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# How Many Samples Do You Need to Be Confident Your Product Is Good?

 Minitab Blog Editor  |  7/12/2017

 Topics: [Reliability Analysis](https://blog.minitab.com/en/blog/tag/reliability-analysis)

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How many samples do you need to be “95% confident that at least 95%—or even 99%—of your product is good?

The answer depends on the type of response variable you are using, [categorical or continuous](https://blog.minitab.com/blog/understanding-statistics/understanding-qualitative-quantitative-attribute-discrete-and-continuous-data-types?hsLang=en). The type of response will dictate whether you 'll use:

1. **Attribute Sampling:** Determine the sample size for a categorical response that classifies each unit as Good or Bad (or, perhaps, In-spec or Out-of-spec).  
    
2. **Variables Sampling:** Determine the sample size for a continuous measurement that follows a Normal distribution.

The attribute sampling approach is valid regardless of the underlying distribution of the data. The variables sampling approach has a strict normality assumption, but requires fewer samples.

In this blog post, I'll focus on the attribute approach.

## Attribute Sampling

A simple formula gives you the sample size required to make a 95% confidence statement about the probability an item will be in-spec when your sample of size *n* has zero defects.

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples1-Jul-06-2025-12-17-37-2220-AM.png), where the reliability is the probability of an in-spec item.

For a reliability of 0.95 or 95%, ![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples2-Jul-06-2025-12-17-39-6796-AM.png)

For a reliability of 0.99 or 99%,  ![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples3-Jul-06-2025-12-17-47-3967-AM.png)

Of course, if you don't feel like calculating this manually, you can use the **Stat > Basic Statistics > 1 Proportion** dialog box in Minitab to see the reliability levels for different sample sizes.  

![one-sample-proportion](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples4-Jul-06-2025-12-17-40-7114-AM.png)

![1-proportion test](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/1_proportion_output-Jul-06-2025-12-17-41-8042-AM.jpg)

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples6-Jul-06-2025-12-17-45-0184-AM.png)

![1-proportion output](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/1_proportion_output2-Jul-06-2025-12-17-44-0060-AM.jpg)

These two sampling plans are really just [C=0 Acceptance Sampling plans](https://blog.minitab.com/blog/applying-statistics-in-quality-projects/attribute-acceptance-sampling-for-an-acceptance-number-of-0?hsLang=en) with an infinite lot size. The same sample sizes can be generated using **Stat > Quality Tools > Acceptance Sampling by Attributes** by:

1. Setting RQL at 5% for 95% reliability or 1% for 99% reliability.
2. Setting the Consumer’s Risk (β) at 0.05, which results in a 95% confidence level.
3. Setting AQL at an arbitrary value lower than the RQL, such as 0.1%.
4. Setting Producer’s Risk (α) at an arbitrary high value, such as 0.5 (note, α must be less than 1-β to run).

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples8-Jul-06-2025-12-17-46-1067-AM.png)

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples9-Jul-06-2025-12-17-38-4942-AM.png)

By changing RQL to 1%, the following C=0 plan can be obtained:

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples10-Jul-06-2025-12-17-42-8910-AM.png)

If you want to make the same confidence statements while allowing 1 or more defects in your sample, the sample size required will be larger. For example, allowing 1 defect in the sample will require a sample size of 93 for the 95% reliability statement. This is a C=1 sampling plan. It can be generated, in this case, by lowering the Producer’s risk to 0.05.

![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples11-Jul-06-2025-12-17-36-3329-AM.png)![](https://blog.minitab.com/hubfs/B2BML%20-%20NEW%20FILE%20MANAGER%20STRUCTURE/Blog%20Images/Imported_Blog_Media/samples12-Jul-06-2025-12-17-48-2669-AM.png)

As you can see, the sample size for an acceptance number of 0 is much smaller—in this case, raising the acceptance number from 0 to 1 has raised the sample size from 59 to 93.

Check out this post for [more information about acceptance sampling](https://blog.minitab.com/blog/applying-statistics-in-quality-projects/attribute-acceptance-sampling-for-an-acceptance-number-of-0?hsLang=en). 

 

 

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