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).

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.

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.

Attribute Chart Determination
		Statistic
		Proportion	Count
Sigma	Binomial	p-chart	np-chart
	Poison	u-chart	c-chart

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.

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.

Rare Event Chart Determination
		Statistic
		Count
Sigma	Negative Binomial	g-chart
	Weibull	t-chart

Control Chart Types Table

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. Control Chart Types summarizes the different control chart types.

Control Chart Types
Chart Types	Control Chart Builder Options
Chart Types	Points > Statistic	Limits > Sigma
Variable Charts without grouping (X) variable or nonsummarized data:
Individual	Individual	Moving Range
Moving Range on Individual	Moving Range	Moving Range
Levey Jennings	Individual	Levey Jennings
Variable Charts with grouping (X) variables or summarized data:
XBar (limits computed on range)	Average	Range
XBar (limits computed on standard deviation)	Average	Standard Deviation
R	Range	Range
S	Standard Deviation	Standard Deviation
Levey Jennings	Individual measurements. Control limits are based on an estimate of long-term sigma.	Levey Jennings or overall Standard Deviation
Presummarize Charts
Individual on Group Means	Average	Moving Range
Individual on Group Std Devs	Standard Deviation	Moving Range
Moving Range on Group Means	Moving Range on Means	Moving Range
Moving Range on Group Std Devs	Moving Range on Std Dev	Moving Range
Attribute Charts
p-chart	Proportion	Binomial
np-chart	Count	Binomial
c-chart	Count	Poisson
u-chart	Proportion	Poisson
Rare Event Charts
g-chart	Count	Negative Binomial
t-chart	Count	Weibull

Run charts, UWMA, EWMA, CUSUM, and Multivariate charts are not available in the Control Chart Builder. Three-way, g- and t-charts are not available in the Control Chart platform. For more information about the Control Chart platform, see Chapter 4, “Shewhart Control Charts”.