Implementation of 8 or 9 Points Above/Below Centerline question

Q

q1spa

I have question on proper implementation of "8 pts above/below centerline" rules.

Our spc charts (semiconductors) consist each "point" being a summary statistic of individual points measured on a wafer. Each wafer is a point on the chart. There are typically anywhere from 1 to 5 wafers from each lot (typical lot size is 25 wafers).

I'm not sure it is proper to mix both wafer to wafer and lot to lot variation on the same chart - but that is probably a different topic.

For the "8 above/below" rule, is the intent to be 8 lots (rather than 8 individual wafers)? Since we now within-lot variation (wafer-to-wafer) is typically much tighter than lot to lot -- it seems you will trigger a trend rule much earlier than makes sense (ex: measure 3 wafers per lot - all slightly above the mean - you wil trigger violation halfway thru the 3rd lot) - but no real special cause of variation to fix. It seems lot-based would make more sense.

Any input or past experience would be helpful.
Thank you

T

t.PoN

Since we now within-lot variation (wafer-to-wafer) is typically much tighter than lot to lot
How do you evaluate the "within lot variation"?

let me get this straight:
You have a lot size of 25 waffer
you have unequal sample size (some times, 3 and others are 5)
You don't take the average of the sample or the range.
You plot each sample 3 or 5 times based on the sample size?

I just want to know how did you calculate your limits?

Y don't you use a simple X' and R chart?

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Steve Prevette

Deming Disciple
Staff member
Super Moderator
Whether it is lots or individual units, there are "rules" for declaration on a series of results in a row the same side of the centerline. I use 7 (based upon Acheson Duncan), but Wheeler uses 8 and Minitab uses 9.

If you are going to use lots, you need the lot size to be consistent for "traditional" xbar - R. Since you lot size is varying, it may make more sense to plot individual wafers. There are ways to construct avg - sigma charts with varying lot sizes, but the control limits (standard deviaion) calculations can get difficult.

Q

q1spa

Sorry for confusion. Thanks for the replies
We do plot the mean and sigma for each wafer (as well as individual raw data for each wafer vs spec) - 3 charts. The mean and sigma chart is summary from raw data pts of each wafer. There is no "lot-level" calculation or summary on the chart. CLs are calculated based on the points on the chart (wafers). Most of the lots will have 3 wafers sampled.

To make it a more straightforward question - assume every lot has 3 wafers, would it make more sense to adjust the data used for the 8 (or 7 or 9) above/below calculation to use 24 points? (3 wafers per lot * 8 lots, for example) since lot to lot variation is much larger than wafer to wafer.

Thanks

T

t.PoN

You either plot it as a lot or as individual.

Go back to the construction of the chart when you first calculated the limits. What variation did you use? the lot to lot or the wafer to wafer?
If you used wafer to wafer variation, then that's the variation to evaluate against.

You can't build your chart based on individual variation and evaluate based on lot variation, can you?

Note: I still suggest a p chart or X'chart, I'm not convinced on how you treat your data? is it normally distributed?

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Q

q1spa

Thanks for the suggestion. Yes, it is normally distributed. I recently joined and not convinced this method is sound (each wafer is a point on chart, but lot-to-lot variation is known to be larger component of variation in this industry) I wanted to get other thoughts from SPC experts.

Steve Prevette

Deming Disciple
Staff member
Super Moderator
To make it a more straightforward question - assume every lot has 3 wafers, would it make more sense to adjust the data used for the 8 (or 7 or 9) above/below calculation to use 24 points? (3 wafers per lot * 8 lots, for example) since lot to lot variation is much larger than wafer to wafer.

Thanks

Whatever you are plotting, stick to whatever rule you settle on (7, 8, or 9). Do not try to multiply by lot size.

Now - if there are dependencies between wafers, such as say three in a row would have the same value, guaranteed, then you need to relook at the use of SPC as an underlying assumption in SPC is you are plotting sequential, independent results. It may be worth having a "first item in lot" SPC chart to see if such dependencies exist.

Bev D

Heretical Statistician
Staff member
Super Moderator
You either plot it as a lot or as individual.

Go back to the construction of the chart when you first calculated the limits. What variation did you use? the lot to lot or the wafer to wafer?
If you used wafer to wafer variation, then that's the variation to evaluate against.

You can't build your chart based on individual variation and evaluate based on lot variation, can you?

Note: I still suggest a p chart or X'chart, I'm not convinced on how you treat your data? is it normally distributed?
your part of the way there, the OP needs to treat each component of variation separately. however, the data do NOT have to be Normally distributed.
by the way, you can have variable limits for continuous data if you have a variable sample size.

the issue here is the choice of subgrouping and control chart type. The OP is charting more than 2 components of variation and eh doesn't have a homogenous process (the factors that affect within wafer variation are not the factors that affect wafer to wafer variation nor are the factors that affect wafer to wafer variation the same as the factors that affect lot to lot variation. a standard X bar R chart will not work.

If the OP can post an example of their data we can give more precise help.