Minimum Accepted Sample Size for Tolerance Interval (confidence interval)

toroprime

New Member
Hi,

I'm using the tolerance interval function in minitab, my sample size is limited to 7 (the parts are expensive blah blah)

I've heard to be statistically significant a sample size of 30 is recommended but in practice how low can I go for sample size when using a confidence / tolerance interval? Is there a generally accepted minimum number of specimens??

Thanks

katxt

Well-Known Member
If you are sure that the data is normal, then you can use a sample size of 7 but probably the interval will be too large to be of use. Have you tried it?

Yggdrasil

New Member
Hi,

I am not an expert in Design Of Experiments but I don't think that there is a one-fits-all answer to the sample size. You need to have some estimations about your specimens before you can calculate a sample size: approximate mean value, approximate standard deviation, do you values roughly follow a normal distribution?

And you have to choose if you are interested in a confidence interval or a tolerance interval.

I posted a similar question this week. You might want to take a look at the answers in this thread:

katxt

Well-Known Member
If you are sure the data is normal, then you can use a sample of 7, but it probably won't be of a great deal of use.
If you suspect that the data is not normal, and you only have a sample of 7 then this table may be of use. It says, for instance, that we can be 95% sure that 50% of the population lies between the largest and smallest values in your sample. kat

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toroprime

New Member
If you are sure that the data is normal, then you can use a sample size of 7 but probably the interval will be too large to be of use. Have you tried it?
Yes I've tried it, the interval isn't that large in comparison to my limits. I don't have enough evidence to suggest it isn't normal...

In this case I have a two sided interval (upper and lower specification)
Upper: 24
Lower: 7.05

Below is from minitab, my mean and stdev come from historical data.
minitab output:
Tolerance Interval Method
Confidence level 95%Percent of population in interval 90%
Statistics
N Mean StDev
7 17.793 1.790

95% Tolerance Interval
Normal Nonparametric Achieved
Method Method Confidence

(11.726, 23.860) (x[1], x[7]) 15.0%

x denotes the ith smallest observation.
Achieved confidence level applies only to nonparametric method.

toroprime

New Member
Hi,

I am not an expert in Design Of Experiments but I don't think that there is a one-fits-all answer to the sample size. You need to have some estimations about your specimens before you can calculate a sample size: approximate mean value, approximate standard deviation, do you values roughly follow a normal distribution?

And you have to choose if you are interested in a confidence interval or a tolerance interval.

I posted a similar question this week. You might want to take a look at the answers in this thread:
Yes, see reply to katxt, but I have mean, stdev from historical data roughly normal.

... that thread was surprisingly enlightening. Thank you, I learned the difference between confidence interval and tolerance interval. In this instance, I want to be using a tolerance interval.

Definition of a tolerance interval
A confidence interval covers a population parameter with a stated confidence, that is, a certain proportion of the time. There is also a way to cover a fixed proportion of the population with a stated confidence. Such an interval is called a tolerance interval. The endpoints of a tolerance interval are called tolerance limits. An application of tolerance intervals to manufacturing involves comparing specification limits prescribed by the client with tolerance limits that cover a specified proportion of the population.
Difference between confidence and tolerance intervals
Confidence limits are limits within which we expect a given population parameter, such as the mean, to lie. Statistical tolerance limits are limits within which we expect a stated proportion of the population to lie.

Despite how enlightening that was, my original question still stands.

Yggdrasil

New Member
Maybe I get this wrong but the data look good to me if I type your values in the website tool that katxt proposed:
https://statpages.info/tolintvl.html

7 samples are sufficient to be 90% sure that 95% of the hypothetic population fall between the upper (24) and lower (7.05) limits.

Despite how enlightening that was, my original question still stands.
I've heard to be statistically significant a sample size of 30 is recommended but in practice how low can I go for sample size when using a confidence / tolerance interval?
This question has been extensively debated here:
www.researchgate.net/post/What_is_the_rationale_behind_the_magic_number_30_in_statistics
As far as I understand the overall conclusion of this debate, it gives the following answer to your question:
Is there a generally accepted minimum number of specimens??
No, there is no generally accepted minimum number of specimens.

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katxt

Well-Known Member
Don't forget that the 95% means at least 95% and there will very probably be more than that in that interval.

Karabiner

TS Contributor
I'm using the tolerance interval function in minitab, my sample size is limited to 7 (the parts are expensive blah blah)
By the way, what is your dependent variable? For example, exponential or Weibull
are common probability distributions for variables used in quality control.

With kind regards

Karabiner