Is possible to determine a frequency inspection based on the Cp or Cpk?

Is possible to determine a frequency inspection based on the Cp or Cpk?

It's a good idea to base decisions on inspection depth and frequency on statistical analysis. Whether or not you use capability indices is dependent on a number of factors, including the stability of processes. Properly done, Cpk analysis will tell you something about how well your processes compare to the tolerance limits, and the likelihood of producing nonconforming parts, and you could use that information to help you determine whether or not increased inspection is necessary.

Is possible to determine a frequency inspection based on the Cp or Cpk?

Sampling frequency or sample size? Sampling frequency is usually a function of the process and natural points and times to sample. For example if you continuosly fill bottles from a 8-head filler, you might sample every 1000 bottles, one bottle from each head. Sampling frequency is a "risk" based decision because should you find a defect in the sample, you would have to quarrantine all items between the two inspection points.

Sample size is a function of the variability of the process, and can be based on Cpk or other capability index.

When you are selecting the sample to study the Cpk of the process.you have to select the sample in such a manner that all the possible variation which can affect quality of the parts should be covered ,then only we can get the true value of our process capability.

Depending upon the value of Cpk you get change the sample frequency or the size for next process study to get correct information.

I have found the best estimation of sampling frequency for SPC is 3 to 5 samples per adjustment (just under the 7 points as a run). The worst scenario is to walk up to a process and find out that the SPC frequency was set at once per hour, and the operator is adjusting every 15 minutes. At that point your data is garbage.

Is possible to determine a frequency inspection based on the Cp or Cpk?

I had the same question.
I had been exploring Minitab 15 and Internet, and I found nothing.

I am in the metalworking industry (Milling, Turning, Drilling, Grinding) and i decided to do this, based on common sense:

CPK < 1.33 => Use 100% In-process inspection AND reduce process variability (CPK and PPK) !
CPK > 1.33 AND PPK < 1.33 => Increase In-process inspection frequency (Decreasing time from subgroup to subgroup) in orden to early detect subgroup process variation (PPK) (shifts, drifts or trends) and make adjustments (in order to increase PPK) and have a better long term process performance. Continue reducing short term process variation in order to have a better CPK.
CPK >> 1.33 AND PPK >> 1.33 => I am allowed to decrease In-process inspection frequency (increasing time from subgroup to subgroup).

Optimal In-process sampling frequency if i have:
CPK >> 1.33 AND PPK >= 1.33
In this case if i increase in-process inspection frequency (decreasing time from subgroup to subgroup) i am only increasing costs, not quality.

I hope this helps.
Victor

"CPK < 1.33 => Use 100% In-process inspection AND reduce process variability (CPK and PPK) !
CPK > 1.33 AND PPK < 1.33 => Increase In-process inspection frequency (Decreasing time from subgroup to subgroup) in orden to early detect subgroup process variation (PPK) (shifts, drifts or trends) and make adjustments (in order to increase PPK) and have a better long term process performance. Continue reducing short term process variation in order to have a better CPK.
CPK >> 1.33 AND PPK >> 1.33 => I am allowed to decrease In-process inspection frequency (increasing time from subgroup to subgroup).

Optimal In-process sampling frequency if i have:
CPK >> 1.33 AND PPK >= 1.33
In this case if i increase in-process inspection frequency (decreasing time from subgroup to subgroup) i am only increasing costs, not quality."

If you are doing precision machining, these calculations do not work. They are only for bilateral normal distributions - and precison turning, grinding and turning (drilling excluded, because it is hard to qualify it as precision) are uniform distribution (non-normal). In fact, you should expect to see trends, for example, on an OD as the tool wears the OD should trend larger. If it is not doing that, then you are not in control! And what is "increased inspection"? Not very qualitative. I stand by 3 to 5 measurements between adjustments.

If you are doing precision machining, these calculations do not work. They are only for bilateral normal distributions - and precison turning, grinding and turning (drilling excluded, because it is hard to qualify it as precision) are uniform distribution (non-normal). In fact, you should expect to see trends, for example, on an OD as the tool wears the OD should trend larger.

