# Non-normal data

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- This topic has 29 replies, 7 voices, and was last updated 6 years ago by Chris Seider.

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- May 31, 2011 at 1:43 pm #53814

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Afternoon all,

Looking for some help reference non-normal data. I have some data on prior to a new machine install and after and want to see if the process is more capable now than it was previously, and not sure which capability analysis to run, so I ran them all. I ran a non-normal capability analysis in minitab which gave me one set of outputs and then also ran it as a box cox transformation. I found that in box cox the resulting PPK values were massively different than in the weibull. In fact it showed the opposite (ie weibull showed that one process was better, and the box cox showed the other way around)

Could anybody help me please?

Thanks

Mike0June 1, 2011 at 3:38 am #191515

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.Mike: Understand that when you transform data, you must also transform the specification limits used to evaluate the transformed data.

If you use a Box-Cox transform in Minitab, you should get an indicator as to the similar distribution being transformed to. Weibull is a very flexible distribution and can take on characteristics of many other distributions.0June 3, 2011 at 10:05 am #191529

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.If testing the impact, You could use nonparametric test – Mann-Whitney.

note should be used if two samples (pre and post) follow same distribution and same variance.Or else if have to check capability , go for multiple variables (non parametric test)

and will take care of spec transformation also.when using non parametric capability , make sure you select the right distribution and could be easily identified by running >Stat>Quality tool>Individual distribution identification.

Hope this helps.

Ashky

0June 3, 2011 at 1:14 pm #191533

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Thanks,

Im still a littel confused as to the process i should follow for non normal data capability analysis.

Could anyone talk me through the steps i should take to understand which method to use, a decision tree anyone has?

Im very new to non-normal data.

Thanks for help in advance

Mike0June 3, 2011 at 1:52 pm #191534Mike,

This ain’t rocket science. Look at histograms of the untransformed data and you will know which of the two is the correct analysis.

When you understand that, you can figure out what was wrong with your method. I believe MBBinWI is leading you in the right direction, your specs probably were not transformed when you did the Box-Cox.

0June 3, 2011 at 2:04 pm #191535

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

be notified via email.Assuming you have checked to make sure that the non-normality isn’t due to something like bimodality, sample truncation, or a few extreme data points (plotting and looking at the data using histograms, box-plots, and normal probability plots are the usual things one does to test for these things) and that you really are looking at data whose usual pattern is non-normal (any kind of a measurement where there is a natural lower or upper bound and you are working close to that bound for example) then the simplest thing to do is plot the data on a normal probability plot, print out the plot, and use a simple manual curve fit of the data to identify where the extrapolated fitted curve crosses the .135 and 99.865 percentiles (you can use the calibrated eyeball or use a plain old French Curve – most graphic arts supply houses have these things).

Subtracting the two values you get from your plotting efforts from one another will provide an estimate of the 6 sigma spread and if you take the difference between your lower and upper spec limits and divide the difference by the estimated 6 sigma spread will give you an estimate of the capability.

The above should provide you with a reasonable answer to your question. The step-by-step details as well as the justification for this procedure can be found in Bothe’s book Measuring Process Capability – Chapter 8 – Measuring Capability for Non-Normal Variable Data. The book is very readable and, if you are going to have to deal with non-normal capability issues I would strongly recommend you either purchase a copy of the book or get a copy through inter-library loan and commit Chapter 8 to memory.

0June 3, 2011 at 2:34 pm #191536

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.Minitab

Step 1 : Identifying distribution : It is essential to choose the correct distribution when conducting a capability analysis. You can use individual distribution identification to select the distribution that best fits your data prior to conducting a capability analysis.

Goto Stat >Quality tool > select individual distribution analysis

Input data and mentioned sub-group size. If sub-groups not formed, mentioned it as 1 and click OK

Step 2 : Check Minitab Result in “Session”. You will find several distribution. Check for P-Value. Identify distribution with the largest p-value (& should be more than 0.05)

Step 3.1 : (1) If Box-cox value more than 0.05, Goto Stat >Quality tool > Capability analysis > select Normal.

