Process or Product Monitoring and Control_13 doc

Case Studies in Process Monitoring Chart sources of variation separately One solution is to chart the important sources of variation separately.. The summary shows the mean line width i

6.6.1.1 Background and Data

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6.6 Case Studies in Process Monitoring

Interpretation This 4-plot shows the following.

The run sequence plot (upper left) indicates that the location and scale are not constant over time This indicates that the three factors do in fact have an effect of some kind.

1

The lag plot (upper right) indicates that there is some mild autocorrelation in the data This is not unexpected as the data are grouped in a logical order of the three factors (i.e., not

randomly) and the run sequence plot indicates that there are factor effects.

Due to the non-constant location and scale and autocorrelation in the data, distributional inferences from the normal probability plot (lower right) are not meaningful.

NUMBER OF OBSERVATIONS = 450

***********************************************************************

* LOCATION MEASURES * DISPERSION MEASURES

* ***********************************************************************

* MIDRANGE = 0.2957607E+01 * RANGE = 0.4422122E+01

* = * MAXIMUM = 0.5168668E+01

* ***********************************************************************

* RANDOMNESS MEASURES * DISTRIBUTIONAL MEASURES

* ***********************************************************************

* AUTOCO COEF = 0.6072572E+00 * ST 3RD MOM = 0.4527434E+00

This summary generates a variety of statistics In this case, we are primarily interested in the mean and standard deviation From this summary, we see that the mean is 2.53 and the standard deviation is 0.69.

There is some variation in location based on site The center site

in particular has a lower median.

Dex mean

and sd plots

We can use the dex mean plot and the dex standard deviation plot to show the factor means and standard deviations together for better comparison.

Summary The above graphs show that there are differences between the lots and

the sites.

There are various ways we can create subgroups of this dataset: each lot could be a subgroup, each wafer could be a subgroup, or each site measured could be a subgroup (with only one data value in each subgroup).

Recall that for a classical Shewhart Means chart, the average within subgroup standard deviation is used to calculate the control limits for the Means chart However, on the means chart you are monitoring the subgroup mean-to-mean variation There is no problem if you are in a continuous processing situation - this becomes an issue if you are operating in a batch processing environment.

We will look at various control charts based on different subgroupings next

6.6.1.2 Graphical Representation of the Data

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6.6 Case Studies in Process Monitoring

Mean control

chart

6.6.1.3 Subgroup Analysis

Mean control

chart

6.6.1.3 Subgroup Analysis

SD control

chart

Interpretation Which of these subgroupings of the data is correct? As you can see,

each sugrouping produces a different chart Part of the answer lies inthe manufacturing requirements for this process Another aspect thatcan be statistically determined is the magnitude of each of the sources

of variation In order to understand our data structure and how muchvariation each of our sources contribute, we need to perform a variancecomponent analysis The variance component analysis for this data set

coefficients needed to write the equations setting MSS values equal totheir EMS's This is further described below

6.6.1.3 Subgroup Analysis

0.42535 = 5*Var(wafer) + Var(site) 0.1755 = Var(site)

Solving these equations we obtain the variance component estimates0.2645, 0.04997 and 0.1755 for cassettes, wafers and sites, respectively.6.6.1.3 Subgroup Analysis

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Chart

sources of

variation

separately

One solution is to chart the important sources of variation separately

We would then be able to monitor the variation of our process and trulyunderstand where the variation is coming from and if it changes For thisdataset, this approach would require having two sets of control charts,one for the individual site measurements and the other for the lot means.This would double the number of charts necessary for this process (wewould have 4 charts for line width instead of 2)

Use boxplot

type chart

We could create a non-standard chart that would plot all the individualdata values and group them together in a boxplot type format by lot Thecontrol limits could be generated to monitor the individual data valueswhile the lot-to-lot variation would be monitored by the patterns of thegroupings This would take special programming and managementintervention to implement non-standard charts in most floor shop controlsystems

6.6.1.4 Shewhart Control Chart

individuals/moving range charts (as seen previously), and a control chart

on the lot means that is different from the previous lot means chart Thisnew chart uses the lot-to-lot variation to calculate control limits instead

of the average within-lot standard deviation The accompanyingstandard deviation chart is the same as seen previously

6.6.1.4 Shewhart Control Chart

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Data Analysis Steps Results and Conclusions

Click on the links below to start Dataplot and run this case

study yourself Each step may use results from previous

steps, so please be patient Wait until the software verifies

that the current step is complete before clicking on the next

step.

The links in this column will connect you with more detailed information about each analysis step from the case study description.

1 Invoke Dataplot and read data.

1 Read in the data 1 You have read 5 columns of numbers

into Dataplot, variables CASSETTE, WAFER, SITE, WIDTH, and RUNSEQ.

2 Plot of the response variable

1 Numerical summary of WIDTH.

2 4-Plot of WIDTH.

1 The summary shows the mean line width

is 2.53 and the standard deviation

of the line width is 0.69.

2 The 4-plot shows non-constant location and scale and moderate autocorrelation.

6.6.1.5 Work This Example Yourself

3 Run sequence plot of WIDTH 3 The run sequence plot shows

non-constant location and scale.

3 Generate scatter and box plots against

7 Dex mean plot of WIDTH versus

CASSETTE, WAFER, and SITE.

8 Dex sd plot of WIDTH versus

CASSETTE, WAFER, and SITE.

1 The scatter plot shows considerable variation in location.

2 The box plot shows considerable variation in location and scale and the prescence of some outliers.

3 The scatter plot shows minimal variation in location and scale.

4 The box plot shows minimal variation in location and scale.

It also show some outliers.

5 The scatter plot shows some variation in location.

6 The box plot shows some variation in location Scale seems relatively constant.

Some outliers.

7 The dex mean plot shows effects for CASSETTE and SITE, no effect for WAFER.

8 The dex sd plot shows effects for CASSETTE and SITE, no effect for WAFER.

6.6.1.5 Work This Example Yourself