Determining Control Limits from a desired Cpk

[kb103]

Good evening everyone, I'm new to stats/process control but I'm trying to gain a better understanding so I can improve some of the processes I'm responsible for.

I have two sets of data, 20 samples of a 'good' part and 20 samples of a 'bad' part. I want control limits that will give me a Cpk of 1.33. Currently I'm adjusting my control limits in to Minitab, generating charts, observing the Cpk, then readjusting limits until I achieve the desired index.

Is there a way in Minitab to enter my sample values, desired Cpk, and have MiniTab generate the limits for me? Seems like I'm working backwards at the moment, thanks for your help.

 

[Miner]

I'm afraid it doesn't work like that. The process variation drives both the control limits and the capability. If you establish the control limits as you suggest, they will not match the process variation. Judging from your question, I would expect the control limits to be too tight for the process, and you will react to a lot of false alarms.

 

[Kales Veggie]

Good evening everyone, I'm new to stats/process control but I'm trying to gain a better understanding so I can improve some of the processes I'm responsible for.

I have two sets of data, 20 samples of a 'good' part and 20 samples of a 'bad' part. I want control limits that will give me a Cpk of 1.33. Currently I'm adjusting my control limits in to Minitab, generating charts, observing the Cpk, then readjusting limits until I achieve the desired index.

Is there a way in Minitab to enter my sample values, desired Cpk, and have MiniTab generate the limits for me? Seems like I'm working backwards at the moment, thanks for your help.

You should approach it differently.

CpK is determined by the tolerance range and the process variation.

Control limits are determined by the process variation and a constant, depending on sample size.

So, CpK and control limits are both dependent on the process variation.

So, you have to determine the process variation. This is often done through a process capability study (run at least 30 piece, 125 is best), measure and chart in production sequence and analyze.

(also CpK is only valid if the process characteristic has a normal distribution)

 

[kb103]

Thank you Miner and Kales Veggie, that really helps. So let me ask you this. Typically when we set up an inspection or a process we collect 20-30 samples of good and bad parts, look at the numbers from the process (critical to quality), then put control limits around the numbers. This is usually a judgement call with no real calculated method. In your opinion what is the best way to determine control limits in this scenario?

 

[Kales Veggie]

Thank you Miner and Kales Veggie, that really helps. So let me ask you this. Typically when we set up an inspection or a process we collect 20-30 samples of good and bad parts, look at the numbers from the process (critical to quality), then put control limits around the numbers. This is usually a judgement call with no real calculated method. In your opinion what is the best way to determine control limits in this scenario?

No, you should manufacture the parts, collect all parts sequentially (probably number them) from the process, no adjustments to the controls, measure the characteristic(s) and plot them and perform your analysis.

Do not select good and bad parts.

 

[kb103]

Kales Veggie:

Thank you for the response. There are times when my 'good' parts test in very close to my 'bad' parts. For example, here are some light intensity values taken from a camera I use to inspect colors. The parts have very similar colors:

Good:
2.42
2.17
2.34
2.25
2.37
2.48
2.45
2.18
2.31
2.37
2.01
1.91
2.13
1.78
2.23
1.83
2.13
2.87
2.36
2.18

Bad:
4.92
4.08
4.22
4.34
3.92
4.89
2.90
5.24
3.95
4.92
4.35
5.08
4.16
5.13
5.40
3.90
3.60
3.33
5.02
4.08

Had I used my I-MR chart to determine a UCL of 2.916 (according to minitab) I'd have exposed myself to risk - without testing the 'bad' parts I'd have no idea my process was not in control.

Am I making sense or completely off base?

Thanks again for your insight I really appreciate it.

 

[Jim Wynne]

Kales Veggie:

Thank you for the response. There are times when my 'good' parts test in very close to my 'bad' parts. For example, here are some light intensity values taken from a camera I use to inspect colors. The parts have very similar colors:

Good:
2.42
2.17
2.34
2.25
2.37
2.48
2.45
2.18
2.31
2.37
2.01
1.91
2.13
1.78
2.23
1.83
2.13
2.87
2.36
2.18

Bad:
4.92
4.08
4.22
4.34
3.92
4.89
2.90
5.24
3.95
4.92
4.35
5.08
4.16
5.13
5.40
3.90
3.60
3.33
5.02
4.08

Had I used my I-MR chart to determine a UCL of 2.916 (according to minitab) I'd have exposed myself to risk - without testing the 'bad' parts I'd have no idea my process was not in control.

Am I making sense or completely off base?

Thanks again for your insight I really appreciate it.

It's hard to tell exactly what you're doing, or trying to accomplish. As Kales and Miner have suggested, if you want to do SPC such that you can calculate Cpk, you need to (a) verify your measurement system; (b) select samples from production in chronological order, with aggregate number of samples being statistically significant; (c) verify that your process is statistically stable and (d) study the results to determine whether or not the process is capable of doing what you need for it to do.

Contrary to popular belief, selecting a sample of parts from a manufactured lot and charting the measurements and doing a Cpk calculation is not a good or even sensible way to understand process capability. Cpk, even when done correctly, is a mostly useless statistic.

Figure out what you need (the specification limits), then see if your production process is capable of achieving it.

 

[rickpaul01]

Am I making sense or completely off base?

Thanks again for your insight I really appreciate it.

IMHO I think you are completely off base.
If I understand correctly: You are making a bunch of parts. Then you are sorting them into "good" and "bad". Then you are testing each part to determine the numberical value. Then applying the rules for a normal distribution to the two different populations.
Is this correct?

 

[Bev D]

You are gettting good advice. taking 'good' and 'bad' parts is a stratified sample and calculating anything statistical or even a 'judgment' call on some type of 'control limit' will not provide useful information - in fact it can be horribly misleading.

perhaps the best approach is to start from the beginning: what are trying to accomplish? adn I,m not askign about what calculations you want to make but you want to do with the results of the calculations...

 

[Mr.Happy]

I have an additional question about Cpk value:
how can I calculate from the Cpk value the amount of parts that I have to check in production to prevent any rejected parts.
In this case dimension 46 +0 / -0,1 mmm with a Cpk (30 parts) of 0,78 ?