Should I use Xbar-R chart?


Blueberry Nut
Hello all,

I work with a semiconductors company. My division manufactures wafers, and from each wafer we'll get thousands of devices. We don't run many wafers, about one wafer every week or so (one wafer/wk makes a LOT of product), so it takes us a long time to gather lot by lot info.

If we sample, say, 9 devices and test them, could we plot an X-bar/R chart of the test results? My concern is that the 9 samples would not be consecutive in time, but taken "at the same time" because they were all created together. About the only thing we could randomize would be the location the samples come from on the wafer itself.

Am I on the right track? Or am I worrying about something irrelevant and I should go ahead with my original chart? All the other industries I've worked with had running production lines so I never considered this question before.

I should probably mention that this question was originated by a new customer for a new part. They want us to sample 9 random test sites, plot them on an SPC chart, CALCULATE Cpk on the 9 and make sure its >1, before shipment (shows how much they know about Cpk's! Scary...At least they seem to know what CPk=1 means) Almost sounds like they want us to plot each inidividual point on the 'SPC Chart' (eeck!!) :frust:

Any wiser heads care to comment/ help me out on this one?
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Laura M

Interesting question. You did a good job describing your process, but I do not understand wafer manufacturing very well, so here's my theoretical opinion.

In order to answer it, you need some understanding of the variation of the process. Your within subgroup variation in the 9 pieces should ensure "common cause variation" is captured. (The Cpk calculation doesn't make sense to me.)
Randomizing location makes sense to me. What % of production does 9 pieces represent? How many do you get from one wafer?

Samples for X'bar R charts must be "rational subgroups." Does the R-bar estimate of std dev. represent the process variation? Can you compare one week's wafer to the next? Have you established if the process is in control?

Rick Goodson


I believe your basic question deals with the sampling technique. Since your are randomly selecting from the wafer you are not using the commonly used instant-time method (all the devices sampled being made one after another). You are using the period-of-time method (similar to random sampling from a lot of material). With period-of-time method the within subgroup variation is maximimzed and the between subgroup variation is minimized. The period-of-time method is less sensitive to changes in the average.

Regardless of the method used for sampling, in statistical process control there is an assumption of homogeneous lots. That is, the pieces in each lot (read wafer) are as alike as possible; same machine, operator, robot, material, etc. I would be more concerned about the week or two time lag between samples and changes to the process. IMHO too many things will change in a week or two for the charts to be of value in process control.
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