Sample size (an interesting question)
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September 2, 2005 at 7:11 am #40574
Hello! I’m a junior BB. I have an interesting question.
Producing 100000 units per day, when we want to assess a real percentage of defect units we have to define a sample size for it. That’s all good when the percentage is about p=0,05 or p=0,01. But the closer to 6 sigma level we are the larger sample size we need to assess the percentage. For example, if p=0,000004 (near 6sigma level) we need a sample size of about 20 millions units. It’s impossible! Even working at 45 sigma level there is a very large sample. What should we do? Should we try to use variable data instead of attribute data? What effects can be in this case? What should we do if we can’t use variable date because of nature of a product?
Help me please to solve this. Thank you.0September 2, 2005 at 12:55 pm #126263Revisit your definition of “defect” or reconfirm your customer specifications. Or else, plot defects per month / quarter/ year til you get a reasonable chart.
0September 2, 2005 at 1:43 pm #126266
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Don’t know where you got the 20,000,000 units. Provide four pieces of information: population size, desired confidence level, current proportion defective and desired precision. I can run the calculations and post them for you.
0September 2, 2005 at 2:22 pm #126273The question isn’t really that interesting, but Darth is right that you estimate of sample size of 20,000,000 is wrong. Give us all the information Darth asked for and you’ll get the right answer.
0September 2, 2005 at 2:32 pm #126275Thank you all for a replies. In fact it was teoretical question. Nevertheless we can take reasonably truthful data below.
Population size: 100 000.
Desired confidence level: 0,95
Current proportion defective: about 0,0001
Desired precision: 0,00001
I can define the sample size here and it is 3 841 070 not taking into consideration the population size and it’s 793 434 taking into consideration the population size. These numbers are too big and I know that they came from very small desired precision. At the same time I think it’s right to choose a precision level smaller than current proportion defective. So my questions are the same: What to do? Thank you.
0September 2, 2005 at 3:09 pm #126277Hi Sergei,
I have same opinion with you. I know the formular of sample size not taking into consideration the population size. Would you please tell me the formular taking into consideration the population size. I do appreciate that.
Michael0September 2, 2005 at 3:12 pm #126279Hi Sergei,
I have same opinion with you. I know the formular of sample size not taking into consideration the population size. Would you please tell me the formular taking into consideration the population size. I do appreciate that.
Michael0September 2, 2005 at 3:26 pm #126284
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Your sample size is 97,463 out of the 100,000. You are correct that it is your desired precision that is driving such a large proportion of your population. You have to decide what to do. On the other hand, if the reason you are deciding whether it is defective or not is a continuous variable, then actually using that measurement for calculating sample size will certainly reduce your sample size. If you reduce your desired precision to .0001 then the sample size drops to 27,753. That is still large. You definitely need to think of a continuous measure to make your sample size smaller. On the other hand, if you are this good, why are you sampling? If you are looking to monitor this over time, then a control chart might be a better tool than the inferential statistics that you are attempting. Be careful using a p chart with proportions that small.
0September 2, 2005 at 3:28 pm #126285I got the formula from one Six Sigma book and I don’t know exactly how it works and why it is true. I just hope that it’s right formula. Anyway it helps to get smaller sample size according to someone opinion.
The formula: if m/N > 0.5 then use n = m/(1+m/N)
‘N’ is the population size.
‘m’ is sample size not taking into consideration population size
‘n’ is the final sample size taking into consideration population size.
0September 2, 2005 at 3:58 pm #126290Thank you, Darth. You are right. it’s 97 463 for 100 000.
So, the one chance to reduce the sample size is to try to use variable data. Am I right?
In this case, what should we do, if we can’t gather continuous measure because of nature of a product (for example almost all data at food industry is attribute)?
I agree also that we have to be careful using a pchart with proportions that small. And I have another question from that: is it effective to monitor a process by control charts if the fraction defective is very very small. The answer I think no, it’s not effective. To use charts we have to have enough defects but to get enough defects we have to check a very big sample. I can’t find the right way from that.0September 2, 2005 at 4:43 pm #126294Regarding the control chart options, you may consider u chart. At that percentage level, a Poisson distribution can be assumed.
Good Luck.0September 2, 2005 at 8:18 pm #126302Try this link:
http://www.cmh.edu/stats/size/population.asp0September 2, 2005 at 8:26 pm #126303You have a great process, so catching the bad parts should be difficult – this is a good problem to have! Instead of having the rigid confidence interval or precision, what about calculating these values based on a given sample size? That is, pick a realistic sample size that you could actually live with and solve for either the confidence interval or the precision. I’d suggest locking in a precision (though higher than .00001) and calculate what your actual confidence interval would be. I’d sacrifice “confidence” for practicality if it’s all you can do…
Regarding the desired precision to the acutal % defective, try this link:
http://www.itl.nist.gov/div898/handbook/prc/section2/prc243.htm
It has an example with p=.1 with desired precision of .1, just an example where precision = defective %.0 
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