Step 3.1 : (2) Click Box-cox and tick mark Box cox power transformation (W=Y…….)ELSE

Step 3.2 : Goto Stat >Quality tool > Capability analysis > select Nonnormal.

Input data and Select the distribution which fits your data. You will find this option in same screen.NOTE : IF Johnson transformation P-value is more than 0.05, instead of selecting the distribution simply click on Johson transformation.

ELSE Select a distribution with the largest p-value. (as checked in Step 2)Step 4 : Input your lower and upper specs and click on OK

The Mintab results will transform the data and Specs also.

Ashky

0June 3, 2011 at 3:06 pm #191537

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Thanks guys,

this is really helpfull. I have just ran the analysis as suggested but i still dont get any decent P Value. The weibull comes out at 0.10 even though the box cox looks better.

I have ran this analysis on a few data sets and the weibull always seems to be 0.10?

Any more help is massively appreciated.

Thanks

Mike0June 3, 2011 at 3:10 pm #191538

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.HI Mike,

Could you run “individual distribution analysis” test and share the Minitab session P-value for all distribution.

Ashky

0June 3, 2011 at 3:12 pm #191539

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.This is the analysis from the session window

Goodness of Fit Test

Distribution AD P

Normal 35.628 <0.005

Exponential 13.129 <0.003

Weibull 12.689 <0.010

Box-Cox Transformation 2.116 <0.005ML Estimates of Distribution Parameters

Distribution Location Shape Scale Threshold

Normal* 0.19160 0.40180

Exponential 0.19160

Weibull 1.02389 0.19429

Box-Cox Transformation* 2.87034 0.81335* Scale: Adjusted ML estimate

0June 3, 2011 at 3:15 pm #191540

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.Mike,

Re-run the test by slecting button “Use all distributions and Transformation”

and share the results.

Ashky

0June 3, 2011 at 3:18 pm #191541

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Distribution ID Plot for Oxygen %

Descriptive Statistics

N N* Mean StDev Median Minimum Maximum Skewness Kurtosis

175 0 0.1916 0.401803 0.12 0.05 5.2 11.3099 140.627Box-Cox transformation: Lambda = -0.5

Goodness of Fit Test

Distribution AD P LRT P

Normal 35.628 <0.005

Box-Cox Transformation 2.116 <0.005

Lognormal 4.235 <0.005

3-Parameter Lognormal 1.082 * 0.000

Exponential 13.129 <0.003

2-Parameter Exponential 7.156 <0.010 0.000

Weibull 12.689 <0.010

3-Parameter Weibull 4.012 <0.005 0.000

Smallest Extreme Value 55.646 <0.010

Largest Extreme Value 9.909 <0.010

Gamma 9.941 <0.005

3-Parameter Gamma 5.086 * 0.000

Logistic 11.900 <0.005

Loglogistic 3.613 <0.005

3-Parameter Loglogistic 1.198 * 0.000ML Estimates of Distribution Parameters

Distribution Location Shape Scale Threshold

Normal* 0.19160 0.40180

Box-Cox Transformation* 2.87034 0.81335

Lognormal* -2.01040 0.67541

3-Parameter Lognormal -2.64071 1.07838 0.04715

Exponential 0.19160

2-Parameter Exponential 0.14241 0.04919

Weibull 1.02389 0.19429

3-Parameter Weibull 0.79877 0.11871 0.04950

Smallest Extreme Value 0.51875 1.23950

Largest Extreme Value 0.12033 0.09325

Gamma 1.54195 0.12426

3-Parameter Gamma 0.78275 0.18154 0.04950

Logistic 0.14578 0.08252

Loglogistic -2.08316 0.36781

3-Parameter Loglogistic -2.70149 0.63939 0.04893* Scale: Adjusted ML estimate

0June 3, 2011 at 3:27 pm #191542

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

be notified via email.Any chance you could just post the numbers you are using – no units necessary just the data?

