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# Cumulative Confidence Levels - Design Verification and Validation Sampling

I

#### Indian Ute

I am having a problem with determining cumulative confidence levels.

This is the situation I have. I am doing design verification and validation sampling. The validation requires three runs of the process to prove effectiveness of the changes. The process is run and I get the same number of samples for each run.

The sampling plan is set up for each run. There are different levels of confidence I can choose. For example 20%, 50%, or 90%.

Lets say I choose the 50% confidence per run. I know that after the first run I will have 50% confidence that the process is producing defects at or below the AQL. What will be my confidence after the second and third runs?

I have been told that confidence does not double with a second run. Is there a formula to calculate what it would be?

Thanks for any help you can give to me in figuring out how the confidence increases with multiple runs of a process.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
what do you mean by 50% confidence? what formula are you using and how are you using 'confidence'?

we need more details to provide a helpful answer...

I

#### Indian Ute

My work has a procedure I am using called "Sampling Plans for Validation, Qualification and Other Special Circumstances". In this document it has tables of different AQL levels down the left hand side, and accross the top are column titles of 20% Confidence 50% Confidence 90% Confidence. Each test I need to perform has an associated AQL. I choose the AQL and desired Confidence to see how many samples I need to test.

I am using no formula. I just use the table described above to find out how many samples I need to test.

In my procedure Confidence is defined as: The term "confidence", in this procedure is related to the statistical sample size needed to provide statisital evidence that the process is producing defects at or below the QL.

If I choose 50% confidence for the first run of a test at the AQL and sample size, and deicde to repeat the test a second or third time, what will happen to the statistics? Do I stay at 50% confidence? or Does my confidence increase?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
If you are taking a second sample of the same lot OR if you are running a second lot with the same conditions, then YES your actual "confidence" increases. To be more specific the accuracy of the estimate increases.

I

#### Indian Ute

Yes, I am taking a second sample of the same lot OR I am running a second lot with the same conditions.

Is there any way to calculate what the new "confidence" or accuracy of the estimate will be?

I

#### Indian Ute

I still need help with this topic. Can anyone give me some tips or an equation to help me figure this out?

The question I have deals with accuracy of the estimates, when I repeat a test at a given sample size on the same lot of product.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
I still need help with this topic. Can anyone give me some tips or an equation to help me figure this out?

The question I have deals with accuracy of the estimates, when I repeat a test at a given sample size on the same lot of product.
Assuming that the runs and samples are independent, then the confidence level is

1-(1-confidence)^number of runs

For example, assuming 90% confidence the overall confidence would be

Run Confidence
1 90.0%
2 99.0%
3 99.9%
4 100.0%

Though typically you run your v&v such that the overall confidence is at a given level. For example if the sample required for 90% confidence is 21, then you would run 3 runs, each with 7 samples, not 3 runs of 21. This gives the true confidence.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
thanks Steven - I lost sight of the thread for some reason.

#### C. Tejeda

##### Registered
Sorry for reviving such an old thread but I am courious. Two cuestions:

Assuming that the runs and samples are independent, then the confidence level is

1-(1-confidence)^number of runs
1. Is this applicable to sample sizes calculated using success-run theorem? Do you have a source (like a book) where I can find that formula?

Though typically you run your v&v such that the overall confidence is at a given level. For example if the sample required for 90% confidence is 21, then you would run 3 runs, each with 7 samples, not 3 runs of 21. This gives the true confidence. This has been eye opening for me and makes absolute sense.
2. Do you have a source book or material that I can use to review this deeply?

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