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Process Screening and Process Capability for three-way charts in JMP 14

Three-way charts were introduced in Control Chart Builder in JMP 10. You can read about this type of chart in my colleague Annie Zangi's blog post “Three-way charts, an evolution of the Presummarize Control Chart.” We are happy to be able to say that in JMP 14, you can also get a three-way chart in two other platforms. The three-way chart is now also available in Process Screening and Process Capability.

As an example, consider a vial fill process in a pharmaceutical company. There is a large complex machine that fills vials in a super clean room. To fill the vials, the machine uses a set of four needles to fill a block of four vials. Once the vials are filled, they are stoppered and sent out of the clean room into another room. In the second room, the fill weight of the vials is tested at regular intervals throughout the day. The target fill weight is 6.1 grams per vial. If the vial fill weight measures below 5.8 grams, the vial will have to be thrown out. We have last week’s production data for the company's Drug Z 10 dose vials. Twelve samples were tested per day with six vials per sample. Let’s take a quick look at the data using the variability chart to see the different types of variation we expect to see.

### Variability Chart

Open Vial Fill Weights, which is provided with JMP sample data, and run the Variability Chart script.

``````dt=Open("\$SAMPLE_DATA/Quality Control/Vial Fill Weights.jmp");
dt<<Run Script("Variability Chart of Fill Weight by Sample");``````

### Variability chart for vial fill weights

Notice the within variation. Every sample does not yield vials with the same fill weight. The range bar for sample 12 shows a wide variation in the fill weights of the six vials. Notice the between variation. All bars are not equal length or in the same location. The range bar for sample 41 is much higher than the range bar for sample 56. The data has been colored by Day. Notice the pattern that appears with days. It looks like the measurements tend to go up at the beginning of the day, and then the measurements fall somewhat, but the ranges tend to get much larger at the end of the day. Given the nested design, we expect to have variation between samples as well as within samples. We will therefore need a three-way chart to analyze this data.

### Process Screening

To create a three-way chart in Process Screening, use the following steps.

• Select Analyze->Screening->Process Screening.
• Select Fill Weight in the Select Columns panel and click Process Variables.
• Select Sample in the Select Columns panel and click Subgroup.
• For Control Chart Type, select XBar MR and S.

Process Screening Dialog

• Click OK.

Process Screening reportThe results give four estimates of sigma.

• Within sigma is the estimate of variation within samples.
• Overall Sigma is an estimate of the overall variation which does not depend on subgroups.
• Between sigma is an estimate of the variation between samples.
• Between-and-Within Sigma is an estimate of the combined variation of within a sample and between samples.

We notice for this example that the within sigma (0.05256) is slightly higher than the between sigma (0.03332). The Between-and-Within Sigma (0.06223) is very close to the Overall Sigma (0.06993).

The Stability Ratio and Cpk are calculated using the Between-and-Within Sigma estimate.

### Process Capability

We could produce a three-way chart in Process Capability by selecting the process in the Process Screening platform and choosing Process Capability for Selected Items. Let’s instead see how to produce a three-way analysis using the Process Capability dialog.

• Select Analyze->Quality and Process->Process Capability.
• Select Fill Weight in the Select Columns Panel and click Y, Process.
• Open the Process Subgrouping panel.
• Select Sample from the Select Columns Panel, Fill Weight in the Cast Selected Columns into Roles panel and click Nest Subgroup ID column.
• Click Calculate Between-and-Within Capability.

Process Capability Dialog

• Click OK.

From the red triangle next to Process Capability, choose Individual Detail Reports.

Process Capability Report

In the Process Summary section, you will notice the same four estimates of sigma that you saw in the Process Screening platform. You will also find capability statistics based on the Between-and-Within Sigma as well as capability statistics based on the overall sigma.

We see from the histogram that the process is slightly above target. All vial fill weights are within the given specification limits. This process is capable.

### Three-way charts in three platforms

Beginning with Version 14 of JMP, three-way charts are available in three different platforms: Control Chart Builder, Process Screening, and Process Capability. This means that, as the user, you have multiple ways of analyzing the same information — that is, you can pick the platform that best suits your needs.

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Level III

Really glad to see this capability being expanded within JMP.  This is something I've had to more often lean on Minitab for since the options in JMP were either not there, or not obvious to me.

Also, I'm curious of your differention of Overall vs B/W variation.  My view on it was that if Overall was substantially larger than B/W then you had some form of variance that was systematic in nature, like a drift or step change.

Staff

I'm glad you find the 3-way charts useful.

There is a good chance that there is something systematic going on if Overall is a lot greater than B/W, but I have not studied this enough to be able to say that is the only possibility.  If there is a systematic change, this should be easily seen in the graphs of the data (Process charts).

Level I

I thought the "Within Sigma" is equal to the square root of the average variance within samples?  [We can use the arithmetic average since the samples have equal Ns.]  When I do that I get 0.058277 for the Within Sigma.

Also, could you say more about the "Between-and-Within Sigma?"  I can't find that term in any of my applied statistics books or on the Internet.  Plus, how is it calculated?

Thanks!  :-)

Staff

These formulas are all given in the documenation.  Please look at the Quality and Processs Methods book for more detail.

The calculation of Within Sigma depends on the type of chart.For an Individual on Means, Moving Range on Means & S Chart, the formula is as follows:

For an Individual on Means, Moving Range on Means & R Chart, the formula is as follows:

where

si=sample standard deviation of the ith subgroup

N=number of subgroups for which ni>=2

c4(ni)=expected value of the standard deviation of ni independent normally distributed variables with unit standard deviation

Ri=range of the ith subgroup

d2(ni)=expected value of the range of ni independent normally distributed variables with unit standard deviation.

The formula for between and within sigma is as follows:

where H is the harmonic mean of subgroup sample sizes.

Level I

Thanks for the quick response, Tonya.  [The sigma-squared-within on the LHS of the first two formulas should be sigma-within.]

I've never heard of calculating a pooled standard deviation estimate using a type of weighted averaging of *standard deviations* - it's always based on the square root of a weighted average of the group *variances,* and the weighting factors are each group's degrees of freedom.

I've checked the "Quality and Process Methods" book and found no citations for the formulas used there.  Can you point me to any?  Thanks.

Staff

Yes, you are correct that the formula should be sigma_within and not sigma^2_within.  I apologize for the typo.  The formulas in the documentation seem to be correct although the one for the Individual on Means, Moving Range on Means & S Chart appears to be missing.  I will make sure that it is added.

The within sigma calculation is the same one that is used for control charts.  A reference for this is

American Society for Testing and Materials (1976). ASTM Manual on Presentation of Data and Control Chart Analysis. Philadelphia: ASTM.