In Process Data Collection and Cpk Calculation

[KCIPOH]

Hello Cove members,

I would like to have advice for the below scenario and we are having it for the first time :

We are supplying one of our products (plastics reel) to one of our customers for them to wound up the solder lead and are having a feedback from customer where they are having concern on the net weight (500gms-505gms) (solder lead weight after wounding on the plastics reel) where there is difference between net weight (the weight for the solder lead, not include the plastics reel weight) at their premises and the one found by their other plant in oversea (which is lower than 500 gms).

They have checked product and found the issue actually due to our plastics reel part weight which is slightly lower (35.90 gms) but still within spec limit (36.00 gms +/-5%) (34.2 gms-37.8 gms). The part weight for cavity 02 is higher than cavity 01 because the material will filled up cavity 02 followed by cavity 01 when injection molding.

Therefore, we have collected data of 30 samples for each cavity (cavity 01 & 02) and listed out the average, after review the data, our customer suggested that to change the spec to 36.70gms+/-0.5gms (36.2 gms - 37.2 gms) to solve the difference issue.

From the above part (plastics reel), our PQC are doing weight checking by taking 5 pcs per shift of 12 hrs for each cavity (cavity 01 & 02) and since this has been an issue feedback from customer (not a complaint), any part weight supplied to customer that is out of the customer suggested spec will be rejected totally for that particular lot. Since this is critical, so i suggested that QC should collect 30 samples per every 2 hrs for each shift to monitor the part weight (would this be reasonable?) because i have been rejected by the QC inspector that this is no need as 5 samples per shift of 12 hours is enough.

Please refer to attachment for the data i collected and i would like to calculate the Cpk for this part, is it possible for me to calculate the Cpk, if yes, need your help to guide me through.

Need help

 

[phloQS]

Hi KCIPOH,

I have reviewed the data you collected. It is obvious, that you are over the expected or "true" value in every sample. So be careful with just calculating cp and cpk. These data means nearly nothing to your values. You could collect more than these two rows of values and calculate the average. If the average is always over your expected value you have to adjust your process. Your deviation is pretty good by the way, as you can see through see resulting cp and cpk. The comparison of cp and cpk shows you that the average is not in the centre of your deviation. I have attached my calculation to this post.

Regards

Florian

 

[bobdoering]

Capability indices really have little to do with your problem. You need an ongoing methodology to track your weight to ensure it is in spec. This is a little different than traditional SPC, which looks for signals of special causes. The signal you are concerned about is meeting the weight specification. One approach is attached, where I used the X hi/lo-R chart to look at both cavity weights versus the specification. I placed limits at 75% of the tolerance to accommodate sampling and measurement error. The range is the difference between the two cavity weights. If that changes, that is much more meaningful information than average weight change over time. It will show a change in the balance between the two cavities, which can be a pressure, flow, temperature or material lot effect that may need addressed.

Since you are not sure about the ongoing capability, I would sample each cavity every 10 shots or so to get a baseline. From that, you may find the variation will allow you to do it less frequently, although you always need to do it after breaks, at setup/startup, beginning of each shift, etc. (all are special causes than can affect the process)

 

[KCIPOH]

Hi KCIPOH,

I have reviewed the data you collected. It is obvious, that you are over the expected or "true" value in every sample. So be careful with just calculating cp and cpk. These data means nearly nothing to your values. You could collect more than these two rows of values and calculate the average. If the average is always over your expected value you have to adjust your process. Your deviation is pretty good by the way, as you can see through see resulting cp and cpk. The comparison of cp and cpk shows you that the average is not in the centre of your deviation. I have attached my calculation to this post.

Regards

Florian

Hello Florian,

Not really understand with "that you are over the expected or "true" value in every sample." can you help explain in simple way? Thank you.

