data table.
To create the chart:
1. Select Help > Sample Data Library and open Quality Control/Bottle Tops.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Status to the Y zone.
4. Drag Sample to the Subgroup zone.
Figure 3.5 Control Chart Builder Window
You can drag other variables into the various zones to augment the analysis and use the “Control Chart Builder Options” to further examine the data. Some of the right-click chart options (for example, show or hide points, limits, warnings, and zones; select statistic and sigma options) also appear on the left hand side of the chart for easy access.
Control charts have the following characteristics:
• Each point plotted on the chart represents an individual process measurement or summary statistic. Subgroups should be chosen rationally, that is, they should be chosen to maximize the probability of seeing a true process signal between subgroups.
• The vertical axis of a control chart is scaled in the same units as the summary statistic.
• The horizontal axis of a control chart identifies the subgroup samples and is time ordered. Observing the process over time is important in assessing if the process is changing.
The green line is the center line, or the average of the data. The center line indicates the average (expected) value of the summary statistic when the process is in statistical control. Measurements should appear equally on both sides of the center line. If not, this is possible evidence that the process average is changing.
• The two red lines are the upper and lower control limits, labeled UCL and LCL. These limits give the range of variation to be expected in the summary statistic when the process is in statistical control. If the process is exhibiting only routine variation, then all the points should fall randomly in that range.
• A point outside the control limits signals the presence of a special cause of variation.
Options in the Control Chart Builder window create control charts that can be updated dynamically as samples are received and recorded or added to the data table. When a control chart signals abnormal variation, action should be taken to return the process to a state of statistical control if the process degraded. If the abnormal variation indicates an improvement in the process, the causes of the variation should be studied and implemented.
When you double-click the axes, the appropriate Axis Specification window appears for you to specify the format, axis values, number of ticks, gridline, reference lines, and other options to display.
Control Chart Builder Options
Control Chart Builder options appear in the red triangle menu or by right-clicking on a chart or axis. Some of the right-click chart options also appear on the bottom left hand side of the chart for easy access. You can also set preferences for many of the options in the Control Chart Builder at File > Preferences > Platforms > Control Chart Builder.
Red Triangle Menu Options
Show Control Panel
shows or hides the following elements:
‒ buttons
‒ the Select Columns box
‒ the drop zone borders
Show Limit Summaries
Shows or hides the Limit Summaries report. This report shows the control limits (LCL and UCL), the center line (Avg), the Points and Limits plotted, and the Sample Size for the chart. Sample size is not shown for rare event charts.
Show Capability
(Available only for Variable plots that have a column with a Spec Limits column property.) Shows or hides the Process Capability Analysis report. For more information about the Process Capability Analysis report, see “The Process Capability Report”.
Get Limits
Retrieves the control limits that are stored in a data table.
Set Sample Size
Sets a subgroup size. Missing values are taken into account when computing limits and sigma.
Save Limits
Saves the control limits as a column property in the existing data table for the response variable. The option does not work with phase variables.
Save Summaries
Creates a new data table containing such information as the sample label, sample sizes, statistic being plotted, center line, control limits, and any tests, warnings and failures. The specific statistics included in the table depend on the type of chart.
Include Missing Categories
Enables the graph to collect rows with missing values in a categorical column, and displays the missing values on the graph as a separate category. If this option is disabled, all rows with a missing X value are removed from the calculations, in addition to being hidden from the graph.
This option is not available for continuous X variables or categorical Y variables because there is no compelling way to display the collected missing values on the relevant axes. By default, this option is enabled.
Note: If Include Missing Categories is enabled, capability analysis results in Control Chart Builder do not match those in the Process Capability platform if a categorical X variable has missing values.
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.
Note: Column Switcher is available only for a single Y variable having two or fewer associated charts. Based on the selected chart type, only columns that are appropriate for the Y role are included in the Column Switcher column list.
Note: In Control Chart Builder, the Automatic Recalc option is turned on by default and cannot be turned off.
Options Panel and Right-Click Chart Options
The following options appear on the left hand side of the chart for easy access and when you right-click a chart.
Points
Provides the following options:
‒ Statistic changes the statistic plotted on the chart. See “Statistic”.
‒ Individual Points show or hides individual observations in a subgroup. Available only with a subgroup variable or Set Sample Size. This option is not available for Attribute chart types or Rare Event charts.
