How to calculate Cp and Cpk for 'normal' spec and unilateral tolerance | Unilateral Cpk revisited

[@mariusr79]

Congratulations, Tom! This is one of the best explanations I ever seen

[@TomMentink]

Thanks Marius, that’s a wonderful compliment. I’m happy you liked it and found it useful.

[@TheExcelEngineer]

Great, now you can go to the next level and explain people how to calculate CPK for SPEC with MMC Modifier!

[@sariddle]

A very nice clear and concise video, just what I was looking for. Great job

[@TomMentink]

Thanks for sharing that, it always puts a smile on my face to hear to somebody receives value from my videos.

[@will5577]

How is the Cpk calculated when I have a target value of 0 and the max allowed is 50.

[@TomMentink]

@@will5577 first off: do you have a lower bound too? (-50 maybe?) Or is 0 the minimum physically possible? In the first case you have a ‘normal’ bilateral tolerance - see if the mean is closer to the upper or lower spec limit and divide the distance between mean and closest specification limit by 3xStDev. If 0 is a pure physical level and general target point, that is, you only have an USL of 50, then you have a unilateral tolerance and always take the difference between mean and 50 and divide that by 3xStDev.

[@teddz2k4]

Question might be late. Is it possible to calculate process capabilities from knowing the nominal dimension of a part? Lets say if a nominal diameter of the shank is .050 with a tolerance +/- .002? I've been trying to see if its possible to even start doing and process capabilities on it before the part even run.

[@TomMentink]

No, nominal dimensions are needed but it’s not enough: Capability is about the VARIATION of the process vs the range of the specifications. So you need to measure multiple actually produced parts to determine the standard deviation (one of the measures of variation) of your measure - in your example you’d want to know the SD of the diameter. For Cp you’d calculate 0.004 / (6 x that SD of diameter). (That 0.004 is the range of your tolerance, so from -0.002 to +0.002) For Cpk we also look at the center of the process, so in stead of just taking the range between lower and upper tolerance limit, we specifically take that limit to which our actual process average is closest - often written as MIN(USL-X; X-USL). Which we then divide by 3 x SD, because we’re only looking to one side: MIN(0.048-X; X-0.052) / (3 x SD). So you see, the standard deviation of the products coming out of the process is needed - and you can only really determine that by measuring those products. And for the most commonly used capability metric, Cpk, you also need to know the actual average of produced products. You can estimate the Cp (so without the centering component) if you’ve run very similar parts on that line before and have a good estimate of the variation in diameters that this machine will produce - you’d use that other product’s SD of diameter to do the calculation. But this will always just be an expected Cp, and you won’t be able to determine Cpk.

[@teddz2k4]

@@TomMentink Thank you so much, this was amazing helpful. Makes sense when my boss says if the tolerance is over the +/- .001 the cpk wouldn't be near the value of 2 but was wondering how he coming up with these calculations without data. But after you said that compare other possible run that looks the same. I think I can get the Standard deviation from those. How do I give you a thousand likes because this was really helpful.

[@narendrabogala7342]

How to decided cpk value 1.33, 1.67 and 2.0 any reasons are there

[@TomMentink]

Usually it's decided by your customer, but sometimes your own salesforce would also like to mention specs with a certain Cpk level. A higher Cpk gives more certainty that you won't get batches with many defects (parts outside tolerance limits). It has to do with the assumption that batch averages will vary over time and that the supplier's quality system won't pick up on every process shift, especially if it stays within 1 to 1,5 standard deviations (SD's) from the mean. A Cpk of 1.33 gives you 1 SD of wiggle room, a Cpk of 1.5 gives you 1.5 SD's wiggle between the real center of the tolerance + 3 SD's (99.7% of produced parts fall within +/- 3 SD's) and the tolerance limit. For a very nice video explanation, hop over to Paul Allen's channel (@paulallen5321) and check out his video: kzbin.info/www/bejne/o36ZdqyDq9t0gc0

[@leowang4078]

Great explanation for CP&CPK，i am a little confused with the calculation of CPK of geometric tolerate like position，is it possible to make the control chart for these Spec, need you kindly explanation

[@TomMentink]

Cpk calculations assume a single dimension measuring unit, geometric is at least two dimensional (and even that doesn’t always describe enough detail) - that’s why it’s difficult to use regular Cpk for geometric targets. You could go for Cpk on the X axis value and a second Cpk on the Y axis. Alternatively, you could use distance from the center as your measuring unit; that would be a unilateral measurement (0 being the ideal). The first option wouldn’t nicely correct an offset on both axes, as that would more outside of the middle than either of the two individual axes, the second option wouldn’t tell you in which direction there is a deviation. So they’re both not ideal, but depending on your process, they might give you the info you need.

[@janmarinic3228]

Very interesting case, indeed. Could we consider as ideal solution for this example deviding value by 2 ? E.g. for position 0.6 is LSL=-0.3 and USL=0.3 ? Based on it could be simple to calculate Cp, Cpk, right ? Thank you very much for your feedback

[@narendrabogala7342]

How to calculate singel side specification?

[@TomMentink]

Great question: we talk about specifications and tolerance limits a lot in Cpk, SPC, Sigma levels, etc; but we don't often go into how to set those limits. The short answer is: you don't. Specifications are decided by your customer or come from legal regulations. But of course your own technology and/or quality teams have a lot to say about the specifications for your own products, and it's common practice that the producer/supplier proposed specifications for their own products and buyers choose what they find acceptable. Single side specifications (unilateral tolerance), however, very often come from regulations. This is because these are usually linked to a quality statement. The producer decides how they want to describe/market their product and the specifications come from that decision. Examples: "This bottle contains 2 liters of soda" the food and drug authority will demand that you fill those bottles with at least 2 liters, but the FDA doesn't really care if you overfill them. (in Europe, you can underfill individual bottles, as long as each hour of production is at least 2 liters on average, but that's another video 🙃) "Alcohol-free beer" can contain up to 0,5% alcohol, but anything over that limit cannot be labeled alcohol-free. "This watch is water-resistant up to 50 meters" you'll have to prove that your watches can stand at least 5 ATM of pressure without letting water in (it's OK if your watches can handle more pressure, just not less).