Does anyone have any insight into how I can calculate the Cp and Cpk values for characteristics that only have a lower spec limit? Cp wants the tolerance divided by 6s and Cpk is the average of the process average subtracted from the LSL divided by 3s.

When I calculate Cp in this manner I get that Cp=2.94 and Cpk=0.52. I believe the Cpk value, but Cp is hard to believe because there are so many points that are out-of-spec in the process. Is the Cp this way due to no tolerance. Is there another way to calculate.

Does anyone else have any experience that would help me.

Thanks,
Jeff

There are statistics gurus here who can probably answer better, but if memory serves me you cannot have a Cpk for a single-sided lower limit spec. -- you can only have Cpl which is (mean - lower spec. limit) / 3 sigma.

I think this is right but will wait to see if someone can back me up on this....

Cpk is the lower of:

X-double bar-LSL / 3sigma (R-bar/d2)

or

USL-x-double bar / 3 sigma (R-bar/d2)

It cannot be used for unilateral tolerances. It's one of a few misconceptions: I think a couple more are:

-- Being estimated sigma, Cpk cannot be condfidently used to predict the process without at least ~ 1,000 subgroups of data
-- Widening spec limits improves Cpk but does nothing to improve the quality of the product
--I can submit a population of parts illustrating a Cpk if >2.0 (2 dPPB) and some of the parts will not function
--Cpk is only accurate if the process illustrates a state of control

Anyway, just rambling on now.........I am bored. Have a day and good luck !
:bigwave:

Cpk is also defined as | X double bar - NSL / 3 sigma |

Where NSL is nearest spec. limit. If there is only one specification limit, why wouldn't this be valid? We are using Cpk to help to understand the capability of the process to meet the specification requirements.

I think the problem comes in when there is a physical limit which causes the data to be skewed (non-normal). Looking at perpendicularity, it's physically impossible to have a value less than zero. The data will tend to be skewed away from zero. If this is the case, other methods must be used to determine the process capability.

Cp really is meaningless though, unless you have a tolerance range. When you calculated Cp, you must have put some number in for an upper limit just to be able to get a value other than infinity.

howste,

I believe that by definition (according to a cheat sheet from long ago I found) Cpk can only be gotten from a 2-sided tolerance -- as nobox says (with a few tweeks):

Cpk is the lower of:

Cpl = (X-double bar-LSL) / 3 sigma

or

Cpu = (USL- X double bar) / 3 sigma

But, IMO, for a 1-sided tolerance, Cpl or Cpu should tell you as much as Cpk for a 2-sided tolerance. Again, I'm no stat's guru, but this is as I remember it and what my old notes say. I didn't consult my Jurans...

Yes, it is due to unilateral tolerances, and also, try PpK for your process.

Al...

Definitely not a stats guru, but I would agree that you would use Cpl to see how capable your process is of making parts to the lower spec limit. ( or cpu for upper spec limit ) I have used these in PPAP submissions in the past & never had any problems with either customers or auditors.

Attached file may help in explaining :rolleyes:

First, thank to all for your insight, I really appreciate the help. Let me see if I have this.

I cannot use Cp because it uses a tolerance, and in my case I only have the LSL to work with. So I must use Cpl and determine how capable my process is of holding to that LSL.

Cpl = (x-double bar minus LSL) / (3 X (R-bar / d2))

However, I am not a stat guru and AIAG SPC manual says that Cpl is calculated as:

Cpl = (x-double bar minus LSL) / 3ô R-bar/d2

Is this the same calculation? :confused:

Yep, I think you have it FWIW. "Sigma hat" is estimated process SD which is rbar/d2 -- looks like they just forgot to explain that.

sigma = R-bar / d2

Cpl = (x-double bar minus LSL) / (3 *sigma)

or you can use autocorrelation factor (usefull for Individuals and moving range).

sigma = MR-bar / d2 * (1 /(1-r^2)^0.5)

but as howste said "the problem comes in when there is a physical limit which causes the data to be skewed"

In my opinion, use Cpmk (or the performance equivalent).

read this article, I tink is great (It's a must see).

http://www.scausa.com/capaqa.pdf

You can also transform the variable or use non-parametrics (median, percentile)

Thank you Mike S. and Darius. I appreciate your help. I will review the attachment Darius.