‒ Show Connect Line shows connecting lines between the points.
‒ Show Points shows or hides the points on the chart.
Limits
Provides the following options:
‒ Sigma specifies the method of computing sigma. See “Sigma”.
‒ Zones shows or hides the zones on the chart. The zones are defined as one, two, and three sigmas on either side of the mean. Control Chart Builder does not extend the size of one zone over another. If the limits are not centered around the mean, (UCL-Avg)/3 is used as the width of each zone. Zones are not drawn below the LCL or above the UCL. Available only for Variables and Attribute chart types.
‒ Spec Limits shows or hides the specification limits on the chart. Appears only if the data table has a Spec Limits column property. The Column Info Window chapter in the Using JMP book includes details about adding this column property.
‒ Set Control Limits enables you to enter control limits for tests. After you click OK in the Set Control Limits window, the specified control limits are set uniformly across groups. Select this option again to remove the specified control limits.
‒ Add Limits specifies additional control limits to be plotted on the chart. These limits are not used in tests.
‒ Show Limits hides or shows the control limits on the chart.
‒ Show Center Line hides or shows the center line on the chart.
Add Dispersion Chart
Adds a dispersion chart to the chart area. Change the chart type with the Points options. A dispersion chart illustrates the variation in the data by plotting one of many forms of dispersion, including the range, standard deviation, or moving range. Available only for Variables chart types.
Set Sample Size
Sets a subgroup size. Missing values are taken into account when computing limits and sigma.
Warnings
Provides the following options:
‒ Customize Tests lets you design custom tests and select or deselect multiple tests at once. After the option is selected, the Customize Tests window appears for designing the tests. Select a test description, and enter the desired number (n) and label. You can save the settings to preferences and also restore the default settings. Available only for Variables and Attribute chart types.
‒ Tests let you select which statistical control tests to enable. For more information about tests, see “Tests”. Available only for Variables and Attribute chart types.
Note: Move your cursor over a flagged point on the chart to see a description of the test that failed.
‒ Westgard Rules lets you select which Westgard statistical control tests to enable. Because Westgard rules are based on sigma and not the zones, they can be computed without regard to constant sample size. For more information about tests, see “Westgard Rules”. Available only for Variables and Attribute chart types.
‒ Test Beyond Limits enables the test for any points beyond the control limits. These points are identified on the chart. This test works on all charts with limits, regardless of the sample size being equal.
Remove Graph
Removes the control chart. Available on the second and subsequent control charts in an analysis that has multiple Y charts.
Note: For a description of the Rows, Graph, Customize, and Edit menus, see the Using JMP book.
Statistic
You can change the statistic represented by the points on the chart. The options available depend on the chart type selected.
For Variables chart types, you can change the statistic represented by the points on the chart using the following options:
Individual
Creates a chart where each point represents an individual value in the data table.
Average
Creates a chart where each point represents the average of the values in a subgroup.
Range
Creates a chart where each point represents the range of the values in a subgroup.
Standard Deviation
Creates a chart where each point represents the standard deviation of the values in a subgroup.
Moving Range on Means
Computes the difference in the range between two consecutive subgroup means.
Moving Range on Std Dev
Computes the difference in the range between two consecutive subgroup standard deviations.
Moving Range
Creates a chart where each point is the difference between two consecutive observations.
Note: The Average, Range, Standard Deviation, Moving Range on Means, and Moving Range on Std Dev methods appear only if a subgroup variable with a sample size greater than one is specified or a sample size is set.
For Attribute chart types, you can change the statistic represented by the points on the chart using the following options:
Proportion
Creates a chart where each point represents the proportion of items in subgroup samples.
Count
Creates a chart where each point represents the number of items in subgroup samples.
For Rare Event chart types, the statistic represented by the points on the chart uses the following option:
Count
Creates a chart where each point represents the number of items in subgroup samples.
Sigma
You can change the method for computing sigma for the chart. The options available depend on the chart type selected.
For Variables chart types, you can use the following options:
Range
Uses the range of the data in a subgroup to estimate sigma.
Standard Deviation
Uses the standard deviation of the data in a subgroup to estimate sigma.
Moving Range
Uses the moving ranges to estimate sigma. The moving range is the difference between two consecutive points.