By the way, i don't really understand on Std Dev, from the Std Dev in your attachment, it is using "n" instead of "n-1",

1. why is it "n"?
2. what is the difference between "n" and "n-1"?
3. when to use "n" and "n-1" when calculating Std Dev?
4. in ideal case, Std Dev should be 1, am i right?
5. then when calculating Std Dev, should it be greater than 1 or smaller than 1, what's the difference between the
2 of them?
6. what is the meaning of +/- 1 Std D, +/-2 Std D and +/- 3 Std D?
7. normally when calculating Std Dev, which one is better and which one should we use, +/- 1 Std D, +/-2 Std D
and +/- 3 Std D?

Sorry for asking so many questions but can you explain more further as i'm really confuse on this statistics tools when put into application, for me to get the idea, Thank you.

 

[KCIPOH]

Capability indices really have little to do with your problem. You need an ongoing methodology to track your weight to ensure it is in spec. This is a little different than traditional SPC, which looks for signals of special causes. The signal you are concerned about is meeting the weight specification. One approach is attached, where I used the X hi/lo-R chart to look at both cavity weights versus the specification. I placed limits at 75% of the tolerance to accommodate sampling and measurement error. The range is the difference between the two cavity weights. If that changes, that is much more meaningful information than average weight change over time. It will show a change in the balance between the two cavities, which can be a pressure, flow, temperature or material lot effect that may need addressed.

Since you are not sure about the ongoing capability, I would sample each cavity every 10 shots or so to get a baseline. From that, you may find the variation will allow you to do it less frequently, although you always need to do it after breaks, at setup/startup, beginning of each shift, etc. (all are special causes than can affect the process)

Hello bob,

Thanks for your attachment but can you explain the interpretation of the graph in a more simple way as i'm very new to Std Dev, Cpk and Cp etc and not quite understand above.

Thank you.

 

[phloQS]

Hi KCIPOH,

With the "true value" i meant the value that you expect, in your sample it is 36 gms without deviation. All the probes you listed in the excel sheet are above this value. The centre of deviation (if it was a is normal distribution) is 36,7 which is not 36. So you can see your process is not deviating around the estimated "true" value, which must be the goal.
2. Sorry mistake, should be n-1=29 in your case -> not much influence on the result
3. right
4. it is always below one if you normalize the deviation. The value i calculated in the sheet is the deviation without normalization
5.The meaning orf +- 1 Std an so on is that there are ranges in the deviation which tells you the how many of your products are in this range. For example, when you are in range of 3 STD you can say that 99,7 % of your products are ok. There are still 0,3 % out of spec.
6. Today it is common to use 6 sigma (google it) which is mor precisely.

Regards,

phloQS

 

[KCIPOH]

Hi KCIPOH,

With the "true value" i meant the value that you expect, in your sample it is 36 gms without deviation. All the probes you listed in the excel sheet are above this value. The centre of deviation (if it was a is normal distribution) is 36,7 which is not 36. So you can see your process is not deviating around the estimated "true" value, which must be the goal.
2. Sorry mistake, should be n-1=29 in your case -> not much influence on the result
3. right
4. it is always below one if you normalize the deviation. The value i calculated in the sheet is the deviation without normalization
5.The meaning orf +- 1 Std an so on is that there are ranges in the deviation which tells you the how many of your products are in this range. For example, when you are in range of 3 STD you can say that 99,7 % of your products are ok. There are still 0,3 % out of spec.
6. Today it is common to use 6 sigma (google it) which is mor precisely.

Regards,

phloQS

Hello phloQS,

2. Sorry mistake, should be n-1=29 in your case -> not much influence on the result

For your information, each boxes contain 320 parts with separate cavity, so i took 1 box containing cavity 1 only and randomly picked 30 pcs for data collection.
Because i refer to some websites on Std Dev, there are 2 types of Standard Deviation which is
Population Standard Deviation (represented by sigma which using "n")
Sample Standard Deviation (represented by S which using "n-1")
So, my mentioned method above, is it correct to use "n" or "n-1"?

