Quality and Process Methods • Shewhart Control Charts • Additional Examples of the Control Chart Platform
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Additional Examples of the Control Chart Platform
This section contains additional examples using the Control Chart platform.
Run Chart Example
Run charts display a column of data as a connected series of points. The following example is a Run chart for the Weight variable from Coating.jmp in the Quality Control sample data folder (taken from the ASTM Manual on Presentation of Data and Control Chart Analysis).
1.
Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2.
Select Analyze > Quality and Process > Control Chart > Run Chart.
3.
Select Weight and click Process.
4.
Select Sample and click Sample Label.
5.
Click OK.
Run Chart
X- and R-charts Example
The following example uses the Coating.jmp data table. The quality characteristic of interest is the Weight column. A subgroup sample of four is chosen. An X-chart and an R-chart for the process are shown in Variables Charts for Coating Data.
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.
5.
Click OK.
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.
Variables Charts for Coating Data
You can use Fit Y by X for an alternative visualization of the data. First, change the modeling type of Sample to Nominal. Specify the interval variable Weight as Y, Response and the nominal variable Sample as X, Factor. Select the Quantiles option from the Oneway Analysis drop-down menu. The box plots in Quantiles Option in Fit Y By X Platform show that the sixth sample has a small range of high values.
Quantiles Option in Fit Y By X Platform
X- and S-charts with Varying Subgroup Sizes Example
The following example uses the Coating.jmp data table. This quality characteristic of interest is the Weight 2 column. An X-chart and an S chart for the process are shown in X and S Charts for Varying Subgroup Sizes.
1.
Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2.
Select Analyze > Quality and Process > Control Chart > XBar.
3.
Select the chart types of XBar and S.
4.
Select Weight 2 and click Process.
5.
Select Sample and click Sample Label.
The Sample Size option should automatically change to Sample Grouped by Sample Label.
6.
Click OK.
X and S Charts for Varying Subgroup Sizes
Weight 2 has several missing values in the data, so you might notice the chart has uneven limits. Although, each sample has the same number of observations, samples 1, 3, 5, and 7 each have a missing value.
Note: When sample sizes are unequal, the Test options are grayed out. If the samples change while the chart is open and they become equally sized, and the zone and/or test option is selected, the zones and/or tests will be applied immediately and appear on the chart.
Individual Measurement and Moving Range Charts Example
The Pickles.jmp data in the Quality Control sample data folder contains the acid content for vats of pickles. Because the pickles are sensitive to acidity and produced in large vats, high acidity ruins an entire pickle vat. The acidity in four vats is measured each day at 1, 2, and 3 PM. The data table records day, time, and acidity measurements. You can create Individual Measurement and Moving Range charts with date labels on the horizontal axis.
1.
Select Help > Sample Data Library and open Quality Control/Pickles.jmp.
2.
Select Analyze > Quality and Process > Control Chart > IR.
3.
Select both Individual Measurement and Moving Range chart types.
4.
Select Acid and click Process.
5.
Select Date and click Sample Label.
6.
Click OK.
The individual measurement and moving range charts shown in Individual Measurement and Moving Range Charts for Pickles Data monitor the acidity in each vat produced.
Note: A Median Moving Range chart can also be evaluated. If you choose a Median Moving Range chart and an Individual Measurement chart, the limits on the Individual Measurement chart use the Median Moving Range as the sigma, rather than the Average Moving Range.
Individual Measurement and Moving Range Charts for Pickles Data
p-chart Example
The Washers.jmp data in the Quality Control sample data folder contains defect counts of 15 lots of 400 galvanized washers. The washers were inspected for finish defects such as rough galvanization and exposed steel. If a washer contained a finish defect, it was deemed nonconforming or defective. Thus, the defect count represents how many washers were defective for each lot of size 400. Using the Washers.jmp data table, specify a sample size variable, which would allow for varying sample sizes. This data contains all constant sample sizes.
1.
Select Help > Sample Data Library and open Quality Control/Washers.jmp.
2.
Select Analyze > Quality and Process > Control Chart > P.
3.
Select # defective and click Process.
4.
Select Lot and click Sample Label.
5.
Select Lot Size and click Sample Size.
6.
Click OK.
p-chart displays a p-chart for the proportion of defects.
p-chart
Note that although the points on the chart look the same as the np-chart in np-chart, the y axis, Avg and limits are all different since they are now based on proportions.
np-chart Example
The following example uses the Washers.jmp data table.
•
Select Help > Sample Data Library and open Quality Control/Washers.jmp.
•
Select Analyze > Quality and Process > Control Chart > NP.
•
Select # defective and click Process.
•
Change the Constant Size to 400.
•
Click OK.
np-chart displays an np-chart for the number of defects. Points 4 and 9 are above the upper control limit.
np-chart
c-chart Example
c-charts are similar to U-charts in that they monitor the number of nonconformities in an entire subgroup, made up of one or more units. c-charts can also be used to monitor the average number of defects per inspection unit.
Note: When you generate a c-chart, and select Capability, JMP launches the Poisson Fit in Distribution and gives a Poisson-specific capability analysis.