Levey-Jennings
Uses the standard deviation of all the observations to estimate sigma.
For Attribute chart types, you can use the following options:
Binomial
Uses the binomial distribution model to estimate sigma. The model indicates the number of successes in a sequence of experiments, each of which yields success with some probability. Selecting Binomial yields either a p- or np-chart.
Poisson
Uses the Poisson distribution model to estimate sigma. The model indicates the number of events and the time at which these events occur in a given time interval. Selecting Poisson yields either a c- or u-chart.
For Rare Event chart types, you can use the following options:
Negative Binomial
Uses the negative binomial distribution model to estimate sigma. The model indicates the number of successes in a sequence of trials before a specified number of failures occur. Selecting Negative Binomial yields a g-chart.
Weibull
Uses the Weibull distribution model to estimate sigma. The model indicates the mean time between failures. Selecting Weibull yields a t-chart.
Tests
The Warnings option in the right-click menu or on the left hand side of the window displays a submenu for Tests selection. You can select one or more tests for special causes (Western Electric rules) from the menu. Nelson (1984) developed the numbering notation used to identify special tests on control charts. The tests work with both equal and unequal sample sizes.
If a selected test is positive for a particular sample, that point is labeled with the test number. When you select several tests for display and more than one test signals at a particular point, the label of the numerically lowest test specified appears beside the point. You can move your cursor over a flagged point on the chart to see a description of the test that failed.
Tip: To add or remove several tests at once, select or deselect the tests in the Control Panel under Warnings > Tests.
Table 3.9 lists and interprets the eight tests, and Figure 3.7 illustrates the tests. The following rules apply to each test:
• The area between the upper and lower limits is divided into six zones, each with a width of one standard deviation.
• The zones are labeled A, B, C, C, B, A with zones C nearest the center line.
• A point lies in Zone B or beyond if it lies beyond the line separating zones C and B. That is, if it is more than one standard deviation from the center line.
• Any point lying on a line separating two zones lines is considered belonging to the innermost zone. So, if a point lies on the line between Zone A and Zone B, the point is considered to be in Zone B.
Tests 1 through 8 apply to all Shewhart chart types.
Tests 1, 2, 5, and 6 apply to the upper and lower halves of the chart separately. Tests 3, 4, 7, and 8 apply to the whole chart.
See Nelson (1984, 1985) for further recommendations on how to use these tests.
Figure 3.6 Zones for Western Electric Rules
1 Nelson (1984, 1985)
Figure 3.7 Illustration of Special Causes Tests1
Westgard Rules
Westgard rules are implemented under the Westgard Rules submenu of the Warnings option when you right-click on a chart or on the left hand side of the window. The different tests are abbreviated with the decision rule for the particular test. For example, 1 2s refers to a test where one point is two standard deviations away from the mean.
Rule 1 2S is commonly used with Levey-Jennings charts, where control limits are set 2 standard deviations away from the mean. The rule is triggered when any one point goes beyond these limits.
Rule 1 3S refers to a rule common to Levey-Jennings charts where the control limits are set 3 standard deviations away from the mean. The rule is triggered when any one point goes beyond these limits.
Rule 2 2S is triggered when two consecutive control measurements are farther than two standard deviations from the mean.
Rule R 4S is triggered when one measurement is greater than two standard deviations from the mean and the previous measurement is greater than two standard deviations from the mean in the opposite direction such that the difference is greater than 4 standard deviations.
Rule 4 1S is triggered when four consecutive measurements are more than one standard deviation from the mean.
Rule 10 X is triggered when ten consecutive points are on one side of the mean.
Right-Click Axis Options
Remove
Removes a variable.
For details about the Axis Settings, Revert Axis, Add or Remove Axis Label, and Edit options, see the JMP Reports chapter in the Using JMP book.
Retrieving Limits from a Data Table
JMP can use previously established control limits for control charts:
• Upper and lower control limits, and a center line value.
• Parameters for computing limits such as a mean and standard deviation.
The control limits or limit parameter values can be either in a JMP data table, referred to as the Limits Table, or stored as a column property in the process column. You can retrieve the Limits Table with the Get Limits option on the Control Chart Builder red triangle menu.
All Limits Tables must have:
• A column of special keywords that identify each row.
