Can Cp and Cpk be zero?

[Rajesh RS]

I was asked this in an interview once.

Can Cp and Cpk be zero? If yes, what could this signify?

Thoughts?

PS: Based on the definition of Cp and Cpk, I suggested that you'd need infinite standard deviation (random process) or USL = LSL. The latter would suggest that the process in question doesn't have a range of specifications, but one target only. I never found out whether my answer was correct (didn't make it through the interview ).

 

[t.PoN]

I think you already answered your question:

1. a product or process with zero tolerance specification (i can't think of any - not even aerospace or medical industry) would suggest that you will have a Cp as zero as long as you have variation within your process.

2. a process that is completely out of control and have a huge variation compared to process/product with tight specification would give a Cp not zero but close to zero.


theoretically: yes, but in practice: No

 

[Bev D]

Correct that Cp cannot be zero. unless there is no tolerance; USL=LSL

however Cpk can be zero if the average lies on one of the spec limits...
Cpk goes from +infinity to -infinity.

 

[Wilderness Woody]

If the process mean equals the lower spec limit, then numerator is zero and it does not matter what the standard deviation is since zero divided by anything is still zero. If the process is further out of control, then it could go negative... however, these conditions break the assumption that the process is actually under control. Control must be met first, then measure, then analyze. Any process in control (meeting control limits within spec limits) is incapable of having zero or negative Cpk.

 

[Bev D]

however, these conditions break the assumption that the process is actually under control. Control must be met first, then measure, then analyze. Any process in control (meeting control limits within spec limits) is incapable of having zero or negative Cpk.

Would that it were...but the only stipulation is that the process be in control. in control doesn't mean capable; it doesn't mean in spec. I have many stable on control processes that are incapable. sometimes even horribly so.

yes a stable process that is horribly incapable is undesirable but they do exist and you can calculate the Cpk index...

 

[Darius]

PS: Based on the definition of Cp and Cpk, I suggested that you'd need infinite standard deviation (random process) or USL = LSL. The latter would suggest that the process in question doesn't have a range of specifications, but one target only.

right USL = LSL, you have just the Target

but if you have a random process, you will still have a not infinite deviation, infinite variation seem to be like trying to put an electron whenever in the galaxy (and still is not infinite) without any target at all, the target is something that increase the likehood of an event in a predectible way.

USL=LSL, the interesting and possible event to happen is variation =0, the value of Cpk or Cp will be undetermined, you can say infinite, but 0 at the same time, you can't move because if you move you are out of specs (Target), if the measure didn't change in that period of time, you will be variation 0 and Cp=Cpk=0, Cpk can't be greater that Cp.

to add a good video
division zero by zero
note: IMHO the answer could be 1 and 0, you are filling the full range of variation and centered (cp=cpk=1), but you are at the spec limit so (cp=cpk=0)

 

[t.PoN]

USL=LSL, the interesting and possible event to happen is variation =0, the value of Cpk or Cp will be undetermined, you can say infinite, but 0 at the same time,

If USL = LSL, that doesn't mean the variation in your process is equal to zero!

SL ,specification limit, simply means the requirements for the process/product. This could be set from external party (Customer, or ISO Standard requirements).
you may still have variation in your process

 

[Darius]

If USL = LSL, that doesn't mean the variation in your process is equal to zero!

SL ,specification limit, simply means the requirements for the process/product. This could be set from external party (Customer, or ISO Standard requirements).
you may still have variation in your process

of course not
but to have cpk=cp=0 yes

The topic of this tread is how to...?, Many people think that a tool like a hammer (cp, cpk) can be used for anything (the instance of critically non-normal distributions), but you get results that defies the logical thinking.

Wilderness Woody is right about that anything multiplied by zero is 0, so cp=0 and the variation could be any number, but to have cpk=0 you will need to be centered on spec. so LSE=LIE was what I said about the question

But I added the case of what if variation= zero , if you take in account the behavior of cpk (if the mean is the spec limit cpk=0) and that cp can't be smaller than cpk, and if the math rule of anything multiplied by zero is 0 is applied (lse=lie) you can conclude that cp=0. but at the same time cp=1, because you are filling the full range of the specs, 0/0 is a case where you can conclude 0/0=1 (the video) and also 0/0=0.

 

[t.PoN]

Oh, i don't think ooops would cut it?

 

[Joelbear5]

If LSL = USL, then the measurement is defined as non-parametric. Cpk and Cp relies on the assumption that the measurement follows the Central Limit Theorem and has a Gaussian/Normal Distribution. Non-parametric values do not follow this, so one should not measure the process capability with Cp or Cpk. It's the wrong analysis equation.