# Capability for one sided specification

Discussion in 'Capability - Process, Machine, Gage …' started by orion, May 10, 2016.

1. ### orionNew Member

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1.Could you please advice me how can I calculate capability of process with one sided specification?
There is Lower specification limit and no upper specification limit. Suppose Cp can not be calculated.

2. Regarding collecting data for SPC from the specific process, I have another question.
What is the best sampling frequency for collecting data for conducting SPC.
Generally we apply rule: 5 pieces per each hour of manufacturing, overall 25 hours = 125 pcs.
Is it a must, or other rules can be applied, for example 1 piece per shift.
What is the minimum sample size?

2. ### MinerModeratorStaff Member

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Regarding item 2 above: The first step is to identify rational subgroups. This will be highly dependent on your particular process.

Include similar things into the subgroup, put dissimilar things between the subgroups. In essence, this means do not mix process streams (i.e., different machines, mold cavities, etc.) unless you can statistically show that the different process streams are not different.

Next, determine the size of the subgroup. If there is no logical basis for a rational subgroup that subgroup size may = 1. Otherwise, select a subgroup size that economically balances your need to detect a process shift with the risk of nuisance adjustments. If your process is stable and highly capable, use a smaller subgroup size. If less capable, you may want to use a larger subgroup size. Do not automatically use a subgroup of n=5. The basis for this was that it was easy to calculate the mean by taking the sum of the 5 values, multiplying it by 2 and shifting the decimal 1 space to the left. Prior to having calculators this was a great solution.

Finally, determine the frequency of sampling. This also should be rationally based. What is the major source of process variation? Material? How often do you change batches/lots of material? Every 2 hours? Set the frequency of sampling at 2 hour intervals. Is the major source of variation due to ambient temperature? Select a frequency based on how rapidly the ambient temperature changes.

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3. ### MinerModeratorStaff Member

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And regarding item 1 above. This is very controversial. The easy way, which is not necessarily the best way, is to just use Cpk and forget about Cp. However, this has the potential to drive some bad behavior. For example, you have a maximum specification with no minimum, but it is more economical to hold to a target value. It is usually easier to move the process average than to reduce the variation, so chasing the Cpk may drive a more costly behavior of moving the process average below the target rather than reducing variation.

4. ### Bev DModeratorStaff Member

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Why are you calculating a capability index? does your customer require it? If so, what is the requirement specifically. See Bob Doerring's resource on this topic. (in the resource section - tab at the upper left)
If you don't have a customer requirement, consider NOT doing it. simply plot your data against the specification limit and see where your process is relative to the specification. if you have defects, understanding the actual defect rate also has value...

5. ### Bob DoeringMember

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See attached for some tips on calculating capability for unilateral tolerance. It only works if both sides are bounded, such as roundness. Remember, if you are automotive, the AIAG PPAP 4th edition specifies that you cannot use Cp, Cpk, Pp and Ppk with unilateral tolerances!

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6. ### _Zeno_Member

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??? Under what conditions are both sides bounded ???

7. ### MinerModeratorStaff Member

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Boundaries are natural limits as opposed to a specification. GD&T specifications that take absolute values rather than negative numbers (e.g., position, roundness, etc.) have a natural boundary of zero even though there is a 1-sided max spec.

8. ### _Zeno_Member

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I understand that, but I know of no specification that is bounded on BOTH sides. Generally, most GD&T is bounded on the lower end (negative numbers are impossible). Min and max are bounded on one side. Can someone give an example of something bounded on both sides?

9. ### MinerModeratorStaff Member

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I think Bob meant that you have a boundary plus a specification. His Roundness example would have a lower boundary of zero plus a maximum roundness spec.

10. ### orionNew Member

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We have to calculate capability of the process as customer request.

11. ### SunilTawaleNew Member

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As we know that Cpk=Cp=either of Cpu or Cpl in case of Unilateral Tolerances, measurement of the same is not relevant.
It's only indicative, in case your process mean is far away from boundary. This may help in monitoring process with Indicator Cpk (or Cp) if the process mean is shifted towards Boundary which is ideal situation in case of Unilateral Situation.

With Weibull distribution, the effect of Normal Distribution is not valid as it's basically for Non-Normal data.

Is there any other better indicator for process with Unilateral Tolerance to see effect of shift of mean or measure of improvements in the process?

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