4. it is always below one if you normalize the deviation. The value i calculated in the sheet is the deviation without normalization

Can you explain on what do you mean by normalize the deviation?

5.The meaning orf +- 1 Std an so on is that there are ranges in the deviation which tells you the how many of your products are in this range. For example, when you are in range of 3 STD you can say that 99,7 % of your products are ok. There are still 0,3 % out of spec.

Can we see it directly from the data you replied, if yes, how to see how many parts are in the range?

Sorry for asking again but i really want to get myself clear on Std Dev issue, please help

 

[Al Dyer]

Actual standard deviation = n
Estimated standard deviation = (n-1)/n x (n-1)/n x (n-1)/n etc...



If you are projecting a possibility use n-1
If you are stating an actuality us n

??????????????/Maybe helps?

 

[Al Dyer]

Maybe this:
--------------------

[FONT=&quot]Calculate the chances of two people having the same birthday:[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]This means for two people, the probability that they have different birthdays is [/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]P(D) = (365) (364) = (365)(364) = 0.9973[/FONT]
[FONT=&quot] (365) (365) 3652[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]and: P(2) = 1 – 0.9973 = 0.0027[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]Therefore, with only two people (who are not twins) in the room, there is a 0.27% chance that they have the same birthday (that is, of course, if they are not twins!) Well, we knew that given only two people, it was highly unlikely that they would have the same birthday, didn’t we?[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]In a room containing three people, calculate the chance that at least two of them have the same birthday:[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]For three people, the calculation looks like this[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]P(D) = (365)(364)(363) = (365)(364)(363) = 0.9918[/FONT]
[FONT=&quot] (365)(365)(365) 3653[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]and: P(2) = 1-0.9918 = 0.0082[/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]With three people in the room, there is a 0.82% chance that two of them have the same birthday. Not much better really. But what happens as the number of people in the room grows? Just continue in the same fashion for more people.[/FONT]

 

[bobdoering]

Thanks for your attachment but can you explain the interpretation of the graph in a more simple way as i'm very new to Std Dev, Cpk and Cp etc and not quite understand above.

Here is your issue: you want to assure that all of your cavities fall within the specification - and you need some warning as to when going out of specification is about to occur prior to making bad parts.

The calculations of standard deviation and average are dealing with describing the range of variation from estimates, using the normal distribution as a model. This is a terrible model for multiple cavities – as their true distribution is very multimodal. It has some hope looking at just one cavity over time, but that is it. These calculations are extra work that do not lead you to the direction you need to assure your process is making guaranteed good parts. My approach is to not to estimate the distribution, but plot the actual values. Also, my approach is not to look for out of control conditions (traditional SPC), but to want to but to look for the signal of process adjustment prior to making bad parts. Big difference.

Your process is in specification and stable. What economic justification would cause you to want to adjust your process? Consider this: if your process is now stable and making part in specification, adjusting the process lower may actually cause the process to become unstable, or other characteristics of the part may become out of spec - such as underfill in some areas. What adjustments can you make? What is there overall effect - not just the effect on weight? What about shrinkage, fill, etc.? You cannot assume - as some may - that centering the process is automatically a good thing, especially in plastics molding!

So, all we are doing with the graph is looking at the highest weight and lowest weight of the shot - not the average. Average is pretty useless. From those two values, we observe how close we are to the specification. We only use 75% of the specification to allow for other errors, such as gage error, measurement error, sampling error, etc. We also look at the range, because if the difference between the high and the low start to increase, it may be a significant clue that you process is starting to change adversely. When we get too close to these limits, then we need to adjust the process.

As long as you keep your weights within those limits, you will meet the customer requirements, which is the goal for this particular issue. Centering is not necessarily the goal (especially as consistent as your data is), capability indices mean very little. In fact, centering may be considered overadjustment. This chart gives you the information to assure your process meets the customer’s needs.