Example of the Control Chart Platform

The following example uses the Coating.jmp sample data table in the Quality Control sample data folder (taken from the ASTM Manual on Presentation of Data and Control Chart Analysis). The quality characteristic of interest is the Weight column. A subgroup sample of four is chosen.

1.	Select Help > Sample Data Library and open Quality Control/Coating.jmp.

2.	Select Analyze > Quality And Process > Control Chart > XBar.

Note the selected chart types of XBar and R.

3.	Select Weight and click Process.

4.	Select Sample and click Sample Label.

Click OK.

Variables Charts for Coating Data

An X-chart and an R-chart for the process are shown in Variables Charts for Coating Data. Sample six indicates that the process is not in statistical control. To check the sample values, click the sample six summary point on either control chart. The corresponding rows highlight in the data table.

Note: If an S chart is chosen with the X-chart, then the limits for the X-chart are based on the standard deviation. Otherwise, the limits for the X-chart are based on the range.

Shewhart Control Chart Types

Shewhart control charts are broadly classified into control charts for variables and control charts for attributes.

Control Charts for Variables

Control charts for variables are classified according to the subgroup summary statistic plotted on the chart:

•	Run charts display data as a connected series of points

•	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

The IR selection gives additional chart types:

•	Individual Measurement charts display individual measurements

•	Moving Range charts display moving ranges of two or more successive measurements

Run Charts

Run charts display a column of data as a connected series of points. Run charts can also plot the group means when the Sample Label role is used, either on the window or through a script.

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.

Moving Range charts displays moving ranges of two or more successive measurements. Moving ranges are computed for the number of consecutive measurements that you enter in the Range Span box. The default range span is 2. Because moving ranges are correlated, these charts should be interpreted with care.

Moving Average Charts

The control charts previously discussed plot each point based on information from a single subgroup sample. The Moving Average chart is different from other types because each point combines information from the current sample and from past samples. As a result, the Moving Average chart is more sensitive to small shifts in the process average. On the other hand, it is more difficult to interpret patterns of points on a Moving Average chart because consecutive moving averages can be highly correlated (Nelson 1982).

In a Moving Average chart, the quantities that are averaged can be individual observations instead of subgroup means. However, a Moving Average chart for individual measurements is not the same as a control (Shewhart) chart for individual measurements or moving ranges with individual measurements plotted.

Uniformly Weighted Moving Average Charts

Each point on a Uniformly Weighted Moving Average (UWMA) chart, also called a Moving Average chart, is the average of the w most recent subgroup means, including the present subgroup mean. When you obtain a new subgroup sample, the next moving average is computed by dropping the oldest of the previous w subgroup means and including the newest subgroup mean. The constant, w, is called the span of the moving average, and indicates how many subgroups to include to form the moving average. The larger the span (w), the smoother the UWMA line, and the less it reflects the magnitude of shifts. This means that larger values of w guard against smaller shifts.

Exponentially Weighted Moving Average Charts

Each point on an Exponentially Weighted Moving Average (EWMA) chart, also referred to as a Geometric Moving Average (GMA) chart, is the weighted average of all the previous subgroup means, including the mean of the present subgroup sample. The weights decrease exponentially going backward in time. The weight (0 < weight ≤ 1) assigned to the present subgroup sample mean is a parameter of the EWMA chart. Small values of weight are used to guard against small shifts.

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 launch window. You can also append a capability analysis by checking the appropriate box in the launch window.

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, 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.

Determining Which Attribute Chart to Use
Each item is judged as either conforming or non-conforming		For each item, the number of defects is counted
Shows the proportion of defective items	Shows the number of defective items	Shows the number of defective items	Shows the average number of defective items
p-chart	np-chart	c-chart	u-chart

For attribute charts, specify the column containing the defect count or defective proportion as the Process variable. The data are interpreted as counts, unless the column contains non-integer values between 0 and 1.

•	p-charts display the proportion of nonconforming (defective) items in subgroup samples, which can vary in size. Since 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.

Note: To use the Sigma column property for P- or NP- charts, the value needs to be equal to the proportion. JMP calculates the sigma as a function of the proportion and the sample sizes.

•	c-charts display the number of nonconformities (defects) in a subgroup sample that usually, but does not necessarily, consists of one inspection unit.

Caution: For a c-chart, if you do not specify a Sample Size or Constant Size, then the Sample Label is used as the sample size.

•	u-charts display the number of nonconformities (defects) per unit in subgroup samples that can have a varying number of inspection units.

Caution: For a u-chart, if you do not specify a Unit Size or Constant Size, then the Sample Label is used as the unit size.

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.