# Negative Binomial Distribution on Minitab?

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• #56018

Javier
Participant

Hello. I am wondering how to use Minitab for what I want to calculate how effective can one brand of gloves used at my facility would perform the best.

So this takes place at a manufacturing facility for bbq kettlegrills

Basically, I want to see if given 1000 units, how many defects would two brand of gloves perform. I believe this can be achieved using a negative binomial regression, but correct me if Im wrong.

Here’s more info just to explain better what I am trying to do.
Once the grills are assembled, they go through an inspection line where two processes happen:
1.- Inspection: grills are checked by operators for any defects (in this case, craters on paint) and if any found, they input them on a computer system. This is where the variable data comes from in the sheet im sending you (number of defects on total units)

2.- Repair: Operators check their computers on each grill and if they find any defects they look for them in the grill and either repair them (good unit) or send them back to repaint as a rerun (defective units) This is where the attribute data comes from in the sheet im sending you (defectives from a sample)

Before this inspection line, there’s a few prep, finishing and assembly lines, where operators wear gloves to protect themselves and the units when manipulating them. We suspect these gloves might be causing craters.

So as you see in the data (attachments), from Feb 20th to March 26th operators were using Vargas Brand. And from March 27th up until June 9th, operators used Ansell Brand.

I want to see if there’s statistical evidence to prove gloves did or didnt have and impact on craters, I could do a 2 Sample T test for a difference of means, but I also would like to simulate what would happen running 1000 units as I sateted before.

I really need to use Minitab for this as is the only statistical software I’m allowed to install on my computer.

Attachments:
QuickSummary
Raw Data

PS. @BKStone you have helped me in the past. Any clues?

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#202662

Robert Butler
Participant

A number of posters took some time to answer this same question on your earlier thread and you were given some good advice which, based on this post, you chose to ignore.

In particular @cseider asked you about the results of your graphical analysis. Given this post it is evident that you did not run a meaningful graphical analysis of your data. If you had done so you would have learned a great deal.

1. Do you believe your sample data to be representative of the process?
a. If the answer is no then running simulations based on the data will be nothing more than an exercise in fertility.
b. If the answer is yes then the big question is what could have possibly driven you to decide to try to generate 1000 sample simulations based on a negative binomial?

2. If we assume your original data set is representative and if we assume your desire to run 1000 sample simulations using an underlying distribution of a negative binomial is based on that data then a careful graphical analysis would suggest the basis for this desire is the existence of 2 data points. If this is indeed the case then you are focusing on the behavior of less than 2% of your sample data and ignoring what the bulk of the data, in conjunction with the two extreme data points, is telling you.

3. A boxplot of your data for defects and defectives split on glove type tells you in no uncertain terms where you should be looking and what you should be considering with respect to the process.

a. The plot for defects says there is a shift in the mean and that’s about it. If I remember correctly one of the posters in the other thread indicated this was a significant shift.
b. The plot for defectives says two things and, I suspect, also highlights the driver for your post on negative binomial simulations.
1. There is a shift in the means between the two glove types
2. There is a marked difference in the VARIABILITY around the means of the two glove
types.
3. There are two extreme data points in Ansell data for defectives – as mentioned, these represent less than 2% of the total sample and, as near as I can tell, they are the sole justification for a desire to run 1000 sample simulations based on a negative binomial.

Based on what you have provided the big news, and the three things that demand investigation, are:
1. Is there any physical connection between glove type and the simultaneous reduction in mean AND variation about the mean for Defectives?
2. If glove types are really a cause for reduction – why don’t Defects follow the same pattern as Defectives?
3. What is the story with respect to the two extreme data points for Ansell Defectives?

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#202668

Chris Seider
Participant

@rbutler
Sighhhhh, graphical analysis has lost favor (popularity?) and not even covered by many folks teaching analytical tools in problem solving.

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