Pooled Standard Deviation - Mintab vs. Excel

Validation2011

Starting to get Involved
Hi All,

Hope you can offer some guidance!

I am currently trying to calculate capability on the results of 3 batches of product.

I am using the Stat-Quality Tools-Capability Analysis-Normal method in minitab.

I want to treat the 3 sets of results as 3 separate groups. Each of the groups is passing capability testing on an individual basis but because the particular feature is quite hard to accurately control all 3 groups are located in different positions within the specification range and when they are combined we fail the capability analysis.

I see in minitab that the default setting is "Pooled Standard Devaition" but when i calculate the capability on the 3 groups of data it seems to automatically combine them all into 1 group and work out the standard deviation for the 1 group rather than pooled standard devation for the 3 groups.


Specfication range is -0.0025 to 0.0025. When i calculate capabilty in minitab i get PpK = 2.39.

When i calculate the capabilty manually in excel using standard deviation (StDev) i also get 2.39.

When i calculate the capability manually in excel using a pooled standard deviation (sp=[((n1-1)s1^2 + (n2-1)s2^2 + (n3-1)s3^2) / (n1 + n2 + n3 - 3))]^1/2 i get 3.10.

Can someone shed some light on exacly what i am doing wrong when calculating the capability in minitab?

Many Thanks
 
Last edited:
B

Barbara B

Re: Pooled Standard Deviation - Mintab vs Excel

Could you please attach a spreadsheet containing your data (maybe instead of posting the values as this tends to make the posting extremely wide)? Thanks :)
 

Validation2011

Starting to get Involved
Re: Pooled Standard Deviation - Mintab vs Excel

Apologies it was nicely arranged in columns before i clicked the submit button
:D

Please see attached data.
 

Attachments

  • Data.xlsx
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B

Barbara B

Re: Pooled Standard Deviation - Mintab vs Excel

As you haven't attached your formulas, they couldn't be checked, so I calculated the values for the standard deviation in the attached Excel sheet and with Minitab. They do exactly match :magic:

Hope this helps,

Barbara
 

Attachments

  • Process capability default settings for standard deviation.png
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  • Process capability formulas for within standard deviation.png
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  • Process Capability of value with unbiasing constant.png
    Process Capability of value with unbiasing constant.png
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  • Process Capability of value without unbiasing constant.png
    Process Capability of value without unbiasing constant.png
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  • Data Capability 2011 08 03.xlsx
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Validation2011

Starting to get Involved
Re: Pooled Standard Deviation - Mintab vs Excel

Thanks for the reply Barbara.

When i work out the Standard Deviation in Excel using the StDev() formulae i also get the same answer as minitab.

It is when i calculate the Standard Deviation in excel using a pooled standard deviation formulae (See attached sheet) i get a different answer to minitab.

See attached sheet with calculations included.

Thanks
 

Attachments

  • Data Capability.xlsx
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B

Barbara B

Re: Pooled Standard Deviation - Mintab vs Excel

If you take the formula for the pooled standard deviation without unbiasing constant as a metric for variation, you have to compare your result (3.1075 in Data Capability.xls) with the Cpk-value listed below "Potential (Within) Capability" (Cpk=3.11 in Minitab).

For the overall standard deviation compare your Ppk=2.3917 with the Ppk in Minitab (listed below "Overall Capability"): Ppk=2.39, so the results do match.

Regards,

Barbara
 

Validation2011

Starting to get Involved
A bit of a follow on question...

As you can see from the data (this is Point 1 of a set of 100 points that has been measured 3 times on a CMM) we are capable of maching the parts within specification.

When we calculate the capability on the individual batches (CpK) we are passing on all 300 points, however when i combine the three point 1's, point 2's etc... the spread of the data is too wide to prove capability.

This is quite a complicated feature to accurately position within the specification range so what we aim to do is place the part within the middle 1/3rd of tolerance and run.

The customer has requested that we obtain a PpK >= 1.53 on this feature.

Can you offer any advise? It seems a shame to prove capability individually and then fail based on the combination of all 3 batches.
 
B

Barbara B

With the data provided the Ppk=2.39 >1.53, so the numbers match the customer requirements. (There are other issues like not normally distributed values neither within the runs nor for all values together and the standard deviations for the three runs differ significantly (see attached pics), but if you only want to report a number which is called Ppk for your customer, don't bother with this.)

Maybe you could provide another data set for which the customer requirement Ppk>1.53 (uncommon number btw) isn't met?

Several questions popped up for me:
  • Are the three runs repeated measurements for 50 parts or do the values represent 150 parts? If these are repeated measurements, were they done
    • sequentially by part (part 1 run1, part 1 run 2, part 1 run 3, part 2 run 1, part 2 run 2,...) or
    • sequentially by run (part 1 run1, part 2 run 1, part 3 run 1,..., part 50 run 1, part 1 run 2, part 2 run 2,...) or
    • in another way?
  • What kind of material are the parts made of? And what kind of type is the production process?
  • Did you conduct a measurement system analysis for this kind of measurement (meaning: for the 100 points of this part)? If so, what were the results?
  • Is there a (sufficient) air-conditioning system at the location were the CMM is placed / the measurements are taken?

Regards,

Barbara
 

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  • Probability Plot of run1-run3.png
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  • Probability Plot of run.png
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  • Test for Equal Variances_ value versus run.png
    Test for Equal Variances_ value versus run.png
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Validation2011

Starting to get Involved
Sorry for the delay in replying.

See attached data for point 13a.

The 1.53 is based on a target of 1.38 (customer requirement). A sample size of 150 parts means that we need to achieve a 1.53 to have ≥ 95% confidence that the true process Ppk ≥ 1.38.

The part is made from Stainless Steel. On the top of the bar are 4 identical features (milled). The CMM measures 25 points on each of these features (surface scan), so in total there are 100 points measured on each part (4 x 25).

750 parts were machined (3 Batches of 250). 50 parts were sampled from each batch (numbers stated in excel sheet attached).

gauge R&R or MSA is 11.92% on this feature.

Yes the CMM is located in a Temperature controlled room.

The data is not normal but there doesnt see to be any better fit available to me:

Descriptive Statistics

N N* Mean StDev Median Minimum Maximum Skewness Kurtosis
150 0 0.0007513 0.0004996 0.0009 -0.0002 0.0022 -0.333843 -0.736723


Goodness of Fit Test

Distribution AD P
Normal 5.909 <0.005
3-Parameter Lognormal 5.950 *
2-Parameter Exponential 15.682 <0.010
3-Parameter Weibull 3.283 <0.005
Smallest Extreme Value 3.253 <0.010
Largest Extreme Value 8.432 <0.010
3-Parameter Gamma 6.566 *
Logistic 5.786 <0.005
3-Parameter Loglogistic 5.787 *


ML Estimates of Distribution Parameters

Distribution Location Shape Scale Threshold
Normal* 0.00075 0.00050
3-Parameter Lognormal 3.46621 0.00002 -32.01430
2-Parameter Exponential 0.00096 -0.00021
3-Parameter Weibull 78.85155 0.03567 -0.03468
Smallest Extreme Value 0.00099 0.00045
Largest Extreme Value 0.00049 0.00049
3-Parameter Gamma 155.49771 0.00004 -0.00558
Logistic 0.00079 0.00029
3-Parameter Loglogistic 3.46579 0.00001 -32.00094


Have i any options besides "Fail and 100% Inspect" on the CMM?
 
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