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# Hello Fellow IE's: Had a question 3

## Hello Fellow IE's: Had a question

(OP)
Hello Fellow IE's:
Had a question regarding data that appears to be somewhat bell-shaped curved, but I do not recall if there is a definite calculation that will tell me whether or not the population follows a normal distribution.  I am looking at starting SPC at my site on our sortation system (Rapistan)and I want to begin by looking at CP/Cpk, Pp/Ppk.  I know the formula changes for Cp's and Pp's if it's non-normal, but before I dig around for non-normality formulas I want to ensure that I do not have a normal distribution.  I am evaluating numbers of sortation errors vs case volume.  Thanks for your help.

### RE: Hello Fellow IE's: Had a question

3
Does the distribution follow the 68-95-99.7% rule?

Normal density curves satisfy the following property which is often referred to as the Empirical Rule.  Almost all values lie within 3 standard deviations of the mean for a normal distribution.

68% of the observations fall within 1 standard deviation of the mean.
95% of the observations fall within 2 standard deviations of the mean.
99.7% of the observations fall within 3 standard deviations of the mean.

*************************************************

Also, in a normal distribution, the mean, median, and mode are equal so that is a quick test of normality.

*************************************************

Look at step two from:

http://www.netgm.com/tools/useful_stuff/process_capability.html

*************************************************

Remember, large sample theory says basically that the larger the sample size, the closer one approaches a normal distribution. See: http://www.stat.sfu.ca/~lockhart/richard/450/99_3/lectures/13/web.html

*************************************************

http://ce597n.www.ecn.purdue.edu/CE597N/1997F/students/michael.a.kropinski.1/project/tutorial
http://www.stat.wvu.edu/SRS/Modules/Normal/normal.html
http://davidmlane.com/hyperstat/normal_distribution.html
http://mathworld.wolfram.com/NormalDistributionFunction.html
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661

### RE: Hello Fellow IE's: Had a question

(OP)
Thank you Leanne for your help.  Your feedback will definitely help me immensely.  Take care.

### RE: Hello Fellow IE's: Had a question

(OP)
Leanne,
On the first link you gave me it shows five steps to calculate process capability.  I am confused about one thing though.  My data showed that it was non-normal so I went ahead and transformed it by grouping the data n=109 samples into 3 groups, took the average, and calculated the Z value of the transformed data and of course the transformed Z plot was a straight line since averages always have a normal dist. In order to calculate my process capability now do I have to calculate the USL and LSL, X-bar, and std. dev. using just the 3 averaged data points or the 3 transformed Z values in order to come up with Cp and Cpk? or did I transform it just to graph which it wouldn't make sense cause I still need my Cp calculation. Please advise the website is not clear.  Thanks.

### RE: Hello Fellow IE's: Had a question

calpoly, let me see what I can dig up. Most of my stat books are about 1200 miles away. I'm not sure what I have here & it's been a long time since I did any CpK/Cp calculations (I only have so much RAM these days - if I don't use a technique daily, I have to look it up.)

Do you have any SPC books? I have the Pyzdek book somewhere, but I'm not sure if it's with me here or in Texas. I'm going to be offline tomorrow - have to drive up to Chi-town to pick up DS' "new" car so it may be a few days.

In the meantime if you have a time crunch, don't wait on me, hit a library and see what you can find on SPC.

### RE: Hello Fellow IE's: Had a question

calpoly, there is a programm you may be know, it's called Arena, you have to give in the data in a matrix, WordPad or Excel, and than when you do the Imput Analyzer, in Arena,  and than the Fit All solution it tells you which is the right distribution, it show you also the grafic.

AxelCS

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