In this example, a clothing manufacturer ships shirts in boxes of ten. Prior to shipment, each shirt is inspected for flaws. Because the manufacturer is interested in the average number of flaws per shirt, the number of flaws found in each box is divided by ten and then recorded.
1.
Select Help > Sample Data Library and open Quality Control/Shirts.jmp.
2.
Select Analyze > Quality and Process > Control Chart > C.
3.
Select # Defects and click Process.
4.
Select Box and click Sample Label.
5.
Select Box Size and click Sample Size.
6.
Click OK.
c-chart
u-chart Example
The Braces.jmp data in the Quality Control sample data folder records the defect count in boxes of automobile support braces. A box of braces is one inspection unit. The number of boxes inspected (per day) is the subgroup sample size, which can vary. The u-chart in u-chart is monitoring the number of brace defects per subgroup sample size. The upper and lower bounds vary according to the number of units inspected.
Note: When you generate a u-chart, and select Capability, JMP launches the Poisson Fit in Distribution and gives a Poisson-specific capability analysis. To use the Capability feature, the unit sizes must be equal.
1.
Select Help > Sample Data Library and open Quality Control/Braces.jmp.
2.
Select Analyze > Quality and Process > Control Chart > U.
3.
Select # defects and click Process.
4.
Select Date and click Sample Label.
5.
Select Unit size and click Unit Size.
6.
Click OK.
u-chart
UWMA Chart Example
In sample data table, Clips1.jmp, the measure of interest is the gap between the ends of manufactured metal clips. To monitor the process for a change in average gap, subgroup samples of five clips are selected daily. A UWMA chart with a moving average span of three is examined.
1.
Select Help > Sample Data Library and open Quality Control/Clips1.jmp.
1.
Select Analyze > Quality and Process > Control Chart > UWMA.
2.
Select Gap and click Process.
3.
Select Sample and click Sample Label.
4.
Change the Moving Average Span to 3.
5.
Click OK.
The result is the chart in UWMA Charts for the Clips1 data. The point for the first day is the mean of the five subgroup sample values for that day. The plotted point for the second day is the average of subgroup sample means for the first and second days. The points for the remaining days are the average of subsample means for each day and the two previous days.
The average clip gap appears to be decreasing, but no sample point falls outside the 3σ limits.
UWMA Charts for the Clips1 data
EWMA Chart Example
The following example uses the Clips1.jmp data table.
1.
Select Help > Sample Data Library and open Quality Control/Clips1.jmp.
2.
Select Analyze > Quality and Process > Control Chart > EWMA.
3.
Select Gap and click Process.
4.
Select Sample and click Sample Label.
5.
Change the Weight to 0.5.
6.
Leave the Sample Size Constant as 5.
7.
Click OK.
EWMA Chart displays the EWMA chart for the same data seen in UWMA Charts for the Clips1 data. This EWMA chart was generated for weight = 0.5.
EWMA Chart
Presummarize Chart Example
The following example uses the Coating.jmp data table.
1.
Select Help > Sample Data Library and open Quality Control/Coating.jmp.
2.
Select Analyze > Quality and Process > Control Chart > Presummarize.
3.
Select Weight and click Process
4.
Select Sample and click Sample Label.
5.
Select both Individual on Group Means and Moving Range on Group Means. The Sample Grouped by Sample Label button is automatically selected when you choose a Sample Label variable.
When using Presummarize charts, you can select either On Group Means options or On Group Std Devs options or both. Each option creates two charts (an Individual Measurement, also known as an X chart, and a Moving Range chart) if both IR chart types are selected.
The On Group Means options compute each sample mean and then plot the means and create an Individual Measurement and a Moving Range chart on the means.
The On Group Std Devs options compute each sample standard deviation and plot the standard deviations as individual points. Individual Measurement and Moving Range charts for the standard deviations then appear.
6.
Click OK.
Example of Charting Presummarized Data
Although the points for X- and S-charts are the same as the Individual on Group Means and Individual on Group Std Devs charts, the limits are different because they are computed as Individual charts.
Another way to generate the presummarized charts, with the Coating.jmp data table:
1.
Choose Tables > Summary.
2.
Assign Sample as the Group variable, then Mean(Weight) and Std Dev(Weight) as Statistics.
3.
Click OK.
4.
Select Analyze > Quality and Process > Control Chart > IR.
5.
Select Mean(Weight) and Std Dev(Weight) and click Process.
6.
Click OK.
The resulting charts match the presummarized charts.
Phase Example
Open Diameter.jmp, found in the Quality Control sample data folder. This data set contains the diameters taken for each day, both with the first prototype (phase 1) and the second prototype (phase 2).
•
Select Help > Sample Data Library and open Quality Control/Diameter.jmp.
•
Select Analyze > Quality and Process > Control Chart > XBar.
•
Select DIAMETER and click Process.
•
Select DAY and click Sample Label.
•
Select Phase and click Phase.
•
Select S and XBar.
•
Click OK.
The resulting chart has different limits for each phase.
Phase Control Chart