That is not true.
As an example, when the machine turn, it first do the rough cut, then automatically changes the tool and do the finish cut.
That shows a bilateral normal distribution on the final measure.
In the worst case, if the operator lacks to control the process as he has to do, it shows a smallest/largest extreme value distribution, but that is good enough.
It never shows a uniform distribution.

That is not true.
As an example, when the machine turn, it first do the rough cut, then automatically changes the tool and do the finish cut.
That shows a bilateral normal distribution on the final measure.
In the worst case, if the operator lacks to control the process as he has to do, it shows a smallest/largest extreme value distribution, but that is good enough.
It never shows a uniform distribution.

For precision machining, the most significant variation you should have is tool wear - which is all you should see in precision machining over time, then as the tool wears for an OD (for example) the resulting parts get larger. As they reach the upper control limit, they should be adjusted to the lower control limit to allow the tool to continue to wear. The resulting curve is a sawtooth curve, which is the uniform distribution. Grinding is a perfect example of that. HOWEVER, with multiple pass tooling (as you described), there can be tool pressure variation as the rougher and finisher wear at different rates. If the tool pressure influences the dimension, then you may not have a perfect sawtooth curve. Then yes, the operator has to chase around the dimension, and the multiple variations will appear to be a normal distribution. But, that's because there is no real control except the operator running to the mean, which ends up being overcontrol. I have even watched roughing/finishing OD dimensions get smaller because of the effect of unbalanced tool pressure between the tools. Remember, to be a true normal distribution process, you should be able to set it at mean and - without operator intervention - the process will stay at mean. Just because you variation appears to be normal, does not mean it should be! As you know, with tool wear that would be impossible. OD's have to grow, IDs have to shrink. Otherwise you have interfering special causes, such as tool pressure variation, roundness measurement error, chip wash, etc. If you have a normal curve in precision machining, you are either lacking control or charting incorrectly.

I'm totally agreed with you on the 3 to 5 samples per Auditor visit to the different stage of the process. The Cp & Cpk seems to be the rationale for doing so.

What would you recommend for attribute data? In my case the Inspector not only sample for SPC but also for attributes. Does the 3 to 5 samples apply?
Does the lot or bath size being produced matters?

What would be a good justification for using 3 to 5 samples (in-process inspection) for variable and attribute data idependently of the frequency and lot size?

Thanks in advanced.

What would you recommend for attribute data? In my case the Inspector not only sample for SPC but also for attributes. Does the 3 to 5 samples apply?
Does the lot or bath size being produced matters?

What would be a good justification for using 3 to 5 samples (in-process inspection) for variable and attribute data idependently of the frequency and lot size?

Thanks in advanced.

I am in the metalworking industry (Milling, Turning, Drilling, Grinding) and i decided to do this, based on common sense:

CPK < 1.33 => Use 100% In-process inspection AND reduce process variability (CPK and PPK) !
CPK > 1.33 AND PPK < 1.33 => Increase In-process inspection frequency (Decreasing time from subgroup to subgroup) in orden to early detect subgroup process variation (PPK) (shifts, drifts or trends) and make adjustments (in order to increase PPK) and have a better long term process performance. Continue reducing short term process variation in order to have a better CPK.
CPK >> 1.33 AND PPK >> 1.33 => I am allowed to decrease In-process inspection frequency (increasing time from subgroup to subgroup).

Optimal In-process sampling frequency if i have:
CPK >> 1.33 AND PPK >= 1.33
In this case if i increase in-process inspection frequency (decreasing time from subgroup to subgroup) i am only increasing costs, not quality.


First, it is important to not that if you are calculating Cpk in precision machining for lengths and diameters, you are most likely not properly controlling your process. Second, attempting to calculate Cpk based on a sample from a properly controlled metalworking process is nearly impossible due to severe effects of sampling error. One needs to control the process correctly, and use the rule of thumb 5 to 7 checks per adjustment driven by the charting methodology, and the problem is solved - for precision machining.

One important clue: If you are precision machining, and you have a normal distribution, your controls are wrong and you are overadjusting.

For information on the correct way to control precision machining see:
Statistical process control for precision machining (http://elsmar.com/Forums/blog.php?b=79)