# CPK and Normality

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- This topic has 10 replies, 3 voices, and was last updated 2 years, 6 months ago by Robert Butler.

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- January 28, 2018 at 1:03 am #55928

Karim MohsenParticipant@feodor85**Include @feodor85 in your post and this person will**

be notified via email.Hi,

I am new in six sigma and i need your help,

i have a data of a process when i test its capability i found the cpk = 1.01 but when i test its normality i found the P-value = 0.04

is this reasonable? and is there a relation between the CPK and the normality of the process?

And how do i have good CPK while the process is not normal?0January 28, 2018 at 6:39 am #202189

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.The Cpk calculation assumes data normality. If your data is non-normal and if you have done all of the things you need to do to make sure that the data from the process is expected to be non-normal (for example, this happens all the time with processes with natural lower/upper process bounds) then you will have to use one of the methods for calculating Cpk for non-normal data.

I would recommend borrowing Measuring Process Capability by Bothe from your library (inter-library loan is your friend) and reading Chapter 8 which deals with this issue and shows you what you need to do.

0January 28, 2018 at 6:44 am #202190

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.Sorry about this – I hit send too quickly – when I mentioned checking the data I meant to add a comment concerning data plotting. If all you are doing is dumping data into a program and hitting run then you are making a big mistake. You really want to look at the data on a normal probability plot and also as a histogram. One thing that can easily happen is if you have either too little or too much data, even from a perfectly normal data set, it is easy to have a situation where one or more of the normality tests will indicate a failure with respect to a test for normality.

0January 28, 2018 at 12:34 pm #202192

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.and think of a time series chart for insight

0January 28, 2018 at 11:40 pm #202193

Karim MohsenParticipant@feodor85**Include @feodor85 in your post and this person will**

be notified via email.Hello Robert,

Thanks for your reply and let me share with you some of my data information

1- my sample size is 30 samples

2- all my data i have got is within the specification limit 14.9 +/- 1

3- I put my data in the control chart I-MR chart to check if there is any special causes or not and the result is that there is no any special causes

4- The P-value I got is 0.04 (left skewed)

5- The CpK i got is 1.01

6- As my data is not normal i test 1-sample wilcoxon test and i got the following :

Confidence

Estimated Achieved Interval

N Median Confidence Lower Upper

s.c 30 14.70 94.9 14.60 14.80Test of median = 14.90 versus median ≠ 14.90

N for Wilcoxon Estimated

N Test Statistic P Median

s.c 30 24 22.5 0.000 14.70Could you help me to judge on this

0January 29, 2018 at 5:21 am #202196

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.What does a plot of the data look like? Plot the data on both normal probability paper and as a histogram.

Left skew would suggest a physical lower bound on the right – is this the case?

If you can answer these questions and perhaps post the plots to this forum then I or someone else should be able to offer more in the way of suggestions

0January 29, 2018 at 6:15 am #202197

Karim MohsenParticipant@feodor85**Include @feodor85 in your post and this person will**

be notified via email.here it is the plot of the data

0January 29, 2018 at 6:38 am #202198

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.You didn’t provide the probability paper plot but if indeed your process does have a physical upper bound of 15 (you will need to check this to make sure – if all you are looking at is a truncation of the distribution due to lot selection based on some internal/external spec then you will need to find the missing data and rerun everything) and, as far as you know it is in control then you should take your data, plot it on normal probability paper and identify the .135 and 99.865 percentile values (Z = +-3).

The difference between these two values is the span for producing the middle 99.73% of the process output. This is the equivalent 6 sigma spread. Use this value for computing the equivalent process capability. As I mentioned in an earlier post Chapter 8 in Measuring Process Capability by Bothe titled “Measuring Capability for Non-Normal Variable Data” has the details. It is also my understanding that Minitab has this feature as part of its program so if you have access to that package you can let the machine run the analysis.

0January 29, 2018 at 7:55 am #202202

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.don’t forget how it’s varying over time

0January 30, 2018 at 11:10 pm #202207

Karim MohsenParticipant@feodor85**Include @feodor85 in your post and this person will**

be notified via email.@rbutler

Hi Robert,

could you please tell me the different between 1 sample Z & 1 sample t ?0January 31, 2018 at 6:17 am #202208

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.The difference is primarily one of sample size. You can find statements to the effect that if the sample is >30 you use the Z test and if it is < 30 use the t-test. The fact remains that you can use the t-test for samples larger than 30 if you wish. You will also find statements to the effect that the data has to be normally distributed before you can use these tests. Again – not true, both are robust with respect to non-normal data.

If you happen to have access to a statistics package such as Minitab or Statistica I would recommend running your own tests to see what has to happen before the two significantly diverge from one another with respect to declarations of significance. I would also encourage you to run the Wilcoxon-Mann-Whitney test in conjunction with these tests to give yourself a sense of just how non-normal the data has to be before you see a difference with respect to declarations of significant differences in the means.

The issue here is not one of different p-values rather it is one of one test stating a difference exists at some chosen cut point for the p-value while the other does not. What you should find is that there is a lot of latitude with respect to both sample size and distribution shape before the tests start offering contradictory statements concerning significance of differences in the means.

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