0June 3, 2011 at 3:37 pm #191543

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Heres the data set im using…. thanks

34.7956

26.8407

27.5982

28.2627

28.0241

28.5170

26.7090

27.6946

26.5507

26.6109

27.1106

27.1987

25.5562

26.9535

25.9623

25.8414

26.3387

27.1976

25.7848

25.6298

25.2313

26.0340

26.0751

26.1579

28.9148

29.6561

29.6696

29.4520

29.8276

29.8614

27.4307

28.0247

27.9960

27.9969

27.9465

28.0591

26.0738

26.9244

27.3275

27.7118

27.9261

27.9071

27.4087

27.8203

28.1117

28.2959

28.2170

28.2986

27.6946

28.0826

28.2375

28.2478

28.3426

28.6024

27.2496

27.7920

28.0731

28.4528

28.5585

28.7453

27.0332

27.5707

27.8537

28.1381

28.5959

28.5170

26.7016

27.0112

27.1330

27.1691

27.3697

27.5656

32.6204

29.2555

29.8183

29.3440

29.8260

30.7933

29.2004

27.9739

27.8901

28.1965

27.9616

28.3761

25.6178

25.9589

26.2786

26.6628

26.7916

27.0770

25.9280

26.3653

26.3974

26.5317

26.8214

27.1037

26.9260

26.9369

26.9410

27.4516

27.4663

27.6769

26.6496

26.9369

27.0602

27.3973

27.7303

27.9285

26.3913

26.6135

26.9135

27.1531

27.2643

27.5955

28.1394

28.2081

29.1518

28.6612

28.4477

28.5848

25.0587

26.2044

25.4356

25.1662

25.1546

25.8400

26.1900

26.0915

26.5535

26.9541

26.9261

27.0047

26.0933

26.7576

27.3581

27.8301

27.9156

28.7666

25.6002

26.2510

26.6499

27.4160

27.7058

28.1594

31.4738

31.0888

32.0138

29.7196

31.7220

33.0185

31.7841

31.6263

32.1091

31.3272

30.6816

30.9591

27.9471

27.4519

27.7643

28.4875

27.8002

28.3449

28.2695

27.9110

28.7224

28.9212

28.2042

28.4878

37.2891

36.4794

36.5538

34.8407

37.0576

36.8199

29.3376

27.8850

26.7118

28.8572

27.0282

26.8887

27.3125

26.5359

26.4336

26.6632

26.3718

26.7741

26.5888

25.9281

25.9868

26.1036

26.7571

26.4790

26.3027

26.8911

27.1491

27.3750

27.7376

27.6690

31.0505

30.1861

30.5296

30.2761

30.4650

30.2560

27.8038

27.1651

27.3153

27.7210

27.7498

27.7579

26.7461

26.6210

26.8018

26.8091

27.3648

27.1790

25.5695

26.2970

27.1850

27.2957

27.1416

28.3137

31.8318

33.8098

33.8048

31.7869

31.3226

33.3913

29.0797

26.2804

28.1706

28.2725

27.7638

28.1400

29.1175

29.6619

30.6951

28.7511

28.9438

29.3498

28.5866

29.7306

31.2539

30.0896

33.6808

32.8666

26.1217

26.6297

26.7408

27.0675

26.7338

27.1886

25.6845

26.0578

26.4023

26.5925

26.9061

27.1112

26.8118

26.8760

26.7835

26.7711

26.7167

27.4371

26.7007

27.7044

27.0059

27.2474

27.4930

27.0218

36.8939

34.4951

35.0471

36.2435

34.1718

35.0347

26.3611

26.6210

26.9345

27.1359

27.4240

27.6216

25.4229

26.2527

26.3901

26.7237

26.7666

26.9844

25.6695

25.9475

26.2830

26.5131

26.8022

26.8726

25.6699

25.3544

26.2830

26.1016

26.0110

26.7766

26.0742

26.4514

26.7077

26.9841

27.0983

27.3415

24.4919

24.2229

24.3698

25.2690

25.2958

25.5700

