Need Help Calculating and Implementing Cs - Wright's Index

S

SPC_Newbie

Hello,

I've played with some data in a speadsheet but have no idea if I've even come close to to calculating Cs properly.

I also don't know what a good number looks like - woul it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?

Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.

I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)

Attached is my worksheet. Am I even close??

I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:


SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.
 

Attachments

  • Cs_andCpmk_Calcs_1st_try.xlsx
    16.4 KB · Views: 100
  • Cs_andCpmk_Calcs_1st_try.xls
    39.5 KB · Views: 104

Stijloor

Leader
Super Moderator
Hello,

I've played with some data in a spreadsheet but have no idea if I've even come close to to calculating Cs properly.

I also don't know what a good number looks like - would it be similar to Cp, meaning am I looking for a 1.33 or better? How would we calculate control limits?

Does anyone have a spreadsheet that does the calculation? I'm very interested in any known test data and results someone might have so I can prove out my sheet/calculations.

I'm using the calculation: Cs = min{USL - Mean, Mean-LSL}/{3*[sigma^2+(Mean-Target)^2+abs(3rd_Moment/sigma)]} (thanks Darius!)

Attached is my worksheet. Am I even close??

I kind of put it together leveraging information from a you tube video as this formula is my first introduction to moments/skew/kurtosis:


SIDE NOTE: I've searched for an article I had been pointed to before (EVALUATION OF PROCESS CAPABILITY INDEX FOR NON-NORMAL DISTRIBUTIONS) but have not turned it up.

A quick bump.

Can someone help?

Thank you very much!!

Stijloor.
 
D

Darius

Well, close enought :D......

I changed a little your file, sorry a little bit messy, but it show the idea.

Control limits, are a different issue.

I try to show you a way, it's not documented:nope:, but I think is a handy way to do it.:bigwave:
 

Attachments

  • Cs_andCpmk_Calcs modif.xls
    47.5 KB · Views: 118
S

SPC_Newbie

What a fantastic reply, I know it took some time to evaluate and correct my sheet - I was really stuck - Mil Gracias!

I'm going through it now, trying to make sure I understand. It'll be a little while before I know what I need to ask more about.:tg:

Thanks Again!!
 
S

SPC_Newbie

OK, Partially digested!!

I have a big question or two, a small one and an observation.

First Big One: I was under the impression that Cs is an index I can use that rewards values closer to the target, in my case 0 (think flatness, parallelism, etc). I simply raised my USL and expected that my Cs would be better. It did not change. I see the the third moment/sigma doesn't take into account USL (near as I can tell). I'm pretty sure this third moment/sigma value is referred to as skew and is what differentiates Cs from Cpmk. Also, looking through the equations, where USL is used, min(USL-mean, Mean-LSL), it is not coming up as the minimum value so is not used. What am I missing?

The next kind of Big one: How/why did the values .68 and .95 get chosen in the DS_up and Ds_dwn calculations?

Small question: what does np stand for in the terms np_UCL and np_LCL

Observation: Kind of cool how the moments are pretty much calculated like a typical Standard deviation, the difference being we don't take the SQRT of the value.

Thank you!
 
D

Darius

“I simply raised my USL and expected that my Cs would be better. It did not change. I see the third moment/sigma doesn't take into account USL (near as I can tell).”
:2cents:Well maybe, just because, the minimum value is domed is this case to be depending from the LSL, maybe, if is no possible the 0, it should not be considered. I will do some tests and tell you my conclusions.

:popcorn:0.68 and 0.95 are the values for “bell shaped” distribution, 68% of the data are between +/- 1 sigma, the 95% of the data are between +/-2 sigma. I know is used in this case for non parametrics (it can be called half-parametrical method).:lol: The method I outlined take the distribution in two halves (using the median), and the ds_up is calculated as it was a normal distribution but taking just one side in account at the time (for ds_up the upper side, for ds_dwn the lower ones). It may sound weir but I worked with it and found it to work fine for me, I saw sometime ago a method that used the percentile for the percentage at +/- 3 sigma to determine the control limits (ones again …, a half-parametrical method), and it can be done that way, but for data with many “outliers”, found this method more robust (the outliers doesn't have any effect). As I told you is a method I tested (and created), you can simulate data that behave as gamma and work fine. I even use it for outlier detection on a "modificated chauvenet" (by me),method.

np in this case, sorry…, is non parametrical.
 
D

Darius

As I spected, as other capability indexes, it take the minimum of upper or lower, but in your case there not seem to be a lsl because is a "natural limit"

You can change the file in two ways (both gave the same results)
first:
clear LSL => d11
change d14 to

=+MIN(IF(D10="",999,D10-D6),IF(D11="",999,D6-D11))/(3*(D13^2+(D6-D12)^2+N10/D13)^0.5)

or

Second:
=+(D10-D6)/(3*(D13^2+(D6-D12)^2+N10/D13)^0.5)

And enjoy your self, changing USL.

Take your time, we will be here...
 
S

SPC_Newbie

OK Darius, I will give these a try and see how they look.Thanks for encouraging me that I still have support :thanks:.

Cheers!!
 
S

SPC_Newbie

:applause:Works great! Thank you very much!!

So now I can see my Cs numbers improving as I increase USL, how do I know what is a good number? What I'm trying to say is what number(s), if any, am I aiming for - do we have a threshold or target Cs?

Getting so close!!
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
Attached is some additional information, if it helps understand what you are looking at.
 

Attachments

  • cs.docx
    92 KB · Views: 97
Top Bottom