# Cp, Cpk, Dpm, or other? Diameter of a Hole - Non-Normal Distribution

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#### mattia.oliosi

I have data about a process. this data are about a diameter for a hole. The process doesn't have a normal distribution. I have to fix goal for a project. What metric can I use for goal? Cp and Cpk? Dpm? Yield? And how can I calculat this metric?

TAL

Mattia

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#### Darius

Re: Cp, Cpk, Dpm, or other?

if the % of defective is high enough, you can use Dpm or Yield.

IMHO, If is small, you can try Cpm or Cpmk (altho they take in account as Cp or Cpk a gaussian distribution, they are robust for non gaussian distributions), or use a non parametrical capability index or transform using box-cox transformations.

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#### mattia.oliosi

Re: Cp, Cpk, Dpm, or other?

What do you mean for Cpm or Cpmk?

My data set is not trasformable. I try with mintab software.

Mattia

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#### Darius

Try search on the forum or on the net Cpm +"capability index"

you can see a discusion here

Need help / feedback on Xbar/R charts and Cpk/Ppk applicability - Assemblies

but for short Cpm or Cpmk uses the difference of the mean to the target value to punish the value as you go farther from the target. Some people name this capability index as Tagushi Capability index as the formula is based on the Tagushi's loss function.

I my self found cases where a period of time because of low variation the Cpk looks better against another with bigger variation but on the target. As Tagushi said more or less "To the target with low variation", but first "TO THE TARGET".

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#### mattia.oliosi

I find a index. Cnpk is a index for no-parameter. It's the minimun between (USL-median)/(percentile(0,99865)-median) and (median-LSL)/(median-percentile(0,00135)-median).
I think It's the wright one for my situation.

TAL

D

#### Darius

Agree; as I told you non parametrics is a good option for non gaussian distributions (maybe the best).

Tagushi's index can be a middle point between traditional capability index like cpk/cp and their non parametrics conterparts. And I have seen articles where comparisson between capability indexes show a better behabiur on box-cox transformations (but as you said, it does not apply in your case).

Good luck.

J

#### jospe.at.liu

I have data about a process. this data are about a diameter for a hole. The process doesn't have a normal distribution. I have to fix goal for a project. What metric can I use for goal? Cp and Cpk? Dpm? Yield? And how can I calculat this metric?

TAL

Mattia

My spontaneous reaction is that your data should logically resemble a normal distribution. Hole diameters usually fit normal distributions quite well. What is your basis for saying that your data is non-normal? Have you checked the data for special causes of variation? I would make three plots to determine this:

1. A time series plot for average or individuals (depending on the process)
2. A time series plot for variability (range or standard deviation), alternatively moving range if individual values are used.
3. A normal probability plot

When you have made these plots, you should be able to find some clues as to why you have a non-normal appearance in your dataset.

M

#### mattia.oliosi

My spontaneous reaction is that your data should logically resemble a normal distribution. Hole diameters usually fit normal distributions quite well. What is your basis for saying that your data is non-normal? Have you checked the data for special causes of variation? I would make three plots to determine this:

1. A time series plot for average or individuals (depending on the process)
2. A time series plot for variability (range or standard deviation), alternatively moving range if individual values are used.
3. A normal probability plot

When you have made these plots, you should be able to find some clues as to why you have a non-normal appearance in your dataset.

My distribution is non normal. I use minitab 15 to check the time series and the X-R chart. Than I check that p-value for a normal distribution (using AD-test) is loss than 0,05.

I use the equation for non normal distribution that uses dpm to give a Cp value.

TAL

Mattia

J

#### jospe.at.liu

I think you will learn more about the behavior of the process through looking at a normal plot as well. Special causes of variation can make the process seem non-normal. You could also check for autocorrelation in the data set. That will also distort the distribution.

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#### Geoff Withnell

My spontaneous reaction is that your data should logically resemble a normal distribution. Hole diameters usually fit normal distributions quite well. What is your basis for saying that your data is non-normal? Have you checked the data for special causes of variation? I would make three plots to determine this:

1. A time series plot for average or individuals (depending on the process)
2. A time series plot for variability (range or standard deviation), alternatively moving range if individual values are used.
3. A normal probability plot

When you have made these plots, you should be able to find some clues as to why you have a non-normal appearance in your dataset.

Hole diameters usually fit normal distributions quite well?! I have not found this to be the case. There is usually a hard lower limit of the drill, punch or whatever tool size to the the distribution, with a tail to the right that can be either long or short depending on the process. Hole size is usually the LEAST normally distributed of mechanical size dimensions.

Geoff Withnell

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