Confidence Interval for Production Sampling

[paizlea]

Hi! This is my first post, so thanks for bearing with me on what I hope is not too simple a question.

We're currently producing an average of 1376 items per hour, and check 5/hr. 4 checks are performed at approximately 15-minute intervals during the production run, and the 5th is checked completely randomly (could be done any time during the hour). The check is attribute-based, and therefore pass-fail. For the year to date, we have a pass rate of 0.995. I’m not convinced we’re capturing our true defect rate, but this pass rate is what we have for now (until we can revamp our line audit system).

Can anyone help me with the following questions? I’ve tried several online calculators, but their results vary significantly.

1) Assuming a 95% confidence level, what’s the confidence interval for this data?
2) What sample size do I need to have a CI of +/- .05?

[brahmaiah - 2010]

In Reply to Parent Post by paizlea

Hi! This is my first post, so thanks for bearing with me on what I hope is not too simple a question.

We're currently producing an average of 1376 items per hour, and check 5/hr. 4 checks are performed at approximately 15-minute intervals during the production run, and the 5th is checked completely randomly (could be done any time during the hour). The check is attribute-based, and therefore pass-fail. For the year to date, we have a pass rate of 0.995. I’m not convinced we’re capturing our true defect rate, but this pass rate is what we have for now (until we can revamp our line audit system).

Can anyone help me with the following questions? I’ve tried several online calculators, but their results vary significantly.

1) Assuming a 95% confidence level, what’s the confidence interval for this data?
2) What sample size do I need to have a CI of +/- .05?

Welcome to Elsmar!
The sampling system is no guaranty at all for zero defect.First tell us what is the PPM rejection you/your customers have specified?Your sampling system interval and sample size depends on that.
The basic requirement is that the the process should be under statistical control and should achieve Cpk of 1.33.
In addition the production personnel should be aware of the intricacies of SPC.Otherwise you would not be able to know where your process has gone off the track.Then you will be left with 100% inspection and heavy rejection.
V.J.Brahmaiah

[amanbhai]

In Reply to Parent Post by paizlea

Hi! This is my first post, so thanks for bearing with me on what I hope is not too simple a question.

We're currently producing an average of 1376 items per hour, and check 5/hr. 4 checks are performed at approximately 15-minute intervals during the production run, and the 5th is checked completely randomly (could be done any time during the hour). The check is attribute-based, and therefore pass-fail. For the year to date, we have a pass rate of 0.995. I’m not convinced we’re capturing our true defect rate, but this pass rate is what we have for now (until we can revamp our line audit system).

Can anyone help me with the following questions? I’ve tried several online calculators, but their results vary significantly.

1) Assuming a 95% confidence level, what’s the confidence interval for this data?
2) What sample size do I need to have a CI of +/- .05?

I am curious about the difference in results of online calculators!

[reynald]

Hi,
First welcome to the cove!!!


There maybe several reasons for the differences. First reason maybe the hypothesized underlying distribution that was used to estimate the confidence interval. If a sampling without replacement is assumed, then the Hypergeometric Distribution is used. If sampling with replacement can be assumed, then usually a binomial distribution is used.
Then with regards to the sample size and probability of seeing a defect, an exact confidence interval may be computed or it could be the easier method of normal approximation to the binomial.
It will help if you would show us the values you got from the online calculators.
I will try to compute them for you as well then we can compare.

Regards,
Reynald

[Bev D]

the difference between the various on-line calcaultors will indeed depend on the underlying distribution used. With such a high yield (low defect rate) the correct distribution would be the Exact Bimomial - many calculators tend to stick to the normal approximation for the Binomial or may even use the formulas for continuous data. Continuous data calculators may use either the t distribution or the Z distribution. (or you may have seleted the wrong distribution?). So depending on the calculator you chose and the assumptions of the calculator you could have gottten any number of incorrect answers. (Incorrect, but potentially useful)


That said, I would advise that a confidence interval is not the best choice for the situation you describe. Confidence intervals are intended for quantifying the accuracy of a single (or very few) estimates. Since you are sampling on a regular basis the best choice is a control chart. The upper and lower control limits will provide you with the expected range of variation of the Yield.

I am also curious as to why you thing the estimate may not be accurate and why you feel the need to be accurate to the +.05 level?
By the way in order to calculate the confidence interval for yoru year to date yield (or defect rate) I would need to knwo the total number of parts samples this year and the total number of defects found in that sample. But *I* would also want to see the year long trend to understand the stability...

[Tim Folkerts]

The confidence interval will depend on the total sample size. For the 95% confidence interval:

• If you test 200, and find 199 good, then CI = (0.972458, 0.999873)
• If you test 400, and find 398 good, then CI = (0.982056, 0.999394)
• If you test 2000, and find 1990 good, then CI = (0.990824, 0.997600)

All of these are 99.5% good, but the larger the sample, the tighter the confidence interval. (These are all according to Minitab.)

Wikipedia has a brief article that might be helpful here. http://en.wikipedia.org/wiki/Binomia...dence_interval
It includes references to several online calculators.


Tim

[paizlea]

Wow, thanks for all the great responses and the warm welcomes! Let me address the questions and comments in one post:

First, the product is a package of books and other items, and each is sent to a different customer. We don't have an established pass rate (I know, arrgghh!!), becuase the current numbers we have are being used to "prove" the process is good enough. Our customer complaint rate is low (0.88 calls per 1000 boxes shipped), which is also used to justify the status quo. Thi=e complaints help establish how many defectives get out the door, but doesn't tell us how good our process is before the product ships. The 5/hr checks are supposed to answer that.

For the year, we have performed 1036 checks, and had 5 failures.

This process is in no way under statistical control. I've been asked to determine answers to the questions I posed in the first post in order to establish some control limits, at least based on what we're doing now. It was specified that the confidence level be +/- 5%.

One of these days, we'll have Minitab, or so I'm promised. If my sample is 5 (per hour), what's the 95% CI? Sorry for the basic stats questions, I'm still a student and don't have much experience in the quality field.

I'll post the results of the different calculators in a separate post (very busy at work today!) I'd love to see any discussion of the causes of the differences.

Thanks again for your input and help!