aasikolo
asked on
Probability of selling a bad part
Good Morning
We have a part that is designed with an estimated 10^-6 failure rate. We perform 100% inspection which is approximately 80% effective.
What is the probability that we will sell a bad part?
Please show your calculations.
Thank You
We have a part that is designed with an estimated 10^-6 failure rate. We perform 100% inspection which is approximately 80% effective.
What is the probability that we will sell a bad part?
Please show your calculations.
Thank You
ASKER
Answer 1) 100,000 per year.
Answer 2) Yes.
Thank you
Answer 2) Yes.
Thank you
Are you actually selling parts, or is this a homework question?
If you didn't do any testing at all, what would be the probability of selling a defective part?
If you didn't do any testing at all, what would be the probability of selling a defective part?
ASKER
It is not a homework question, I am trying to confirm my own calculations.
SOLUTION
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ASKER
Olaf
As you know, 100% inspection is 80% effective, I believe Deming came up with that one, but I don't have a direct reference at the moment. It isn't that we are throwing away 20% of OK parts, 20% of the parts aren't adequately inspected just as an assumption taking Deming's observation into consideration.
As ozo observed above, with the false positive and negative rates inquiry, I am attempting this problem using Bayes' Theorem and wanted to see if my calculations were correct, and even if using Bayes' was necessary but didn't want to poison the well. I wade in and out of this subject once every 5 years and thought I would give EE a try.
Short answer, my result does not match your conclusion.
As you know, 100% inspection is 80% effective, I believe Deming came up with that one, but I don't have a direct reference at the moment. It isn't that we are throwing away 20% of OK parts, 20% of the parts aren't adequately inspected just as an assumption taking Deming's observation into consideration.
As ozo observed above, with the false positive and negative rates inquiry, I am attempting this problem using Bayes' Theorem and wanted to see if my calculations were correct, and even if using Bayes' was necessary but didn't want to poison the well. I wade in and out of this subject once every 5 years and thought I would give EE a try.
Short answer, my result does not match your conclusion.
If 100% inspection is 80% effective is really part of the process, you have to define it better.
If it is an irrelevant quote from Deming, you should have said so.
How good is your estimate for estimated 10^-6 failure rate?
Do you actually have data that is worth using for calculations?
If the failure rate is really 1 in 10^6, the probability of selling a defective part is also 1 in 10^6.
(Assuming failure and defective mean the same thing.)
If inspection catches 80% of the defective parts (4 out of 5), then the probability of selling a defective parts goes up to 1 in 5x10^6.
If you sell (and continue to sell) 100K parts per year, you can expect to sell one defective part every 50 years.
If it is an irrelevant quote from Deming, you should have said so.
How good is your estimate for estimated 10^-6 failure rate?
Do you actually have data that is worth using for calculations?
If the failure rate is really 1 in 10^6, the probability of selling a defective part is also 1 in 10^6.
(Assuming failure and defective mean the same thing.)
If inspection catches 80% of the defective parts (4 out of 5), then the probability of selling a defective parts goes up to 1 in 5x10^6.
If you sell (and continue to sell) 100K parts per year, you can expect to sell one defective part every 50 years.
"If the failure rate is really 1 in 10^6, the probability of selling a defective part is also 1 in 10^6.
(Assuming failure and defective mean the same thing.)
If inspection catches 80% of the defective parts (4 out of 5), then the probability of selling a defective parts goes up to 1 in 5x10^6.
If you sell (and continue to sell) 100K parts per year, you can expect to sell one defective part every 50 years. "
dglitch has illuminated your problem above, especially the last sentence which puts everything in a correct perspective.
the big unanswered information lies in the relationship between the estimated failure rate and the testing as has been pointed out.
Unless lift is involved, sell you parts with a replacement guarantee. If one fails your company may already been bought by somebody and it will not be your problem. Or the testing may cost more than the replacement.
In general there is no relationship between failure rate and testing effectiveness.
"life" not "lift" in last paragraph
ASKER CERTIFIED SOLUTION
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I just saw aburr's comment.
Isn't this saying the same thing as Olaf said in http:#a41269705
Or the testing may cost more than the replacement.
Isn't this saying the same thing as Olaf said in http:#a41269705
doing no QA you still have a low rate of sold failures. As soon as (sic. asuming "assuming that") a failure doesn't harm someones life it sure is easier to handle this via insurance or refunds than doing any QA at all
ASKER
Phorrific:
I didn't indicate that anyone's conclusions were wrong. My statement was that my conclusion did not match their results. My results are attached for your review and comment. From ozo's observation, only the true and false positives were considered in my results, the true and false negatives were not. Hence my results may be incorrect. (3.9 x 10^-6)
Failure-Probability.xlsx
Aburr:
As you know, failure rate and failure probability are not the same thing. Bayes needs the rate at which the inspection program in this case is effective. Deming's 80% is an assumption based on the known effectiveness of 100% inspection programs, I was looking for worst case.
Thank you
I didn't indicate that anyone's conclusions were wrong. My statement was that my conclusion did not match their results. My results are attached for your review and comment. From ozo's observation, only the true and false positives were considered in my results, the true and false negatives were not. Hence my results may be incorrect. (3.9 x 10^-6)
Failure-Probability.xlsx
Aburr:
As you know, failure rate and failure probability are not the same thing. Bayes needs the rate at which the inspection program in this case is effective. Deming's 80% is an assumption based on the known effectiveness of 100% inspection programs, I was looking for worst case.
Thank you
As far as I know, failure rate and failure probability are the same thing.
Deming's 80% is a quip to suggest that you should put more effort in quality production than into inspection. I can't imagine any real inspection process for a precision part that would be only 80% effective.
I don't believe you are applying Bayes' Theorem correctly.
Deming's 80% is a quip to suggest that you should put more effort in quality production than into inspection. I can't imagine any real inspection process for a precision part that would be only 80% effective.
I don't believe you are applying Bayes' Theorem correctly.
SOLUTION
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If you sell 100,000 per year,
then the chance that none of them are defective is (1-1/3,999,997)^100,000
so the chance of selling a defective part during the year is (1-1/3,999,997)^100,000 = 0.02469
The chance of selling a bad part sometime during n years would be 1- (1-1/3,999,997)^(n*100,000
then the chance that none of them are defective is (1-1/3,999,997)^100,000
so the chance of selling a defective part during the year is (1-1/3,999,997)^100,000 = 0.02469
The chance of selling a bad part sometime during n years would be 1- (1-1/3,999,997)^(n*100,000
Overall it seems to me you're mixing rough estimates like the 80:20 rule with a precise calculation of probabilities via Bayes Theorem. It's quite useless to put these assumed probabilities into Bayes Theorem to get some unprecise prediction.
If you don't have 20% parts failing QA tests, then the QA precision is higher than 80:20 so the outset is wrong and you can't determine something with a precise calculation based on wrong estimates. If you don't have a rate of 80% false negatives which you don't throw away or reenter into the production process, then you already know the 80:20 estimate is wrong.
Bye, Olaf.
If you don't have 20% parts failing QA tests, then the QA precision is higher than 80:20 so the outset is wrong and you can't determine something with a precise calculation based on wrong estimates. If you don't have a rate of 80% false negatives which you don't throw away or reenter into the production process, then you already know the 80:20 estimate is wrong.
Bye, Olaf.
Does 80% effective mean a false positive rate of 0.20 and a false negative rate of 0.20?