HI Guys,
I am new here. I was wondering if you guys may be able to help me. I am trying to find some information on how to calculate process capability using Mode Method and Percentile Method. So far I have found out that for the mode method these are the following formulas:
Cp = USL-LSL/[3*sigma1)+(3*sigma2)]
Cpk = min{[(Ts-xbar)/(3*sigma2)];[(xbar-Ti)/(3&sigma2)]}

and the formulas for percentile method are:
Cp = (USL-LSL)/(Up-Lp)
Cpk = min{[(USL-M)/(Up-M)];[(M-LSL)/(M-Lp)]}

But what does Ts and Ti stand for?
Where does sigma1 and sigma2 come from?
I understand how the percentile method, but I cant seem to find any information on how to calculate Pp,Ppk using Percentile Method?
Also I didnt find any information on how to calculate Pp, Ppk using Mode Method.
Any help is greatly appreciated

Thanks in advance.

Welcome to The Cove! :bigwave:

Is this a class assignment?

My books don't talk about a Ti or Ts value, but NIST describes T as target value here (http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm).

NIST also has pages of related discussions here (http://www.itl.nist.gov/div898/handbook/pmc/pmc.htm).

Statistics isn't my strongest point, so anyone else please feel free to chime in.

But what does Ts and Ti stand for?
Where does sigma1 and sigma2 come from?
I understand how the percentile method, but I cant seem to find any information on how to calculate Pp,Ppk using Percentile Method?
Also I didnt find any information on how to calculate Pp, Ppk using Mode Method.



Hello,

I will try to answer ... But i think that statistical expert will come soon

1. Ts is your upper tolerance (Also known as USL) and TI is your lower tolerance (also know as LSL)
2. From my documentation the mode method could be use when the distribution is "non-symetric". So this is your case.
In fact, you have to determine the 2 normal distribution for your distribution. This like the folded normal distribution (See a thread recently)

Sigma1 is the standard deviation for the left normal distribution : That is to say that you have to mirror on the right the left distribution to have a normal curve and then you will find the Sigma1 for that normal distribution.

Sigma2 is the standard deviation for the right normal distribution.That is to say that you have to mirror on the left the right distribution to have a normal curve and then you will find the sigma2 for that normal distribution.

You could look at the attachments for an example
I hope this will help you enough.

Hi Guys,

Thanks for all your replies. But I am still confused as to how I am supposed to go on about this. I have attached the histogram. Could you please have a look at it and let me know if I am on the right path and correct in using the Mode Method. If not, I still am very interested in understanding it.

Currently I am using the Statistica software to help me with this.
l.malaspina - thanks for clarifying what sigma1 and sigma2 stand for. This may be a stupid question but how do I try to find out the sigma1 and sigma2?

Once again, thank you for all your help

First, your histogram really lacks much resolution to verify a distribution. Secon, what is the process? Is there any time order data (run chart) avaialble to analyze the process? :cool:

The histogram resolution (Min-Max) is bad.

You need to change the min and max to realy see the distribution, unless the measurement equipment doesn't has a good resolution and you are obtaining just 2 values.

If you want something, you need to post your data.

Sigma1 and Sigma2, as I understand them are Standard deviation estimate for the distribution upper and lower bounds, so looks like you have equation (Cp) for non normal distribution. The Cpk doesn't reflect Sigma1, so, looks like a typo or from different source.

Should be

Cpk = min{[(Ts-xbar)/(3*sigma2)];[(xbar-Ti)/(3&sigma1)]}