Now that I can confidently calculate the Cpl, I only now need to figure how to reduce the variability...:rolleyes:

Small steps though.

Originally posted by Darius
sigma = R-bar / d2

Cpl = (x-double bar minus LSL) / (3 *sigma)

or you can use autocorrelation factor (usefull for Individuals and moving range).

sigma = MR-bar / d2 * (1 /(1-r^2)^0.5)

but as howste said "the problem comes in when there is a physical limit which causes the data to be skewed"

In my opinion, use Cpmk (or the performance equivalent).

read this article, I tink is great (It's a must see).

http://www.scausa.com/capaqa.pdf

You can also transform the variable or use non-parametrics (median, percentile)
Darius,

I'm confused. I scanned part of your attachment and do not understand section 4. How can there be a Cpk calculated for a one-sided (upper-spec limit only)?

It says Cpk is unsuitable for a one-sided tolerance, which I agree with, but IMO it gives the wrong reason. It says example A and B both give the same Cpk while the parts in process B are much better. But Cpk -- by definition (Cpk = min of Cpl and Cpu) -- cannot exist for a one-sided tolerance -- it is intended for a 2-sided tolerance. You would use Cpu which would show that the parts in example B are much better than the parts in example A.

Statistics is difficult enough for me -- seeing stuff like this makes it even more difficult. JMO.

It said "The use of Cpk is not suitable for an S-type tolerance" but it sould said "Why the use of Cpk is not suitable for an S-type tolerance", I didn't wrote the article, but the ideas have great insight. I take it, as one of the few articles about that problem in an example way (easy to understand the point of view of the writer).

I my self found many cases where the Cpk (for one sided tolerance), gets better farter from the target because of the variation reduction (but the Cpmk is worse), even cases where all the data (from that set of data) is farter that the maximum of the set nearer from the target.

In most of the books or articles, said that in S-type tolerance, just use the one that can be calculated saying Cpk = Cpu or Cpk = Cpl depending of the spec limit that you have. Maybe could be a different way to tell the same thing: "Use the Cpu" or "Cpk = Cpu". I don't tink that matter, it's just nomenclature.

:confused: I tink that the calculus of capability-performance is important in order to find where we are, many practitioners said Cpk can be only calculated in stable state, others don't care about stability, others that said that you can not use any index at all because of the non normality of the data, and at the last group, like me, tink it as a mean to find if something change, agreed that if the process is not stable the values tend to fluctuate a lot, but I we chart the values (Cpk, ppk, Cpmk of different periods) in a control chart, as Wheeler said in one article on quality magazine the values out of the chart show a change in the process.

If Quality is get nearer from target and with less variation (IN THAT ORDER, Cpmk is better that Cpk because it take the target in account (Cpk take target as in the middle of the specs and in one sided spec the "target" of Cpk is lost).

:thedeal:

We have to use a process tracking spreadsheet from our customer for Cpk. You enter the upper and lower bounds, and the spreadsheet breaks it up into 10 bands. For bilateral dimensions (i.e. .250 lower and .260 upper bounds, it works as-is, but for unilateral dimensions, we had questions.

One of the characteristics we're measuring is perpendicularity, which has a lower bound of zero. Since Cpk takes the smaller result of the upper or lower bound, and the process is very much under control, the lower bound always drives the Cpk and as a result, generates the wrong number.

I considered modifying their spreadsheet to do Cpu, using just the upper bound, but the same thing can get accomplished by entering -.001 and .001 as the bounds, and never using the negative numbers. Since the sample points are never negative, the lower bound will never drive the formula, and you get an accurate Cpu number. Only drawback is you lose resoluton on the 10 bands, since four are "wasted" as negative numbers. This might not be technically the best way to do things, but everyone seemed to buy in on the idea.

