Sampling Question - Random Sample of 100 pcs and 11 pcs. have been rejected

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Steve Prevette

Deming Disciple
Staff member
Super Moderator
#12
Thank you very much. I thought that this is one tail test, this is a reason that I choose 1.283.
How do you came to conclusion regarding that probability to find defective is between 6.85% and 17.21%? Could you send me formula for calculation?
Whether or not this is a one tail vs two tail test depends on why you are doing the test. If you want to be sure you are not rejecting the lot on a false alarm, you are interested in the lower limit (supplier's risk). If you want to be sure you are not accepting the lot based upon a lucky sample, you are interested in the upper limit (buyer's risk).

It would help to know the context for this question - real world application, or a statistics course?
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#14
Thank you.
Real world application: this is example from my plant inspection.
OK, so you are most interested in the worst case failure rate. Now, it does depend upon what level of significance you want - 90% is usually the lowest accepted, but 95% is very common, also 99%.

If you wanted to go upper 90% single sided, then the formula would be .11 + 1.28 x sqrt( .11 x (1-.11)/100). You would be 90% sure that the failure rate is less than that number for the population sampled, with the following assumptions:

1. Your sample was random, each part had an equally likely chance of being chosen.

2. Failures are independent from part to part

3. The failure rate is uniform throughout the population.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#15
there are many ways to establish confidence intervals about your defect rate from your sample. you can pick and confidence level you want (the higher the confidence the larger the confidence interval). All this does is give you idea of the precision of the estimate of the defect rate. you can pick any approach you want to try to get the answer you want...but that doesn't mean you should.

you have an 11% defect rate in your sample. it may be a little high or it may be a little low. but it's pretty large. that's pretty poor quality any way you look at it.

The real answer depends on the real question: WHY are you asking about the statistics regarding this estimate? Will it somehow change the action you take on this lot? are you trying to estimate the defect rate of the process stream - rather trying to decide whether or not to accept or reject the lot? Is this lot a validation lot and you are trying to estimate if it meets the capability requirements?
 

Bill McNeese

Involved In Discussions
#18
From a process stream? Your sample has 11% defects. That is your estimate of the defect rate - and you can put which confidence limit you want around it. Bev is correct - that is not very good quality any way you look.

If you want a better estimate of the defect rate, you can collect samples over time and use a control chart to estimate the average defect rate and the stability of the process. You have lots of opportunities for process improvement. Start with the reasons for defects and use the chart over time to see your improvements.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#19
Bill is correct, the best way to estimate the defect rate for the process stream is to take 'small' samples over time and plot them on a run chart if not control chart.
 

Mike S.

Happy to be Alive
Trusted Information Resource
#20
MY conclusion regarding the batch would be that I have an unacceptable situation that I need to get to the root of immediately. I would not waste time calculating confidence intervals around such a poor yield. It would be better to use that time fixing the problem(s).
 
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