24.2427

24.8514

25.2029

25.5368

25.0419

25.5963

26.5402

26.3338

26.3020

26.6214

26.9099

26.3791

23.6948

23.7258

23.7252

23.2964

24.1735

23.8892

25.5572

26.1148

26.5335

26.8512

27.1508

27.2778

25.5469

26.3975

26.2776

26.1952

25.6502

25.6393

26.2231

26.1593

26.1949

26.7796

26.7510

26.7322

27.3824

27.4510

27.8248

27.9959

28.0076

27.4788

24.7737

26.0821

26.6679

26.9115

26.8756

27.0165

25.1133

26.0836

26.2061

26.7339

26.9681

27.0353

26.8872

26.6035

26.9758

26.7511

27.3441

26.9257

26.6280

26.5230

26.4236

27.0349

27.0189

27.2362

27.6946

27.0698

26.8508

26.7322

26.6823

27.0009

30.8092

30.1542

29.6811

28.8638

29.6141

29.6047

27.3978

27.2643

27.7867

27.4393

27.8973

27.6674

29.5683

29.2834

28.9750

29.3176

29.3082

29.5079

25.6699

25.9878

26.3601

26.6649

26.9844

27.1390

30.9969

31.2682

30.3084

31.6985

30.3726

30.7860

28.4472

28.2375

28.0390

27.8368

28.2416

28.6905

26.6076

26.5888

26.6732

27.0251

26.9844

27.0420

26.1023

25.7791

25.8738

25.7900

25.8699

26.5662

26.5283

26.8287

26.8424

26.4742

26.7511

26.8474

25.2658

25.7601

26.4801

26.3354

26.2701

26.3636

27.1786

27.7303

27.0659

27.1946

27.2856

27.5092

26.8449

27.3690

26.4078

26.7404

27.0059

26.8944

25.3596

25.8513

26.1941

26.4474

26.8860

27.1946

28.1601

28.0247

28.2682

28.1226

28.1525

27.8758

29.3656

28.4575

28.7647

28.9819

28.8436

29.0577

35.2271

34.3236

34.6877

35.5343

37.1490

34.6552

27.1224

27.7240

27.7775

27.6616

27.5416

27.4472

33.7149

39.5269

38.6333

38.7396

35.8785

34.05480June 3, 2011 at 3:47 pm #191544

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.Check the minitab results ..

You could use Johnson transformation as P-value is more than 0.05

Step 1 :Goto Stat > Quality tools > Capability Analysis > Select Nonnormal…

And click button “Johnson transformation”Step 2 : Input data and specification limit and click OK and you will get the output.

Have attached Minitab process capability nonnormal test result. Assuming Spec as LSL 26 and USL 28

Check the attachment.Ashky

Goodness of Fit Test

Distribution AD P LRT P

Normal 30.411 <0.005

Box-Cox Transformation 5.528 <0.005

Lognormal 23.988 <0.005

3-Parameter Lognormal 9.423 * 0.000

Exponential 194.741 <0.003

2-Parameter Exponential 76.712 <0.010 0.000

Weibull 50.231 <0.010

3-Parameter Weibull 21.746 <0.005 0.000

Smallest Extreme Value 58.701 <0.010

Largest Extreme Value 8.483 <0.010

Gamma 26.043 <0.005

3-Parameter Gamma 13.128 * 0.000

Logistic 16.000 <0.005

Loglogistic 12.750 <0.005

3-Parameter Loglogistic 4.293 * 0.000

Johnson Transformation 0.347 0.4790June 3, 2011 at 4:03 pm #191545

KharooParticipant@ashkharoo**Include @ashkharoo in your post and this person will**

be notified via email.due to some tech issues, i am not able to attach the image file.

Mike, Hope you have the results.

