Non-Parametric Testing for Widget Defectivity: Sample Size Considerations

[DeShark]

Hi all. I'm trying to come up with a way to determine if the defectivity of a particular widget is 'different' to the usual defectivity of a widget. The difficulty comes from the fact that widgets are made in batches of 25. We'd like to investigate any widgets which have a higher (or lower) defect count than should be expected.

Is it Ok to use a non-parametric test on the widget defect count, despite the fact that the variance of defectivity within a batch is less than the variance between batches. E.g. if only 3 batches have been made, what is the sample size? 75? This doesn't seem right to me...

Any insight or suggestion is very welcome. Thank you!

 

[Stephen Tashi]

I'm trying to come up with a way to determine if the defectivity of a particular widget is 'different' to the usual defectivity of a widget.

It isn't clear what that means. Taken literally it implies that there is a variable type of defectivity in widgets, but you didn't elaborate on what would make one type of defect different than another and without getting into those details, I don't think there is a general answer to your question.

 

[DeShark]

Sorry for not being clearer: each widget itself is made up of parts, each of which can be 'working' or 'defective'. The exact manner in which the parts are defective is unimportant; just the number of defective parts (or equivalently, the proportion of parts which is defective).

 

[DeShark]

I should have said:

I'm trying to come up with a way to determine if the defect count of a particular widget is 'different' to the usual defect count of a widget.

 

[pbuk]

How many parts make up a widget and what is the usual defect count?

 

[Stephen Tashi]

My general advice is not to approach real life statistical problems as general problems! Textbooks pose problems involving widgets and being an expert on astronomy or strength of materials etc.doesn't help you solve them. In real life, if you have expertise in a situation, you shouldn't lobotomize yourself by thinking of it as a problem with "widgets".