• A column for each of the variables whose values are the known standard parameters or limits. This column name must be the same as the corresponding process variable name in the data table to be analyzed by the Control Chart Builder.
The Control Chart Builder identifies the appropriate limits from keywords in the _LimitsKey column. A list of limit keywords and their associated control chart is shown in Table 3.10.
Note the following:
• Rows with unknown keywords and rows marked with the excluded row state are ignored.
• Except for _Sample Size, any needed values not specified are estimated from the data.
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Keywords
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For Charts
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Meaning
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_KSigma
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All except Control Chart Builder
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multiples of the standard deviation of the statistics to calculate the control limits; set to missing if the limits are in terms of the alpha level
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_Alpha
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All except Control Chart Builder
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Type I error probability used to calculate the control limits; used if multiple of the standard deviation is not specified in the CCB window or in the Limits Table
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_Std Dev
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X-, R-, S-, IM, MR
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known process standard deviation
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_U
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c-, u-
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known average number of nonconformities per unit
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_P
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np-, p-
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known value of average proportion nonconforming
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_LCL, _UCL
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X-, IM, p-, np-, c-, u-, g-, t-
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lower and upper control limit for Mean Chart, Individual Measurement chart, or any attribute or rare event chart
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_AvgR
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R-, MR
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average range or average moving range
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_LCLR, _UCLR
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R-, MR
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lower control limit for R- or MR chart
upper control limit for R- or MR chart
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_AvgS, _LCLS, _UCLS
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S-Chart
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average standard deviation, upper and lower control limits for S-chart
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_AvgR_PreMeans
_AvgR_PreStdDev
_LCLR_PreMeans
_LCLR_PreStdDev
_UCLR_PreMeans
_UCLR_PreStdDev
_Avg_PreMeans
_Avg_PreStdDev
_LCL_PreMeans
_LCL_PreStdDev
_UCL_PreMeans
_UCL_PreStdDev
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IM, MR
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Mean, upper, and lower control limits based on pre-summarized group means or standard deviations.
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In the Control Chart Builder red triangle menu, you can save limits as a data table column property. To save limits as a new data table, use the Control Chart platform. See “Saving and Retrieving Limits” for details.
Excluded and Hidden Samples
The following bullets summarize the effects of various conditions on samples and subgroups:
• Excluded subgroups are not used in the calculations, but appear in the chart (although dimmed).
• Hidden observations are used in the calculations, but do not appear in the chart.
• Both hidden and excluded rows are included in the count of points for Tests for Special Causes. An excluded row can be labeled with a special cause flag. A hidden point cannot be labeled. If the flag for a Tests for Special Causes is on a hidden point, it will not appear in the chart.
• For partially excluded subgroups, if one or more observations within a subgroup is excluded, and at least one observation within the subgroup is included, the excluded observation is not included in the calculations of either the point statistic or the limits.
• Checks for negative and non-integer data happen on the entire data (even excluded values).
• Tests continue to apply to all excluded subgroups. Excluded samples are flagged when tests are turned on.
Additional Examples of the Control Chart Builder
The following are additional examples of the Control Chart Builder. Some examples show the Control Panel while others do not. To show or hide the Control Panel, select Show Control Panel from the red triangle menu.
X and R Chart Phase Example
A manufacturer of medical tubing collected tube diameter data for a new prototype. The data was collected over the past 40 days of production. After the first 20 days (phase 1), some adjustments were made to the manufacturing equipment. Analyze the data to determine whether the past 20 days (phase 2) of production are in a state of control.
1. Select Help > Sample Data Library and open Quality Control/Diameter.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag DIAMETER to the Y role.
4. Drag DAY to the Subgroup role.
Figure 3.8 Control Charts for Diameter
The first 20 days appear to have high variability, and in the Average chart, there are three observations that are outside of the control limits. An adjustment was made to the manufacturing equipment and new control limits were incorporated.
To compute separate control limits for each phase:
5. Drag Phase to the Phase role.
6. In the Average chart, right-click and select Warnings > Test Beyond Limits.
Figure 3.9 Control Charts for each Phase
Including the Phase variable means that the control limits for phase 2 are based only on the data for phase 2. None of the phase 2 observations are outside the control limits. Therefore, you can conclude that the process is in control after the adjustments were made.