We have to use a process tracking spreadsheet from our customer for Cpk. You enter the upper and lower bounds, and the spreadsheet breaks it up into 10 bands. For bilateral dimensions (i.e. .250 lower and .260 upper bounds, it works as-is, but for unilateral dimensions, we had questions.

One of the characteristics we're measuring is perpendicularity, which has a lower bound of zero. Since Cpk takes the smaller result of the upper or lower bound, and the process is very much under control, the lower bound always drives the Cpk and as a result, generates the wrong number.

I considered modifying their spreadsheet to do Cpu, using just the upper bound, but the same thing can get accomplished by entering -.001 and .001 as the bounds, and never using the negative numbers. Since the sample points are never negative, the lower bound will never drive the formula, and you get an accurate Cpu number. Only drawback is you lose resoluton on the 10 bands, since four are "wasted" as negative numbers. This might not be technically the best way to do things, but everyone seemed to buy in on the idea.


Your custoemr is requiring you to use a vanilla spreadsheet they developed that doesn't acknwowledge or allow for the practical realities of physics so you 'cheat' it to get a number that will make them happy. This just isn't statistical process control it's statistical terrorism. (your customer and those that perpetuate teh myths of a homogenous world that behaves in an exactly Gaussian distribution are the terrorists...)

The problem looks like, the process has a physical bound, and of course IMHO it's wrong to set the lower limit to that bound, and one sided Cpk is also wrong as I stated in other posts. Why don't try Cpm or Cpmk?, may be your ticket out.

If it is an automotive customer asking you to rubber stamp Cpk calculations on your data, you may want to direct them to AIAG PPAP 4th Edition:

2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center). When this is not true, using this analysis may result in unreliable information.

I love that section...:cool:

I have a question, how do you calculate Pp or Ppk if the standard deviation is zero?
For example, USL is 140, LSL 100, Standardard deviation is zero.

I have a question, how do you calculate Pp or Ppk if the standard deviation is zero?
For example, USL is 140, LSL 100, Standardard deviation is zero.

Welcome to The Cove Forums! :bigwave: :bigwave:

Standard deviation is ZERO??? That means there's no variation.
And that is impossible.....

Stijloor.

Standard deviation is ZERO??? That means there's no variation.
And that is impossible.....

Unless your measurement system has insufficient discrimination....

What kind of process are you getting these results from?:cool:

The factor is Time with 35 measurements all coming out to 115. So the standard deviation would be zero correct? So I guess my question is, what do you ask yourself if you see no variation for Pp & Ppk calculations?

The factor is Time with 35 measurements all coming out to 115. So the standard deviation would be zero correct? So I guess my question is, what do you ask yourself if you see no variation for Pp & Ppk calculations?

How do you measure "Time?"

Stijloor.

Its a problem given to me, so how time is calcuated is not part of the revealed equation.

Its a problem given to me, so how time is calcuated is not part of the revealed equation.

Is this some kind of a "homework" assignment, and you don't know the process?

To echo my Fellow Cover Bob, if not, what process is this measurement associated with? Again, what device is used to measure time?

Please keep in mind that any measuring device is subject to variation.

No variation means that the device is unable to differentiate between subsequent measurements.

Bob?

Stijloor.

From my prospective this is not a process with Zero variation this is a MSA issue, the instrument that is used to collect the information did not have the resolution needed to detect the variation.

Its a problem given to me, so how time is calcuated is not part of the revealed equation.

If time is a calculation, the issue may lie with the formatting of the equation. That is, it may be truncating or rounding the calculated result to an integer.

If it is picking up whole number time, with a spec range of 40 units, it should be OK (well over 10:1). If there is an GR&R issue, it should show up in the ndc. It may be that the sample was too small to show the variation, or if you have an automated controller set for 115, and it hits 115 every time, then with the discrimination required by your process it may very well show no significant variation. We know there is always variation, but there is no economic value if 115 is seconds and your tolerance is 100-140 going to milliseconds to search for it. You are capable, it exceeds 2.00 in that the calculation will be n/0 or approaches infinity. Darn capable for government work. :cool: