# ISO 3951 - Sampling procedure for Inspection by Variables Data

B

#### biju-joseph

Hi
need help on revised iso 3951 sampling procedure for inspection by variable , looks like the new procedure is more complicated and we need to identify the "K" factor and do the calculation to compare to analyze the lot is acceptable or not.
can I use 2859 for variable

Biju joseph

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: ISO 3951 -sampling procedure for inspection by variable

The short answer is you cannot use 2859 which is for attribute sampling for variable data. Where are you having an issue with 3951. If you look at the example, the calculations are pretty straightforward.

W

#### Waeller

Re: ISO 3951 -sampling procedure for inspection by variable

Hi Statistical Seven,

Thank you for the statement concerning the use of 3951 vs 2859.
But still - I have some questions:

1) E.g.: Measuring a length having an upper and lower spec limit, uncertainty considerations included in the measurement. Isn't it possible to define parts in within spec as "confirming" and out of spec as "non confirming" and use this judgement as attributive and use 2859?

2) Asuming non normality:
Transforming the distribution into normality, means transforming the limits as well. What about the k-factors? Aren't they calculated based on a normal distribution?

Thanks for any hint
Waeller

P.S.
I Would like to ask my company statistician, if there is one!

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: ISO 3951 -sampling procedure for inspection by variable

Hi Statistical Seven,

Thank you for the statement concerning the use of 3951 vs 2859.
But still - I have some questions:

1) E.g.: Measuring a length having an upper and lower spec limit, uncertainty considerations included in the measurement. Isn't it possible to define parts in within spec as "confirming" and out of spec as "non confirming" and use this judgement as attributive and use 2859?
You can always convert a continuous measurement into a attribute measurements as you described. Understand that the sample size requirement per 2859 is much larger than the 3951 for the same coverage.Not usually worth the additional work (i.e. 200 for attribute versus 33 for variable)

2) Asuming non normality:
Transforming the distribution into normality, means transforming the limits as well. What about the k-factors? Aren't they calculated based on a normal distribution?
Yes they are based on the normal distribution, but the transformation makes your data normal, so the K value is not transformed.
Thanks for any hint
Waeller

P.S.
I Would like to ask my company statistician, if there is one!
Without a company statistician, you should get a consultant or contract statistician on retainer.

W

#### Waeller

Re: ISO 3951 -sampling procedure for inspection by variable

Hi Statistical Seven,

I need to follow up on the ISO-3951 and in addition on 11608-1.
Both need normal distributions to calculate the tolerance limits (x_bar +- K* S).

My question:
Is it possible to judge the tolerance limits - even the distribution is not a normal one - with the equation above?
Wouldn't it be more critical if not centered distributions with higher standard deviations
would be traeted as if they were normal distributions?

Thanks for any hint
Waeller

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Re: ISO 3951 -sampling procedure for inspection by variable

The ISO-3951 is based on normality. There are some adjustments for non-normal data, but in general when the data is non-normal it helps to understand the underlying distribution to calculate the sample size.

I use 16269-6 for tolerance intervals. It has the formulas for non-normal tolerance intervals. Be aware that the minimum sample size for non-normal or distribution free tolerance intervals are quite large to get the coverage you desire.

Hi Statistical Seven,

I need to follow up on the ISO-3951 and in addition on 11608-1.
Both need normal distributions to calculate the tolerance limits (x_bar +- K* S).

My question:
Is it possible to judge the tolerance limits - even the distribution is not a normal one - with the equation above?
Wouldn't it be more critical if not centered distributions with higher standard deviations
would be traeted as if they were normal distributions?

Thanks for any hint
Waeller

W

#### Waeller

Hi Statistical Seven,

thank you very much for the fast reply. But as usual 1 answer lead to more questions.

In the 3951 there is a relation between AQL =0,01, n=63 and k=3.2xx for code letters P or Q for the s-method.

In 16296 only ordered statistics are mentioned e.g. v+w for 1 to 20 and a sample size number.
Is there a way to relate a given/definded AQL to this distribution free sample size and/or distribution free 2-sided tolerance limits?

Thank you very much
Waeller

PS
...im still looking for a company statistician ....

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Not sure I follow your question, but 3951 does index by AQL. ISO 3951 is for acceptance sampling by variables and the k-values are not the same k-value for tolerance intervals.

16269 gives distribution free and normal tolerance interval methods.

Hi Statistical Seven,

thank you very much for the fast reply. But as usual 1 answer lead to more questions.

In the 3951 there is a relation between AQL =0,01, n=63 and k=3.2xx for code letters P or Q for the s-method.

In 16296 only ordered statistics are mentioned e.g. v+w for 1 to 20 and a sample size number.
Is there a way to relate a given/definded AQL to this distribution free sample size and/or distribution free 2-sided tolerance limits?

Thank you very much
Waeller

PS
...im still looking for a company statistician ....

W

#### Waeller

Hi Statistical Seven,

I'm sorry for not cleary getting to the point. Yes, I'm looking for some acceptance sampling plans or methods.

What do I have to apply, if I have an AQL=0,01 to fullfil and the data of the measured variable is not normal distributed - and can not be transformed into normal data. And the lot size is about 100k to 150k.

e.g destructive Dial Torque meaurements, no target value, only upper and lower limits.
LSL 10mNm
USL 95mNm

Waeller

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Hi Statistical Seven,

I'm sorry for not cleary getting to the point. Yes, I'm looking for some acceptance sampling plans or methods.

What do I have to apply, if I have an AQL=0,01 to fullfil and the data of the measured variable is not normal distributed - and can not be transformed into normal data. And the lot size is about 100k to 150k.

e.g destructive Dial Torque meaurements, no target value, only upper and lower limits.
LSL 10mNm
USL 95mNm

Waeller
Waeller

Here are several options, not are better than others, but just how I approach a problem like this.

First I try to under why my data is not normal for a two-sided specification of torque. I expect non-normality with a one-sided specification, but usually do not see normality unless it's bi-modal. If the data is in fact bi-modal, then acceptance testing is a complex issue as you need to know the distribution of the parts from each mode. Without a fundamental understanding of the data, using continuous (either normality or non-normality) acceptance is an exercise in futility.

My usual response is that though we measure torque as a continuous value, we can use attribute based sampling as the parts either pass or don't pass. Again, without a distributional assumption about the data, cannot calculate the mean and standard deviation to predict percent out of specification.

You can use reliability type models to predict probability of exceeding the specification using different sample sizes based on exponential or weibull models. This is NOT a perfect solution, and requires an iterative process for finding the best solution.

Assume normality and use 3951. This is ONLY used if the lack of normality is small and the cause is from "outliers".

Otherwise, I am stumped!

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