Add Color to Delineate Phases
If you have distinct phases in your control chart, you can illustrate them by adding different background colors to the different phases.
1. Starting from Figure 3.9, double-click in the X axis.
The Axis Settings window appears. In the Reference Lines panel, notice that there is an existing line reference value at 19.5. This value is the midpoint of the range for DAY and also happens to be the dividing value between the two phases.
2. Select Allow Ranges.
3. Enter -0.5 for the Min Value (the scale minimum).
4. Enter 19.5 for the Max Value (the dividing line).
5. Choose a color, say yellow. Change the opacity to 40%.
6. Click Add.
7. Click Allow Ranges.
8. Enter 19.5 for the Min Value (the dividing line).
9. Enter 39.5 for the Max Value (the maximum of the axis).
10. Choose a color, say light blue. Change the opacity to 40%.
11. Click Add.
You can see from the preview how the chart will look.
12. Click OK.
Figure 3.10 Diameter Phases with Color
p-chart Example
The Washers.jmp sample data contains defect data for two different lot sizes from the ASTM Manual on Presentation of Data and Control Chart Analysis, American Society for Testing and Materials. To view the differences between constant and variable sample sizes, you can compare charts for Lot Size and Lot Size 2.
1. Select Help > Sample Data Library and open Quality Control/Washers.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag # defective to the Y role.
An Individual & Moving Range chart appears.
4. Select Shewhart Attribute from the drop down to change the chart to an attribute chart.
A c-chart appears.
5. Change the Sigma to Binomial to change the chart to a np-chart.
6. Change the Statistic from Count to Proportion to change the chart to a p-chart.
Figure 3.11 p-chart of # defective
7. Drag Lot Size to the nTrials role.
Figure 3.12 p-chart of # defective with sample size
To view the differences between constant and variable sample sizes, you can compare charts for Lot Size and Lot Size 2 by simply dragging the variables to the nTrials zone.
np-chart Example
The Bottle Tops.jmp sample data contains simulated data from a bottle top manufacturing process. Sample is the sample ID number for each bottle. Status indicates whether the bottle top conformed to the design standards. In the Phase column, the first phase represents the time before the process adjustment. The second phase represents the time after the process adjustment. Notes on changes in the process are also included.
1. Select Help > Sample Data Library and open Quality Control/Bottle Tops.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Sample to the Subgroup role.
4. Drag Status to the Y role.
Figure 3.13 np-chart of Status (Nonconforming)
The original observations appear to have high variability and there are five observations (Samples 13, 15, 21, 22 and 23) that are outside of the upper control limit. Samples 15 and 23 note that new material and a new operator were introduced into the process, respectively. At the end of the phase, an adjustment was made to the manufacturing equipment. Therefore, the control limits for the entire series should not be used to assess the control during phase 2.
To compute separate control limits for each phase:
5. Drag Phase to the Phase zone.
Figure 3.14 np-chart by Phase
Including the Phase variable means that the control limits for phase 2 are based only on the data for phase 2. None of the phase 2 observations are outside the control limits. Therefore, you can conclude that the process is in control after the adjustment.
c-chart Example
The Cabinet Defects.jmp sample data table contains data concerning the various defects discovered while manufacturing cabinets over two time periods.
1. Select Help > Sample Data Library and open Quality Control/Cabinet Defects.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Type of Defect to the Y role.
4. Drag Lot Number to the Subgroup role.
A np-chart of Type of Defect appears.
5. To change to a c-chart, select Poisson from the Sigma list.
6. Open the Type of Defect disclosure button. Note all of the defect types are listed. Currently, only Bruised veneer is selected and displayed in the chart. You can select additional defect types and the chart updates immediately.
Figure 3.15 c-chart of Type of Defect
7. To add to phase variable, drag Date to the Phase zone.
Figure 3.16 c-chart of Type of Defect with Phases
You can now view the results on the two different days. Both appear to be within limits. To examine other defect type behavior, select another defect type under the Event Chooser and view the results as the limits are updated.
u-chart Example
The Shirts.jmp sample data table contains data concerning the number of defects found in a number of boxes of shirts.
1. Select Help > Sample Data Library and open Quality Control/Shirts.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag # Defects to the Y role.
