# Computing Cpk with out determining if my data is normal

#### kuyakut

##### Involved In Discussions
Hi Covers,

What would be the implications if I directly compute the Cpk with out determining if my data is normal. What should I use in computing using Minitabd - Stat >QualityTools >Capability Analysis >Normal? Between/ Within?.
I was just confuse because some of my costumers dont ask me to find out if my data is normal. Other costumers ask me to do normality test before cpk computation.

Kuyakut

#### Miner

##### Forum Moderator
Staff member
Cp and Cpk assume normality. If your data are not normal, Cpk will be incorrect. For example if your data were right skewed. Cpl would be understated and Cpu would be overstated. Customers that don't request it either assume that you already know, or they themselves do not know.

Use Capability Analysis > Normal if your data are normal. Use Capability Analysis > Nonnormal if your data are nonnormal. Between/Within is used more as a diagnostic to determine where the variation comes from.

#### kuyakut

##### Involved In Discussions
Thanks Miner,

I always do normality test when ever I compute the Cpk. But with recents process capability report that I do. The costumer suggested not to do normality test and straight away compute the cpk.

Kuyakut.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
unfortunately many Customers don't really understand what they are asking for...the fact that they are even askign for Cpk is a sign that they are just looking for a check the box action. by suggesting that you not perfrom a Normality test they are simply confirming it.

for your own sake, if you must supply a Cpk value, always check for Normality.

As for the within/between choice it really depends on your customer. In general Cpk is commonly used to mean long term capability and is calculated using the total standard deviaiton of all of the values. (within AND bewteen).
Since your Customer is suggesting that you not do the Normality test I would assume that they are really looking for this long term capability number.

#### bobdoering

Trusted Information Resource
unfortunately many Customers don't really understand what they are asking for...the fact that they are even askign for Cpk is a sign that they are just looking for a check the box action. by suggesting that you not perfrom a Normality test they are simply confirming it.
Amen!!! Rubber stamped again!!

#### kuyakut

##### Involved In Discussions
My knowledge of statistic is only limited. Just a few more follow up question..

1. If the data is non normal , normally the process capability graph in the minitab will indicate only ppk not cpk . Am i correct?
2. You base your normality data check via p - value?
3. If my cpk is low ie. 0.88 does this mean my data is not normal or just my data's are not enough to compute cpk. Or my data is skewed to left or to right.

Thanks again,

Kuyakut

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
1. If the data is non normal , normally the process capability graph in the minitab will indicate only ppk not cpk . Am i correct?
No. (at least it shouldn't - I'm not a minitab user) Normality has nothing to do with the calculation of Ppk or Cpk.

Please note that the value your Customer is most likely looking for is the Ppk value. It has become common language to ask for Cpk when actually asking for the value as calculated by Ppk.

2. You base your normality data check via p - value?
yes.

3. If my cpk is low ie. 0.88 does this mean my data is not normal or just my data's are not enough to compute cpk. Or my data is skewed to left or to right.
NO. it means your process variation is such that there are parts outside the spec limits. this can be from a Normal distribution or any other type of distribution including skewed distributions.

IF you assume Normality when your Process isn't Normal you may get a lower Ppk value than your process actually has if it is not Normal. ALWAYS plot your data in a time series chart and look at the actual distribution vs the spec limits (histogram).

I would also recommend that you read up on Process Capability indices here at the cove (there are several good links below and a simple search will yield you many threads addressign this topic) and then perhaps buy a good book on the topic.

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