Ashky

0June 3, 2011 at 4:04 pm #191546

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Thanks!! A great lesson.

I didnt see the Johnson data p value, not heard of that one before.

Thanks again.

Mike0June 6, 2011 at 9:35 am #191552

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.I now have some more data (all part of the smae thing) and the best distribution is the weibull (although only 0.010 p value)

When i do a capability analysis on this the PPK is great and shows no defects. However i know that there are many defects. I guess i need to transform the LCL and UCL? How can i do this?

Any help would massively be appreciated.

Thanks

Mike0June 6, 2011 at 12:51 pm #191555

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

be notified via email.I’m missing something here. If I understand the comments made by others concerning Minitab output it look like a P< .05 means that the fit is not correct. If that is the case then P = .01 for Weibull would mean this isn't the correct fit.

I went ahead and plotted the data you provided – a quick eyeball says the curve crosses .135 and 99.865 at 23.6 and 40.2. If you take the difference of these two numbers and divide the tolerance by this difference how close is it to the capability estimate you got when you ran the Johnson transform (by the way – which Johnson family does Minitab use Su, Sl, or Sb)?

0June 6, 2011 at 2:34 pm #191556

BuckleParticipant@mikebuckle**Include @mikebuckle in your post and this person will**

be notified via email.Hi.

The p value were looking for in normality checks is P>(greater)0.005 and the weibull is the best fit at 0.010 so is higher than the above but not great. The data set you did the anlysis on which was posted above is different to the analysis im doing now. This has 4000 data points so i cant publish it here. I have tried to attach file….

This is the output i get in session window from the new data set. None are great but weibull is the best…… Im now stuck as to what to do? Any help is massively appreciated.

Goodness of Fit Test

Distribution AD P LRT P

Normal 2883.764 <0.005

Box-Cox Transformation 110.589 <0.005

Lognormal 162.833 <0.005

3-Parameter Lognormal 148.337 * 0.000

Exponential 963.921 <0.003

2-Parameter Exponential 658.669 <0.010 0.000

Weibull 968.306 <0.010

3-Parameter Weibull 708.063 <0.005 0.000

Smallest Extreme Value 4422.141 <0.010

Largest Extreme Value 652.429 <0.010

Gamma 765.221 <0.005

3-Parameter Gamma 623.345 * 0.000

Logistic 926.114 <0.005

Loglogistic 57.526 <0.005

3-Parameter Loglogistic 73.337 * 0.0000June 6, 2011 at 2:56 pm #191557

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

be notified via email.I don’t follow the logic concerning the p-values so I’ll just chalk that up to not knowing how Minitab presents its output. In the meantime – did you try plotting the data on normal probability paper?

If you look at the curve for the data listed above then a plot of either the raw data or log transformed data gives about the same crossing points for the percentages mentioned before. I’d recommend trying this with data set you listed as well as with the expanded data and see what you see. If the crossings are about the same then the method outlined in Bothe’s book would be the approach I would recommend.

0June 10, 2011 at 2:29 am #191564

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.**Robert Butler wrote:**The above should provide you with a reasonable answer to your question. The step-by-step details as well as the justification for this procedure can be found in Bothe’s book Measuring Process Capability – Chapter 8 – Measuring Capability for Non-Normal Variable Data. The book is very readable and, if you are going to have to deal with non-normal capability issues I would strongly recommend you either purchase a copy of the book or get a copy through inter-library loan and commit Chapter 8 to memory.

Hey, Robert – excellent reference. And believe it or not, Davis is a neighbor of mine (at least we share the same zip code). Want an autographed copy?

0June 10, 2011 at 2:47 am #191565

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.**Robert Butler wrote:**I don’t follow the logic concerning the p-values so I’ll just chalk that up to not knowing how Minitab presents its output. In the meantime – did you try plotting the data on normal probability paper?