4. Drag Box to the Subgroup role.
An Individual & Moving Range chart for # defects appears.
5. To change the chart to an Attribute chart, select Shewhart Attribute from the drop down list.
A c-chart of # Defects appears.
6. Change the Statistic from Count to Proportion to change the chart to a u-chart.
Figure 3.17 u-chart of # Defects
All of the points are within the control limits.
g-chart Example
Rare event charts are helpful when you know your data will not follow a normal distribution (for example, when measuring counts or wait times). The g-chart is an effective way to understand whether rare events are occurring more frequently than expected and warrant an intervention. A g-chart counts the number of possible opportunities since the last event. If you plot this type of data using a standard Shewhart control chart, you might see many more false signals, as the limits might be too narrow. The Adverse Reactions.jmp sample data table contains simulated data about adverse drug events (ADEs) reported by a group of hospital patients. An ADE is any type of injury or reaction the patient suffered after taking the drug. The date of the reaction and the number of days since the last reaction were recorded.
1. Select Help > Sample Data Library and open Quality Control/Adverse Reactions.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Doses since Last ADE to the Y role.
4. Drag Date of ADE to the Subgroup role.
An Individual & Moving Range chart of Doses since Last ADE appears.
5. To change the chart to a Rare Event chart, select Rare Event from the drop down list.
A g-chart of Doses since Last ADE appears showing the number of doses given since the last event.
Figure 3.18 g-chart of Doses since Last ADE
t-chart Example
Rare event charts are helpful when you know your data will not follow a normal distribution (for example, when measuring counts or wait times). t-charts are used to measure the time that has elapsed since the last event. If you plot this type of data using a standard Shewhart control chart, you might see many more false signals, as the limits might be too narrow. The Fan Burnout.jmp sample data table contains simulated data for a fan manufacturing process. The first column identifies each fan that burned out. The second column identifies the number of hours between each burnout.
1. Select Help > Sample Data Library and open Quality Control/Fan Burnout.jmp.
2. Select Analyze > Quality and Process > Control Chart Builder.
3. Drag Hours between Burnouts to the Y role.
4. Drag Burnout to the Subgroup role.
Figure 3.19 Individual and Moving Range Chart of Hours Between Burnouts
5. To change the chart to a Rare Event chart, select Rare Event from the drop down list.
A g-chart of Hours between Burnouts appears. All points appear to be within the control limits.
6. Change the Sigma from Negative Binomial to Weibull to change the chart to a t-chart.
Figure 3.20 t-chart of Hours Between Burnouts
In the t-chart, all points appear to be within the control limits. It’s clear that the Individual & Moving Range chart was inappropriate for the analysis, as the limits were too narrow.
Statistical Details for the Control Chart Builder Platform
This section contains statistical details for specific types of supported charts in the Control Chart Builder platform.
Control Limits for X- and R-charts
JMP generates control limits for X- and R-charts as:
LCL for X chart =
UCL for X chart =
LCL for R-chart =
UCL for R-chart =
Center line for R-chart: By default, the center line for the ith subgroup (where 3 is the sigma multiplier) indicates an estimate of the expected value of Ri. This value is computed as: 
, where 
is an estimate of σ.
, where is an estimate of σ.The standard deviation of an X/R chart is estimated by:
where:
= weighted average of subgroup meansσ = process standard deviation
ni = sample size of ith subgroup
d2(n) is the expected value of the range of n independent normally distributed variables with unit standard deviation
d3(n) is the standard error of the range of n independent observations from a normal population with unit standard deviation
Ri is the range of ith subgroup
N is the number of subgroups for which
Control Limits for X- and S-charts
JMP generates control limits for X- and S-charts as:
LCL for X chart =
UCL for X chart =
LCL for S-chart =
UCL for S-chart =
Center line for S-chart: By default, the center line for the ith subgroup (where 3 is the sigma multiplier) indicates an estimate of the expected value of si. This value is computed as 
, where 
is an estimate of σ.
