# CpK in Minitab when 0.0 is the lower spec limit

#### Stamping QA Manager

##### Registered
I am performing a capability study using Minitab. The dimension is a True Position with a specification of 1.5. If I list 0.0 in the lower spec limit and 1.5 in the upper spec limit, I get a 1.31 Cpk. If I leave the lower spec limit blank, I get a Cpk of 3.40.

My data consists of 50 measurements. The results are the same if I consider the 50 as a subgroup of 1 or 5. My Max is .63, my mean is .42, my min is .21

Which result would be correct; 0.0 in the LSL or leave it blank?

#### Miner

##### Forum Moderator
Staff member
Re: CPK Question Using Minitab

Looking at this from a practical perspective, Cpk is a measure of how much safety margin you have before the customer has a problem.

In the True Position scenario, 0 is not a specification, it is an artificial boundary created from the conversion of a Cartesian coordinate to the absolute value of a polar coordinate. Zero is the ideal value from the customer's perspective, so leave the lower spec blank.

#### Stamping QA Manager

##### Registered
Re: CPK Question Using Minitab

Thanks for the reply Miner. I just don't understand how Minitab Cpk calculation is so different depending if the LSL is left blank or 0.0 is added.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: CPK Question Using Minitab

When you tell Minitab that 0 is your lower specification, but do not check the boundary box, Minitab assumes that a value less than 0 (less than your LSL) is possible. So it assigns a probability of having a value less than 0 which is impossible. So you really have a one-sided specification of 1.5 since it is not possible to get values below 0.

Does that help?

#### Stamping QA Manager

##### Registered
Re: CPK Question Using Minitab

That makes perfect sense. Thank you.

#### Miner

##### Forum Moderator
Staff member
Re: A question on CpK in using Minitab when 0.0 is the lower spec limit

In addition to what Steve stated, Minitab provides the smaller of Cpk upper/Cpk lower. Since your average is closer to zero than to 1.5, Minitab will report the Cpk lower. When you leave the LSL blank, Mintab does not calculate Cpk lower and reports CPK upper.

#### Stamping QA Manager

##### Registered
Re: A question on CpK in using Minitab when 0.0 is the lower spec limit

Thanks Miner!

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
Re: CPK Question Using Minitab

Looking at this from a practical perspective, Cpk is a measure of how much safety margin you have before the customer has a problem.

In the True Position scenario, 0 is not a specification, it is an artificial boundary created from the conversion of a Cartesian coordinate to the absolute value of a polar coordinate. Zero is the ideal value from the customer's perspective, so leave the lower spec blank.
Actually, Cp is a measure of how much safety margin you have before the customer has a problem. Cpk is a function of how well centered the mean of the data is. Since the optimum value is not at the center, Cpk is not a correct index. Using "half an index" (either Cpu or Cpl) answers a totally different question than the original point of calculating Cpk. For automotive customers, this is clearly spelled out in the PPAP handbook - that Cpk is to be used for normal distributions with the target centered in a bilateral specification. Otherwise, the results may be unreliable. In fact, if you are forced to use this nonsense, a more accurate approach is to transform the data using the correct original distribution, not the "half an index" calculation.

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