# Standard Deviation for CP/Cpk

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• #40137

AB
Participant

Hello:
I work in the Electronics Manufacturing industry and had a question about calculating the standard deviation.
Say for example we are printing 50 circuit boards and inspecting a device with 128 pads on it and collecting data for all 128 pads. One of the ways people analyze the data (I personally think that this is not the correct way of doing this, but it seems to be a  fairly common approach) is to average the data for all the 128 pads and compare that average over 50 boards. Assuming that this approach is correct, how do I calculate the the standard deviation to estimate Cp/Cpk? I would take the standard deviation of the averages for the 50 boards.(considering the average as a single pad data). But my professor thinks that this is statistically incorrect.
Any ideas?
thanks, AB

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#123638

Oli
Participant

Hi AB,
Cp and Cpk values can only be calculated for continuous data.Actually you are dealing with defects (PCBs) or/and defectives (Pads) which is nominal, thus attribute data.
One common approach to deal with attribute data is DPMO (Defects per Million Opportunities) whereby e.g. each single pad is treated as one opportunity.For an online process control (SPC) you may want to use attribute SPC charts such as U-Chart or P-chart.
Hope that helps a bit.Greeting from sunny Germany.
Best regards,Oli

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#123640

AB
Participant

Hello Oli:
Thanks for the reply. I agree with your solution and that is the method that I follow while analyzing my data. But the method of averaging the data is frequently used by some of our customers and it is very difficult to get them to change their ways.
But even though the method of averaging is wrong, do you think that taking a stadard deviation of averages is wrong as well?
Thanks.

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#123651

“Ken”
Participant

AB,
I was following your thread, and thought I would jump in to add to the confusion.  Oli provided you an anwser if you are dealing with count data, viz. defects, with one exception.  In the past, common practice has been to count each connection on a PCB as an opportunity.  However, doing this reduces the dpmo estimate, and subsequently inflates the Sigma Qualtiy Level estimate.  I suggest an adjustment to Oli’s recommendation that a PCB is a value-add piece of work having a single opportunity.  Observing a bad connection, or a bad measure would be considered a defect.  This counting method squarely supports a Poisson distribution (multiple events from an area of opportunity)-which inturn supports the calculation for dpmo.  There may be other value-add pieces of work supporting the total product that add to the opportunity estimate of the product.  However, the PCB should be considered a single opportunity.
It sounds like you did not receive complete guidance in how to handle the other data you collect from PCB testing.  Are these data considered continuous measures, (able to compute means and SDs from)?  Could you provide an example of the types of data collected during PCB testing, i.e. continuity, etc.?
Ken

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#123716

AB
Participant

Hello Ken:
Thanks for the post. I agree that a PCB should be considered as a single opportunity, but isn’t that only when I am analyzing that PCB building process on a whole? what if, I am just trying to estimate the performance of a stencil printer, or the stencil quality? Shouldn’t I consider every pad as an opportunity?
I used to work for a stencil printer manufacturer and the way I would measure the performance of the printer was as follows: (Just as an example)
Say I collect solder paste deposit volume and height data for QFP120. I would either select a few pads all over the device or collect data for each of the 120 pads. After printing 50 boards, i would inspect them. Then I would group the pad data from board to board.(Pad1Board1, Pad1Board2….)(Pad2Board1, Pad2Board2..) and so on. I would find standard deviation for each pad and use that to estimate the Cp or Cpk.(Total 120 Cp/Cpk values)
Is this right?
AB

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#123719

Mikel
Member

The ideas of opportunity counting started with PCBA. There are PCBA’s done for JCI that have a single LED or switch and PCBA’s done for Cisco with 2000 components and 5000 connections done in the same facility. How does your idea of 1 opportunity for each of them play?

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#123726

Peppe
Participant

What is the exact method you use to analize pads quality ? Which measurement you take ? Displacing, diameter, thickness, metallization or what ? If it is one of that, data are continuous and you can use standard way for Cp/Cpk.
Rgs, Peppe

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#123748

“Ken”
Participant

AB,It seems we are discussing measures of quality from two different perspectives, attribute vs. continuous data. I suspect that I may have caused the split in this discussion based on the responses from other posters. I apologize for any confusion. Please note if you do work with attribute data in connection with PCB manufacturing I would like to refer you to the book entitled, “Measuring Process Capability”, Davis R. Bothe, pp. 546-549 section 9.5. This section provides a complete step-by-step approach to measuring capabilities at both the unit and at the opportunity level–Example 9.14 is of particular interest, because it details the capability assessment of a circuit board soldering opperation of two boards having different complexities and therefore different areas of opportunity. Catch the book description link here:http://www.amazon.com/exec/obidos/tg/detail/-/0070066523/qid=1122483037/sr=1-1/ref=sr_1_1/104-5410670-6311930?v=glance&s=books I believe your original question spoke to handling variable data collected from each board. So, I will try my best to address your original question using the example you provide. You make 120 measures each of solder paste deposit volume and paste height. The measures of interest are paste volume and height. Question–are the requirements for each the same across the board? For height, I might expect yes, but for volume it might depend on the area of the pad. For height, I see no reason why you could not combine the measures across the board given they have the same requirement. On the paste volume measure, I’m thinking that paste height and volume are co-dependent quantities. Do you find when the capability is low for height it is also low for volume, or vice-versa? The reason I say this is because for paste volume I was thinking of standardizing the measures using area. But, when I do that I end up with height as the measurable. A bit circular here. Well, those are my ramblings on this specific subject. BTW, Chapter 12 of Bothe’s book provides details on combining capability measures. In fact, if you deal with multiple process streams Bothe suggests using an average Cpk calculation. However, if your computing a product capability Bothe suggests rendering the measures to counts of defective pads per board found during the capability study, (something that makes me a bit nervous), computing the proportion of average defects to total pads/board across a number of boards, determining Zmin from this proportion, then estimating Cpk by dividing Zmin by 3. The product Cp can be approximated by taking half the earlier average defect proportion, and calculating Zmin/3 from this estimate. It seems to me your approach of combining all the Cp and Cpk values may not be quite correct, because you are not dealing with a process stream. Well, I’ll leave you with this post. It’s guaranteed to generate some follow-up by others. BTW, Dr. D. J. Wheeler has an approach to capability determination centered around Taguchi’s Loss Function. It’s yet another approach of many for rendering meaningful metrics from processes. You can get more details at http://www.spcpress.com.Good luck,Ken

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#124281

Da Agent
Participant

Stan,
So which method would be correct? Following the suggesstion posted making all opportunities as one (DPMO = PPM) or counting each opportunity for a process? How do you know when to apply either or???

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