Emission probability failure 1

[harmony]

Hi,
I am looking at the probability of emission failures during a European emissions test. could any one please explain the following text:
With a minimum sample size of 3, the sampling procedure is set so that the probability of a lot passing a test with 40 % of the production defective is 0,95 (producer's risk = 5 %) while the probability of a lot being accepted with 65 % of the production defective is 0,1 (consumer's risk = 10 %).

Thanks,

Derek

 

[yates]

This means that for each manufacturing batch size of similar parts, the sample size to be tested should be calculated so that testing would result in a probability of 0.95 of finding at least one defective part in a batch known to contain 40% of bad parts, and a probability of 0.1 of finding no defective parts in the batch known to contain 65% of bad parts. The minimum sample size being three whatever the manufacturing batch size is. The same requirement can be put on any measurement results applied to a population of measurements, e.g. in the case of emission controls, over the max allowed limit of concentration is 'bad' and under is 'good' and the batch size is the toal number of concentration measurements made.

 

[zekeman]

Your explanation does not jive wth the probabilities I get.
For 40 % defectve parts the probability that at least one is defective of a sample lot of 3 is
1-.6^3=.784, not .95
For 65% it is
1-.35^2=.957, not .90

 

[zekeman]

Correction. The second result should be
1-.35^3, not 1-.35^2

 

[yates]

Nobody says the sample size should be three. What the original text said was that the sample size was to be determined in order to achieve the results stated, and that in any case, the sample size chosen was not to be less than three.

 

[harmony]

All,
Thanks for taking the time to explain this. I think I get the gist of what is required. Have a good 06 one and all

Derek