Wow! It’s the rare day that I can teach (or at least communicate) something to RB. Here you go (direct from Minitab help):

Anderson-Darling (AD) statistic

Measures how well the data follow a particular distribution. Smaller Anderson-Darling values indicate that the distribution fits the data better. Use the Anderson-Darling statistic to compare the fit of several distributions to see which one is best or to test whether a sample of data comes from a population with a specified distribution.

If the p-value (when available) for the Anderson-Darling test is lower than the chosen significance level (usually 0.05 or 0.10), conclude that the data do not follow the specified distribution. Minitab does not always display a p-value for the Anderson-Darling test because it does not mathematically exist for certain cases.

If you are trying to determine which distribution the data follow and you have multiple Anderson-Darling statistics, compare them. The distribution with the smallest Anderson-Darling statistic has the closest fit to the data. If distributions have similar Anderson-Darling statistics, choose one based on practical knowledge.

0January 30, 2013 at 10:38 am #194652Hello. I have similar case. My set of data (85) is arround the same five values. It does not adjust to any distribution. I cannot chenge my lecture instruments and i have to demmosntrate capability for a tolerance of 6 +/-0,5 (obviously this process is capable). What do you recommend me to do?

6,03

6,01

6,02

6,03

6,01

6,05

6,02

6,03

6,03

6,02

6,03

6,01

6,02

6,02

6,02

6,02

6,02

6,01

6,02

6,01

6,04

6,04

6,01

6,03

6,03

6,01

6,02

6,05

6,04

6,04

6,02

6,01

6,01

6,02

6,02

6,02

6,02

6,04

6,02

6,04

6,01

6,03

6,02

6,05

6,02

6,03

6,02

6,05

6,05

6,03

6,03

6,03

6,03

6,05

6,05

6,03

6,02

6,03

6,03

6,03

6,03

6,05

6,03

6,04

6,05

6,06

6,01

6,02

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6,04

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6,04

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6,02

6,020January 30, 2013 at 1:32 pm #194654

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

be notified via email.You could increase precision or just use the % estimated outside spec and convert that to a process capability index. Have you done a precision study at a minimum? Is the device accurate? If it was off by .02, it would have bad process capability.

0January 31, 2013 at 2:00 pm #194663Buckle,

1. Did you plan and oversee the collection effort for both data sets?

2. How is this capability comparison going to be used (assuming its resolved)?0February 7, 2013 at 2:09 pm #194701

Joel SmithParticipant@joelsmith**Include @joelsmith in your post and this person will**

be notified via email.@mikebuckle – Assuming the data you posted are in time order, then the reason you cannot find a good distribution fit is that they are not in control. Try making an I-MR Chart of your data and it should be obvious.

When data are not in control, then your data are not all coming from the same or even similar distributions. Throw a bunch of wildly varying distributions together and you get a mess that does not match a known distribution.

More importantly, if your data are not in control then doing capability analysis does not have much value to you.

0February 7, 2013 at 2:15 pm #194702

Joel SmithParticipant@joelsmith**Include @joelsmith in your post and this person will**

be notified via email.Adriana – Your data also show a slight shift around point 48 but nothing compared to the other dataset shown.

In any event, I’m not sure distribution fit is all that important here…you don’t have any data that is even remotely in the ballpark of your specs, and barring a process shift or special cause you will never ever see a part out of spec. Assigning a specific sigma level, Cpk, etc. is a pointless exercise. Make a histogram of the data and plot the specs as reference lines.

0January 9, 2015 at 11:52 am #197716Hello,

Right now I am working on some equipment validation, and when identifying distributions data, shows that 3-parameter weibull is the one with a P value > .05.

But, need to transform data to fit 3-parameter weibull distribution and how can I transform limits to same dist???

Need the transform limits as well, please help me…

Thanks for your help…

0January 9, 2015 at 2:13 pm #197718

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

be notified via email.Don’t make yourself sweat so hard. If using Minitab, use capability analysis non-normal. Pick the distribution you want and then it will transform the data into a best fit curve and the original data is still shown.

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