# Help With A Statistical Problem

#### E Wall

##### Just Me!
Trusted Information Resource
I'm Statisically Challenged! Will anyone help?

I have a question, and since I don't know much about statistics...I don't have a clue how difficult it is to answer. Here goes:

Example:
One Lot of 80 parts

I am told that each part has a 7% chance of not meeting spec (as opposed to 7% of the Lot).

I am thinking that the overall accuracy % isn't 93% per lot as has been stated, but do not know if I am right, so before I open mouth and insert foot with the folks saying this...Can/Will anyone help with what the true accuracy would be? and Why?

Thanks in advance for any effort to help!
Eileen Wall

M

I am not sure I understand the question because I am not sure what you mean by accuracy but here is some information.

If every part has a probability of 93% of being within spec (7% out of spec) then the probability of the entire lot being good (all 80 parts) is 0.93^80 = 0.3% NOT GREAT!

If you want a probablity of 79 part out of 80 being good, then 79/80 = 98.75% to the 80th square root = 99.984%. That is the probability of being within spec that each part has to meet to have 79 out of 80 good parts.

I hope this helps.

B

#### Bill Levinson

I'm not sure what you mean by "accuracy." Yield, perhaps?

If each piece has a 7% chance of being bad and there are 80 pieces in the sample, you can expect 5.6 bad pieces per sample. The binomial distribution shows the chance of getting x bad pieces (x ranging from 0 to 80) pieces in the sample.

If c is the acceptance number (number of bad pieces you're allowed to have without rejecting the lot), the cumulative binomial shows the chance that the lot will pass. If c=0 (see Michel's post) is the acceptance number, the chance of passing is 0.93^80 = 0.0030 (0.3%)!

#### E Wall

##### Just Me!
Trusted Information Resource
Thank you for helping me cover my assets!

Michel & Bill: Thank you both for the responses!

The accuracy was the supplier term used and I was trying not to suppliment or rephrase in my own terms. According to them their process is 93% accurate, that is the overall % they claim for running a part through their process. This is a new process for them based on our requirements, and is a work-in-progress toward 100% part accuracy.

On a single part basis, I felt they were correct. However; they also tried to apply that % to the lot (liklihood of all good parts), which I felt was inaccurate...but didn't know how to prove it.

My boss is getting me more involved in problem solving and I think I need to take a class or two in statistics to help. I do fine in the abstract, but when it comes to proving out hypothesis...they want numbers.

Thank you both again
Eileen

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D

#### Dave Strouse

How would that work?

Eileen -

You seem to believe that there is some difference in the % meeting specification per lot and per piece. How would that work?

Consider 100 colored beads. Red beads are "good", white beads are "bad". There are 93 red beads and 7 white beads.

If we reach blindly into a well stirred and mixed bowl of the 100 beads, our chances of pulling any one white bead out are 7%. Then we would say the likelihood of any one bead being bad is 7%.

The total % bad in the lot of 100 is 7 out of 100 or 7%.

That is I believe what the supplier is telling you. How would they arrive at an estimation of the probability of any one part being bad without having an estimation of the lot % bad and how could those two numbers be different? I'll suggest one way how they could be different later on.

Their use of "accuracy" to describe this situation is questionable and in fact downright incorrect.

The statistical concepts involved here are random sampling ( why the bowl must be reached into blindly) and homogenaity ( why the bowl must be well mixed).

If those two pricnciples of randomnous in sampling and homogenaity of production are violated, you might have reason to question that the per piece probability and lot probability are different based on the place or time sampling occurs.

The previous posters were correct in their assessment of finding 0 defects if all are examined. You can devise a sample plan to find with any assurance the % defective if you want to track the suppliers improvement. For instance 32 pieces with 0 defects will assure you the lot is less than 7% defective with 95% confidence.