, where is an estimate of σ.The estimate for the standard deviation in an 
/S chart is:
/S chart is:
where:
= weighted average of subgroup meansσ = process standard deviation
ni = sample size of ith subgroup
c4(n) is the expected value of the standard deviation of n independent normally distributed variables with unit standard deviation
c5(n) is the standard error of the standard deviation of n independent observations from a normal population with unit standard deviation
N is the number of subgroups for which
si is the sample standard deviation of the ith subgroup
Control Limits for Individual Measurement and Moving Range Charts
LCL for Individual Measurement Chart =
UCL for Individual Measurement Chart =
LCL for Moving Range Chart =
UCL for Moving Range Chart =
The standard deviation for Individual Measurement and Moving Range charts is estimated by:
where:
X = the mean of the individual measurements
MR = the mean of the nonmissing moving ranges computed as (MR2+MR3+...+MRN)/(N-1) where MRi = |xi - xi-1|.
σ = the process standard deviation
d2(2) = expected value of the range of two independent normally distributed variables with unit standard deviation.
d3(2) = standard error of the range of two independent observations from a normal population with unit standard deviation.
Control Limits for p- and np-charts
The lower and upper control limits, LCL, and UCL, respectively, are computed as:
p-chart LCL =
p-chart UCL =
np-chart LCL =
np-chart UCL =
where:
p is the average proportion of nonconforming items taken across subgroups
ni is the number of items in the ith subgroup
3 is the number of standard deviations
Control Limits for u-charts
The lower and upper control limits, LCL, and UCL, are computed as:
LCL =
UCL =
The limits vary with ni.
u is the expected number of nonconformities per unit produced by process
ui is the number of nonconformities per unit in the ith subgroup. In general, ui = ci/ni.
ci is the total number of nonconformities in the ith subgroup
ni is the number of inspection units in the ith subgroup
u is the average number of nonconformities per unit taken across subgroups. The quantity u is computed as a weighted average
N is the number of subgroups
Control Limits for c-charts
The lower and upper control limits, LCL, and UCL, are computed as:
LCL =
UCL =
The limits vary with ni.
u is the expected number of nonconformities per unit produced by process
ui is the number of nonconformities per unit in the ith subgroup. In general, ui = ci/ni.
ci is the total number of nonconformities in the ith subgroup
ni is the number of inspection units in the ith subgroup
u is the average number of nonconformities per unit taken across subgroups. The quantity u is computed as a weighted average
N is the number of subgroups
Levey-Jennings Charts
Levey-Jennings charts show a process mean with control limits based on a long-term sigma. The control limits are placed at 3s distance from the center line.
The standard deviation, s, for the Levey-Jennings chart is calculated the same way standard deviation is in the Distribution platform.
Control Limits for g-charts
The negative binomial distribution is an extension of the geometric (Poisson) distribution and allows for over-dispersion relative to the Poisson. The negative binomial distribution can be used to construct both exact and approximate control limits for count data. Approximate control limits can be obtained based on a chi-square approximation to the negative binomial. All data is used as individual observations regardless of subgroup size.
Let X have a negative binomial distribution with parameters (u, 3). Then:
P(X ≤ r) ~ P(X2v < 
)
)where:
is a chi-square variate with v = 2u/(1+3u) degrees of freedom.Based on this approximation, approximate upper and lower control limits can be determined. For a nominal level α Type 1 error probability in one direction, an approximate upper control limit is a limit UCL such that:
P(X > UCL) = 1 - P(X2v < 
) = α
) = αLikewise, an approximate lower control limit, LCL, is a limit such that:
P(X < LCL) = 1 - P(X2v > 
) = α
) = αThus, an approximate level lower and upper control limits, LCL and UCL, respectively, are computed as:
UCL =
LCL =
where:
is the upper (lower) percentile of the chi-square distribution with v = 2u/(1+3u) degrees of freedom. Negative lower control limits can be set to zero.Control Limits for t-charts
If there are no 0’s in the data, the estimates of the shape and scale parameters are calculated from the data and used to obtain the percentiles of the Weibull distribution.
To estimate limits from the data:
If
p1 = normalDist(-3) for Normal (0,1)
p2 = normalDist(0) for Normal (0,1)
p3 = normalDist(3) for Normal (0,1)
Then
CL = Weibull Quantile (p2, β) * α
UCL = Weibull Quantile (p1, β) * α
LCL = Weibull Quantile (p3, β) * α
where:
β is the shape parameter and α is the scale parameter for the Weibull Quantile function. For more information about the Weibull Quantile function, see Help > Scripting Index.
1 Nelson (1984, 1985)
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